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cncUHaJlbHOrO 06pa30BaHilst CCCP
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MOCI\BA «BbIClIIA5I lllKOJIA» 1984




EEK 22.3
K 31
YllK 53
P e u C H 3 e H T bI:
Karj>ellP3 4>1I311KII MOCKOOeKOrO IIII)l..CIICpHO.t!>1I3J1'1CCKOrO IlIIeTIlTyra;
,AOU. D. C. Denlll\oo (MOChOBChllii allllaUHOHULUt IlIleTIlTYT)
KaWHHa C. H., Ce301l0B 10. H.
l( 31 C60pHlIK 3a.ll.aIJ no 4>1I3I1KC:
nO.ll.roT. OT,:!.. nY30B. - M.: BbICIlI.
11.1.
35 K.
Y'Ic6. nocoGuc .lI.J1Sl
IlIK., 1984 - 207 C.,
noc0611c npeJlCTaa.TJlCT co6011 cllcn..aTllqeCKHR C(\OpIIHK 1I0npOCOB
II 3aAa'l. cocTaoncllllbli'i II COOTIICTCTIIHH C nporpa....oli no e!>.I3HKC Jl.1R
nOJlrOTOIIHTc,,'hHhlX OTJleneHHII: no KalKJlQII Te..c 38Jl8qH pacno.10;KCHhi
II nOpRJlKC BOJpaCT8HHJI CTcnellH HX TpYAnOCTH. qTO n03110.,,,eT Hcno..'b30-
BaTh noco6Hc JlnJl HIIAIIBHJ1)'8JlhllbiX 3aJlallHR npH pa(\OTC Ha ypoKe H no-
'1a. Kpo..c Toro. II C60PIIHK IIK.TIO'IeHhI 28Jl8qH nOllbilUcHIIOii TPYJlHOCTH
(B npc;J.enax nporpa....bI), 8 T8KIKC 3aJl8'1H. npcJl.T8raIlW.lecR C.T)W3TC.l""
lIoArOTOBHTe.llblloro OTAcnClIlIR MOCK01JCKOrO HIiCTHTjTa 3J1CI\ TpOlilloro Md.
WHHt}("TPl HIIH.
1\ 4306021100-05 3 8
001 (01 )-8 4 0- 81t
66K 22.3
53
, 113.llaTc.1LCTDO cEb!C'waSi WKO.la-, 1983

nPEJI.HCJ10BlfE
noe06He npe.lleTaBJJHCT e060H eHeTCMaTH'ICeKHii eoopHIIK BonpoeOB
H 3a,Aa'l, eOeTaBJleHHblii B eOOTBCTeTBHH e nporpaMMoii no <jJ1I3HKC A.H
nO.llrOTOBHTC.lbllbiX OT,AMeHHii DbleWHX Y'Ie6HblX saBCAeHllii.
C60pHHK eO.llepJKHT no KaJK.llOH TeMe 6oJli>woe KOJlK'IeeTBO TpeHH-
pOBO'lHblX 3a.lla'l O,AHHaKOBoro Tllna, paenOJlOJKeHHblX no B03paeTalO-
Il.\cii eTcnCHH TpY.llHoeTlI, 'ITO n03Bo.1HCT HenOJlb30BaTb cro KaK noe0611e
A.1H HH.llIIBI!.nyaJlbHblX 3a.zr.aHllii npH pa60Te B KJlaeeC H .llOMa. OCHOBHaH
llCJ\b sa.zr.a'l :noii rpynnbl - npHBHTb He06xo.llHMbI HaUblKI! K PCWCIlIlIO
3aAa'l H 3aKpenHTb MaTepRaJi TCMbI.
HapHAY c Sa.lla'laMH !lTOH rpynnbl B C60PIIHK BK.llO'IeHbI 3a.lla'lll
epc.llHeii H nOBblweHHoii TPY,AHOeTH, KOTopble n03BOJlHT nOBTopllTb H
yrJly6HTb 3HaHHH no pa3AMaM nporpaMMbI Kypea.
B e60pHHK BOWJJH HSBeeTHble, MeTO,AH'IeeKH IlCHllblC, HO pa36po-
eaHHb!e no pa3Hb!M H3.llaHIIHM 3a.lla'lH, a TaKJKe opHrHHaJlbllble, eoeTaB-
JICHllblC aBTopaMH 3a.lla'lH, KOTopble npe.llJlaraJiHeb B TC'ICIIIIC pHAa JJeT
e.lywaTeJlHM nO.llrOTOBHTeJlbHOrO oT,AMeHHH H a6HTypHeHTaM MoeKoB-
eKoro HlleTHTYTa 3J1eKTpOHHoro MaWHHoeTpoeHHH.
B eoop"HK BKJlIO'IeH enpaBO'lHblH MaTCpllaJl, Heo6xo!tHMblii .ll.1H
pcweHIIH 3aAa'l.
HeXO,AHblC .llallllble .llaHbI C Y'IeTOIII TO'lIlOeTH H3MepeHIIH eOOTBeTeT-
BYIOW.IIX BeJlH'IIIH H np8BHJI npllMHJKCHHblX BbI'IHeJleHHii.
3a.lla'lHHK npe,AHa3Ha'leH .llJlH nO.llrOTOBHTeJlbHblX OT,AMCllllii BY30B.
Ero MO>KHO peKOMCHAOBaTb TaKJKe npenO.llaBaTMHIII <jJH3HKH epe,AHHX
WKOJI H Y'Iaw.IIMeH .llJlH n0.llrOTOBKH K BCTymITMbHbI\I 3K3aMeHaM B
BY3b1.
ABTOpbl BblpaJKalOT rJly60KYlO CiJlarO;J.aplIoeTb .llOU,
I KY3bMI!HY lI.. B. I H CT. npen. A, cJ>. TeHblweBY 3a 60JlbWYIO nOlllow.b
H BHllMaHHC, OKa3aHHble HMH B npolleeee pa60TbI Ha.ll PYKonHeblO .llall-
1I0ii KHHrH, a TaKJKC peueH3eHTaM .llolt. B. C. BCJlHKOBY, .llolt.
A. SI. BHHoKypoBY H KaH.ll. 4>113, -MaT. HayK P. B. KOIIOnJlH'I 3a
nOJle3HblC eOBCTbI H BblCKa3aHHble 3aMC'IaHHJI,
A Bmopbl

BBE.lI.EHIIE. BEKTOPHblE If CKAJUIPHblE BEJIIIIJIIHbI
1. lI.aHbI .lI.Ba BeKTOpa ;; H b (pHC. I). HauTH cYJ\my 3T1IX
-+ -+
BeKTopoB. MO.ll.YJIH Be}{TOpOB paBHbI: lal == 5,0, Ibl = 4,0.
. --+- -to- .
2. lI.Ba BeKTopa 3a H 2a pacnOJlO>KeHBf B O;J.HOM HanpaB.le-
HHH Ha QJl.HOH npSlMoiL Onpe.ll.eJIHTb: I) CYMMY 3THX BeKTopoB;
2) p33HOCTb Me>Kj\Y I-M 112-M BeK-
b TOp3!.m; 3) pa3HocTb Men<.n.y 2-M
.. -- H I-M BeKTopafH.
3. B.lI.OJlb npSlMoil AB Ha-
BCTpellY .lI.Pyr .lI.Pyry uanpaB leHbI
.lI.Ba paBHbIx no MO.vYJlIO BeKTOpa, Onp.e.ll.eJIHTb CYMMY II pa3-
HOCTb 3THX BeKTopoB. .
4. CnO>KUTb .lI.Ba BeKTopa  TaK, IlTOObI HX C}:\1Ma ohI.'Ia pan-
-+ -+
ua: 1) 0; 2) 2a; 3) a.
-+ -+
5. Yro.'I a Me>K.lI.Y .D.BYMSI BeKTopaMII a H b paBeH 60 0 . Onpe-
-to- -1»-+0 .... 
.lI.eJIHTb MO,!!.YJlb BeKTopa c = a + b H yro;r 13 MeIK;J.Y a II C.
-+ -+
MO.ll.YJlH BeKTopoB paBHbl lal = 3,0, Ibl = 2,0.
-+
6. BeKTop a, MO.ll.YJlb .]{OTOporo paBeH 4,0, COCTaBJlSIeT yro.'I
o -+
a = 240 C BeKTOpO:lI b, MO.ll.YJlb KOTOporo paBeH 6,0. Onpe.ll.e-
-+.... -+ -+-.
nHTb MO.ll.YJlb BeKTopa c = a - b H yroJl 13 Me>KJlY a H,C.
7. lI.JI1I BeKTOpoB, 3a.u.aHHbIX B 33.l1.31le 6, onpe.ll.e.1HTb MO.ll.Y.1Jb
-+ -io'  .... -..
BeKTopa C = b - a H yroJlj3 Me>K,!!.Y a H C.
-+ -+ -+
8. lI.aHbI TPH B38HMHO nepneH.aHKYJlSlpHbIX BeKTopa a, b, c,
MO;1.ynH KOTOpblX paBHbI COOTBeTC1BeHHO 3,O:t;,0; Vrr: HauTu
..... ....
MO.ll.YJIb BeKTopa d = a + b + c.
9. B Koop.ll.HHaTaX x, y 3a;I.aHO nOJlon<eHue TO'lKII 1\1 : x-=
-
= 5,0, Y = 5.0. Onpe;I.e.'IHTb MO,!!:}Jlb BeKTopa T, Coe.iJ.HHSlY.l-
m.ero HallaJlO Koop,!!.HHaT H TOIlKY M, a TaK>Ke }rOJl a MeIKJlY
3THM BeKTOpOM}I OCblO x.
-
<l
.
-- a
PRC. 1
4

-
10. BeKTop r, MO,aYJlb KOToporo paBeH 6,0, HanpaB.'IeH noli.
yr.'IoM ex = 30° K ocn x. Onpe..'1.€.'IIITb npoeKLUIll :.roro BeKTOpa
Ha KOOp..'1.HHaTHbie ocn x. y,
-
11. ECJIu.KoHel.{ BeKTopa a, MO.aY"lb JWTOporo paBeH 4,0, co-
- -
e,aIlHHTb C HalIa.'IOM BeKTopa b, TO MO.n.y.'1b BeKTOpa c, coe,'{IIIISlIO-
w.ero uaqa.'Io BeKTopa ; c KOHI.{OM BeKTopa h, oy,aeT paBeH 4VI
Yro.'l a: r.te*.ity ;; u; 6Y;J.eT panCH
30°. Onpe,a€.'IHTb yro.'I  Men<.'J.Y
- -
BeKTopar.m a If b, a TalOKe Mo,aY.'Ib
-
DeKTopa b.
y
10
y
-
 0
----- . ..
It I. I
1 I I
3 -----'t"- I
C S "
0 t Ii 6 x - ------ .
PHc.2 PHc.3
-
12. BeKTop a, paBHI>lU no MO,aYJIIO 3,0, COCTaB.'ISieT }TO."
ex = 30° c npSlMoH AB. nO A KaKIiM }r.lo  K AB H3..'1.0 Jla-
npaBHTb BeKrop b. paBHblH no MO.il.Y.'I1O V3", I!T06b1 BeKrop -; =
= ;; -+- b 6b1JI napaJIJIeJIeH AB? 4ey paBeH MO;J.y.lb neKTopa
-
c?
13. .llam>! TOIlKII M 1 (2; 10) A11 (5; 6), OnpeemlTb MO;J.y.'lb
BeKTopa, COC,aHHSlIOUJ.ero TO'lKY M 1 c Al 2 .
14. B Koop,auHaTax x, y (puc. 2) 3a,aaHbI ;r.Ba BeKTopa. Onpe-
. -
.neJIUTb MO,aY.'Ib cYMMaplloro neKTopa C H yro.'1 ex ero HaKJIOHa
K OCII x.
15. BeKTOpbI ;; U b 3a,aaHbI B Koop,'{HHaTaJ\. x, y (puc. 3).
-+ -9" -+ -to- ..... -too
Onpe.n.e.nIlTb MO.aYJIU BeKTopoB C 1 = a + b U C 2 = a-b.
16. nOCTpOl:Tb rpa4>IIK 3aBHcn:'fOCTU CKaJISIpHoro npoll3De-
- -
AeHJISI BeKTopoB au bOT yr.'Ia ex Me)K.itY HHMII.
17. .llaHbl ABa Beh.TOpa ;; U b, MOYJIU KOTOpblX paBHbl
-- -
lal = 2,0, Ibl = 1,0. Yro.'1 MeJK.nY HU'>IU ex = fit. HaiiTn BeK-
-+ .....-...... ......... ..... -+
TOpbl C = (a.b).a +- bud = 2b - a/2.
5

51
J 8. Pa3.nO>KHTb lIeK'topb1
Ha COCTaB.1S1JOI.U.He no 3a-
,aaHHblM HanpaB.neHIHIM
(puc. 4. a - 2).
J 9. Y BeKTopa (; 113BeCT-
Jla o,aHa 113 COCTaB.nSlJOllJ.JlX
;;1 (pIlC. 5. a, 6.) HauTII BTO-
-
PYIO COCT3B.1S1IOllJ.YJO Q2'
-+
20. BeKTop d SlB.1S1eTCSI
-+
CYMMOH Tpex BeKTOpOB a.
b,. 3a.naHbl BeKTOpbl d u-+c
II HanpaBJIeUIISI MN If Ml'¥ 10
B)J.o.'Ib KOTOpbIX pacnOJIO>KHbl BeKTOpbl ; II b (pIlC. 6) Onpe;!.c-
-+ -+
JIJlTb BeKTopbl a II b.
-+ -+
21. D.Ba napaJIJIeJIbHblX BeKTopa a u b HanpaBJIeH1>1 B O,aH)'
CTOPOHY, PaCCTOSlHJle Me>K,ay BeKTOpaMH paBHo 6,0 CM. Haunl
-+
paccToHHlle ,ao cY"IMapHoro BeKTopa, eCJIJI 113BeCTlIO, tjTO a =
-
= 2b.
0.1

B) 1 1)

l1 J j(
c,
-
o

P IIC. 4
51
't
. ]I
Pile. 5
N.
/;M
_d,-
PHC 6
22. ]lBa aHTllnaJr.\.1.ne.1bHblX BeKTopa. MO,aYJIJI KOTOpblX
paBHbI 8,0 II 2,0, Haxo,aSlTCSI Ha paccToSlHIIII 12 CM ,apyr OT
jl,pyra. Onpe)l.e.nHTb CyP.IIY 3THX BeKTopoB Ii JIHHIIIO ,aeiicT-
BJlS! no.1Y'leHtlOrO BeKTopa?
,

1.JACTb nEPBASI. MEXAHI-IKA
r nAB A I. KHHEMATHKA
 I. PaBHOMcpHOC npHMo.lIIHeHHoe ,lJ.BH>KeHHe
1.1. Ha pHC. 7 npe,lJ.cTaBJleHb! rpa<pIIKH 3aBHCliMOCTil KOOp-
Jl,IIHaTbl TeJIa OT BpeMeHH. fpa<pIIKH KaKHX ABH>KeHIIH nOKa3a-
IIbl? KaKoii BHA IIMe!OT rpa<pltKH 3aBIICH\lOCTH CKOpOCTH II
nYT't, npOHJlellllOrO Te.'IOM. OT BpeMeHII?
X,H
11.'"
2
t,c
Pile. 7
PIIC. 8
J .2. fpa<puKIt KaKHX ;J.BmKeHHH Te.'I nOKa3aItbl H3 pllC. 8?
KaK OTJIlillaIOTCS! CKOpOCTH ABlliKeHHH TeJI? B KaKoH MOMeHT
BpeMell1l Te'la BCTpeTIIJIHCb? KaKlle. nYTH TeJIa npOlllJIH .11.0
BCTpeqll?
'.3. fpa<puKIl SaBHCIt'fOCTH KoopAHHaT .ll.BYx TC.'1 OT Bpe-
MeHH nOKa3aHbI Ha pliC. 9. Onpe;J.eJIHTb BpeMS! ABII.>KeHIIS! TCJJ
Jl,0 BCTpeqll, KooPAHHaTY MeCTa BCTpellH, ,H
nyrh, npOHJI,eHHblH TeJIaMH .11.0 BCTpellll,
B KaKlle MOMeHTbI BpeMeHH paccToHHHe
Me.>KJlY TCJJaMH paBHo HallaJIbHoMY?
1.4. TOIIKa Jl,BH>KeTCH C nOCToslHHoH
- -+
6
I
CKOpOCTblO V o nOA yr JIOM ex K OCII X
(pIiC. 10). B HallaJIbH.bdi MOMeHT BpeMeHit
t = 0 TOIJKa HMe.'1a KOOpJlHHaTbI (x o ; Yo)'
HanHcaTb ypaBHeHHe ABH.>KeHHS! TOIJKH H
ypaBHeuHe TpaeKTOpllU,
o t,c
Pile. 9
7

,.5. Rant>< ypaBHeH1IS! J1BJPKeHIlSI T€.'1a: x = vxt, Y = yo+
+ 't'yt. 3anHcaTb ypaBHHIIC Tpa':KTopllll 11 nOCTpOltTb rpa-
$1IK, ec:w V:x = 25 OI.'C, !fo = 0,2 M, v y = I,D M 'c.
1,M
g ..
 -
I......
I ...... ....
I
!J( ....
0 A X 0 'f t C
3
PIIC. 10 Pile II
1,6. Onpc,!J,c.'IIITb nYTb, npoii,!J,cHHbIH T€JIOM 3a 3,0, 4,0 II
8,0 C, Cc.'1l1 3aBIIC1IMOCTb Koop;J,llIIaTbI TCJla OT BpeMclIlI J1aHa
Ha puc.ll.
1.7, Ha pllC. 12 npeJ1cTBB.1ell rpaqJHK 3aB1IC1IMCCTif IWOp.:l.H-
HaTbI Te.1a OT BpeMeHII. CKO.'1bKO BpeMel1ll re.'lO HaAO;J.II.10Cb B
J1BlI}KCl-Il:H? nOCTpOJITb rpa!}JIIKH 3aBIICII\IOCTII CKOpOCTH II nYTH
OT Bpefemf.
1.8, Teno npOlllJIO nYTb 5 = 10,0 1.1 33 t = 10,0 C. H3BCCT-
110:-- 'lTO, npoii;J.H n}Tb 51 =6,O:\f 33 11 = 2,0 C, Te.'lO OCTaHOB,I-
JIOCb II CTO£.'10 B Te'lenne I: = 3,0 c. C KaKOl1 CI\OpOCTblO Te.1C
nr01ll,lO OCT3B1ll) IOCS! 'laCTb n}'TII? nOCTpOIITb rpa'HKII 3aBIIC1I.
MOCTII n}TII II CKOpOCT1I OT npe!\leHIl.
v: HIC
J,M
z
g t.c
I
o I I I
J iI. 9. t,c
I I
-3 _______.1....-..1
PIIC. "12
P\;c.13
.. 1,9. fpaq111J( 3aBHC:IMOCTII CKOpOCTIf TeJIa OT BpeMeH.1I 11306-
pa>KeH 113 pllC. ]3. HailepTIfTb rpaIIKI 3aBHCHMOCTII KOOPA:f-
lfaTLI, a T3K>KC npoii.a.cHI!Oro nYTII OT Bpc\-leHH. HaHTlI CP(.]HIOIC
CKOPOCTb ,!I.BH>KeHIIH TeJIa H Cr;J.HG:'J .IireaylO CKOpOCTb 33 nep.
r:,xc 8,0 c. \'0 c: 51.
1.10. fpp nepeMe!1l.aeTC BepTm..a.'1bllo. nOJIb3)"srcb rpa
q:IIKD:\f noro nepe!\lern.emu!', nmm:;;:JHl1O:\f Ha pilC. 14, onpe;:.e
.'lIlTb Cl\OpGCTIl nO;J.'LeJ'ofa If cnycKa, a 1c1J.>Ke nYTb, KOTOpblii npc
8

ruen -rpY3 3a 70 c. 1..JeMY paBna Xl'
Cpe!l.HSUI CKOpOCTo .nmln<eHIHI rpY3a  jO
HaI.JepTIITb rpaqJIIK 3aBHCIIIOCTII 2C
CKOpOCTI! rpY3a OT BpeMelll!.
I. II. nepBYIO nonOBlIHY nYTH
8BTOM06n.lb npoexa 1 CO cpe;J.Heil
ChOpOCTblO VI = 60 KM/'I, a BTO-
PYIO - co cpe.nHe(1 CKOpOCTbJO V 2 = Pile. 14
= 40 KM/'l. Onpe.ncnHTb cpe.n1l101O
CKOpOCTb aBToM06nnSI Ha DeeM nYTIL
1.12. nepBYIO nO"lOBIIHY Bpe\fel!ll aBTOM0611.1b 1Bnra.1CSI
co cpe.nHeii Cl<OpOCTblO <:'1 = 40 J<\I''I, a BTOP}IO - co cpc.J.lleii
CKOpOCTblO v 2 = 60 K!lI/'I. Onpe;J.c"lIlTb Cpe;I.1I101O CKOpOCTb
aBTmIo611.IISI Ha Bce, nYTI!.
1.13. KaTep npOllIeJI nepBYiC> nonoBIiHY nYTII co Cpe..1.IleH
CKOpOCTblO B n = 2.0 pa3a 6oJlbllIeH. '1eM BTOpyJO. Cpe.nHSlSI
cKopoeTb Ha Bce.., nYT;r COCTaBH.la v cp = 4,0 K'.! IJ. KaKoBbl n:o-
pOCTII KaTGpa Ha nepBoif II BTOpOH nOIIOBlIIl8X nynl?
1.14. KaTep, .nBHranCb BHH3 no Tel.JeHllIO, 3aTpaTHn BpCJ\1S1 B
n = 3,0 pa3::l MeHbllIe, '1C1 H3 06paTHbIH nYTb. Onpe;!.e.1HTb,
C KaKHMII CKOpOCTSIMII QTIIOCJlTe,,1bUO 6epera .nBHrancSI KaTep,
ecnll cpe..!tHSISI CKOpOCTb Ila BceM nYTII COCTaBH.lIa v CP = 3.0 KM/tJ.
1.15. nepnyJO no.loBHHY BpcMeHH Te.'10 .D.BH)!{eTCfl co CKO-
pOCTblO VI = 30 ""/c no;!. yrno' a l = 30" K 3a..'l.allHo:\IY nanpcIB-
..neHHIO, a BTOPYIO - no)J. yrJIO'-I 0: 2 = 120 9 K TmlY n<e HanpaB-
.'1eHlllO co CI<OpOCTblO v 2 = 40 M,'C. HaihH CpC;J.HIOIO CKOpOCTb
nepe\lell\eHII. Ka1<OH nYTb TeJIO npOif..'l.eT 3a Bpe:\ISI t =4,0 c?
1.16. y!3 nYHKTOB A II B. pacnOJIon<eHHblx H3 paCCTOSIHHII
1 = 120 KM .nPyr OT .nPyra, o;J.HoBpe1'vIeHIlO HaBCTpeqy J[.Pyr ..!tpy-
ry uaqanll J[.BHraTbCSI Jl.Ba aBTO'106HJISI. CKOpOCTb nepBoro an-
TOM0611JISI VI = 70 KM/q, Bmporo V 2 = 50 Y..:lf/IJ. Onpe;J.e.1HTb.
'1epe3 lI.aKGe Bpe'fSi II Ha haKOM paCCTOSIHnIl OT nYHKTa A OHli
BCTpeTSlTCSI. KaKoe paCCTOSllllle J[.O BCTpeIJH npoH,.J.eT OJ[.IIH aB.
TO!.10611.'1b B ClICTe!lfC Koop.nIlHaT. CDSl3aHHOH C .nPyrH\f aBTOMO-
611neM?
1.17. 1-13 .ll.BYx Hace.::eHHblX nYHKTOB A II B, pacnOnO>KeH-
HblX B.nOJlb rnocce Ha pacCTOsIHHII 1 = 3,0 K\f ,.J.pyr OT .ZI.pyra, B
OAROM HanpaB.'1eHII.1I o.nHonpe\feHHO H8'IJanl! .nBH:iKeIlHe BeJIOCI!-
ne,IUICT I! nernexo.n. BeJIOCII(le.J..I!CT, .nBHn<YlllHHCSI"113 nYHKTa A.
"Men CKOpOCTb VI = 15 KWIJ, a nemcxo..'l., .nBIDKyw.uikSI 113
nYHKT3 B. HMeJI CKOpOCTb V! = 5.0 K.\f/q. 1..Jerc3 CKOlJbKO BpC-
MeH" Be:IOCIIJ!eAHCT .norOH"T nellIexop.a? Kahlle nyr" 01111 npoii-
.nYT npll 3TO\f?
....
9

1.18. 113 ,anyx ropo.ItOB no rnocce lIaBCTpetIy ,aP} r ,aPFY
BbleXaJIH .D.Ba aBT06yca: O;J.UH - B MOMeHT TI = 9 tI 00 MHH,
a .D.Pyroii - B MOMeHT T 2 = 9 tI 30 MUH. nepnbIH ;J.BuraJICS!
co CKOpOCTblO VI = 40 KM. IJ, a .D.pyroH - co CKOpOCTblO v 2 -=
= 60 KMIIJ. D.JIllHa MaprnpYTa / = 120 KM. B KOTOpOM tIacy If
Ha KaKOM paccToHHHIf OT ropo.ItoB BCTpeTUJIHCb aBTo6ycbl?
1.19. 113 nYHKToB A U 8, paccToHHHe Me}f{,ay KOTOpblMIf /,
,aBli}f{YTCH B 0.D.1I0'>l HanpaBJIeHUU ,aBa Te.'1a co CKOpOCTHMU VI If
V 2 , npHtIeM H3 TOtIKU 8 TeJIO HatIaJIO ,aBHraTbCH cnYCTH BpeMH
to nOCJIe HatIa.r1a .ItnU)KeHHH Te.rra H3 TOtIKII A. lJepe3 KaKoe Bpe-
MH BCTpeTHTCH TeJIa?
1.20. 113 nYIlKTa A BbIeXaJI Be.nocune.D.HCT co CKOpOCTblO VI =
= 25 KMIIl. CnycTH BpeMS! to = 6,0 MUH 113 nYHKTa 8, HaXO.D.H-
l1lerOCH Ha pacCToHHHH / = 10 KM OT nYHKTa A, BblrneJI nerne-
xo,a. 3a BpeMS! 1 2 = 50 C nerneXO.D. nporneJI TaKOH )Ke nYTb, Ka-
KOH BeJIOCHne;J.lICT npeo.1l.o.neJI 3a J3peMH 11 = 10 c. r,ae BCTpe-
TSiTCH nernexo,a H Be.'10Clme;J.uCT?
1.21. naCCa)f<HP e,aeT B noe3;J.e, CKOpOCTb KOTOpOro VI =
=80 KM/q. HaBCTpetIY 3TOMY n0e3,ay ,aBHiKeTCH TOBapHblH noe31t
,aJIHIlOH / = 1,0 KM co CKOpOCTblO V z = 40 KMiq. CKOJIbKO Bpe-
MeHl1 TOBapllblH n0e3.D. 6Y.D.eT Jl.BHraTbCH MHMO nacca}!<Hpa?
1.22, ABTOM06HJIb, .D.BHraHCb paBlloMepllo co CKOpOCTblO
I = 45 KM!q, B TeqeHHe BpeMeHII t 1 = 10 C nporneJI TaKO" >Ke
nYTb, KaKoH aBTo6yc, .D.BUraIOI1lUMCH B TOM >Ke lIanpaBJIemm,
nporneJI 3a Bpe!>iH Iz = 15 c. KaKoDa HX OTIIOCUTeJIbllaH CKO
pOCTb?
1.23. 3cKaJIaTop MeTpOnOJIIiTeHa nOJl.HII>,laeT HenO)).BH>KHO
CTOHllI.erO Ha HeM naCCa>KHpa B TetIeHHe BpeMeHH t l = 1,0 MUH.
no HenoJl.BH)KHOMY 3CKaJIaroPY naCCa)KHp nO.D.HHMaeTCH sa
Bpe'H Iz = 3,0 MUH. CKOJIbKO BpeMeHH 6YJl.eT nO)).Hu>,'aTbCH nac-
ca)f<.lIp no .D.BU>KYllI.eMycH 3CKaJIaropy?
1.24. TenJloxo,a KypCHPYeT no peKe Me>KJl.Y Jl.BYMH npHCTa-
IIHMH, Haxo,aHllI.HMHCH lIa paCCTOHHUH / = 60 KM. no TelleHHIO
peKII 3roT nYTb TenJIOXOJl. npOXOJl.HT 3a BpeMH 11 = 3,0 q; npo-
TIIB - 3a BpeMH 1 2 = 6,0 tI. CKOJIbKO BpeMellu nOTpe60BaJIocb
6bI TCnJlOxo,ay .lI.JlH Taro, qT06bl npOnJIblTb paCCTOHHHe Me>K,ay
npHCTaHHMII no TeqeHUIO npH BblKJllOtIeHHOM )).BHraTe.ne? Ka-
KOBbI CKOpOCTb TeqellHH peKl1 H CKOpOCTb TenJIOXOJl.a OTHOCII-
TeJIbHO BOJl.bl?
1.25. C Karepa, .D.BH>KYlllerocH no TelJeHHIO peKH, yna.n hpyr.
lJepe3 15 MHII nOCJIe 3TOro KaTep nOBepHY.'1 U lIaqa.'1.D.BHraTbCH B
06paTHYlO CropOHY. lJepe3 KaKoe BpeMH OH nOpaBIiHeTCH C
KpyrO\I?
10

1.26. MlIMO npliC'l'aHJI npOnJIbiBaer nJIOT. B OT MOMeHT B
noce.n:OK, Haxo;I.suu.lIikSi Ha paccromnm 1 = 15 KM OT npHCTaJlII,
BHH3 no peKe OTnpaBJISIeTCSI MOTopHaSi JIO;J.Ka. OHa )J.OIlJIblJIa )J.O
noce.1Ka 3a BpeMSI t=3/4 II H, nOBepH}'B 06paTllo, BCTpeTlfJIa
n.10T Ha paccToSlHUH S = 9,0 KM OT nOCeJIKa. KaKoBLI CKOpOCTb
TeL[eHiISl peKH H CKOpOCTb .:JOJ).KH OTJlOCIlTeJlbHO BO;J.bl?
1.27. newexoJ). nepexoJ).HJI )J.opory co CKOpOCTblO v =
= 4,2 KM/Il no npSlMoi'i, COCTaBJISlIOIlleH yroJI a = 30° C Ha-
npaB.'leHueM J).c>POfH, B TeL[eHHe BpcMeHII t = 1,0 MHH, Onpe)J.e-
JIIITb WHPUHY J).oporu.
1.28. JIoJ).Ka J).BIDheTCSI no peKe nepneJlJ).HK)"JISlpHO 6epery
co CI<OpOCTblO V. CKOpOCTb TeL[eHHSI peKH u, OnpeJ).e.n:HTb, no)J.
KaKHM yrJIOM a K 6epery J).BilLKeTCSI JIO)J.Ka.
1.29. JIo;J.Ka, J).BHraSlCb nepneHJ).HKYJISIpHO 6epery, OKa3a-
.'laCb Ha J).pyroM 6epery Ha paccToSlHUH S = 25 M HHLKe no TeL[C-
IIHIO L[epe3 t = I MHH 40 c. IllH;;:HH; peKH 1 = 100 M. OnpeJ).e-
.'JJlTb CKOpOCTb JIO)J.KH H CKOpOCTb TeL[eHHSI peKH.
1.30. 113 nYIiKTa A no B3aHMII0 nepneH)J.HKYJISlpHblM )J.OpO-
raM BbleXaJIH J).Da aBTO10611"lSI: OJ).HH - co CKOpOCTblO 30 KM'Il,
J).pyroii - co CKOpOCTblO 40 KM/Il. C KaKOU OTHOCHTeJlbHOH CI\O-
pOCTblO OHII YJ).aJISIIOTCSI J).pyr OT J).pyra?
1.31. Baroli WHpHHOH b = 3,6 M, J).BIILKYlllUi1cSl co CKO-
pOCTblO VI = 15 ",,'c, 6b1JI np06HT nYJIei'l, JIeTeBWCH nepneHJ).H-
hYJISlpHO lIanpaBJIeHUIO J).BULKeHHSI BaroHa, CMcII1.ellHe OTBep-
CTHi'1 B CTeHax BaroHa OTIiOCHTCJIbHO J).pyr J).pyra paBHo S = 9,0
CM. Onpe,!!.e.n:IITb CKOpOCTb )J.BHLKeHHSI nYJIU, CL[HTaSi ee nOCTO-
SI 11I10ft.
1.32. OXOTlUiK cTpe.n:SleT )J.P06blO B nTHl.(y, JIeTSIYIO no
npSlMoH co CKOpOCTblO VI = 15 wc. KaKoe ynpeLK.ll.€HHe S HYLK-
HO CJ).e.n:aTb, eCJIH B MOteHT BblCTpeJIa nTHl.(a HaXO)J.HJIaCb Ha MH-
HHMaJIblfOM OT OXOTHHKa paCCTOSIIIHH, paBHoM 1 = 30 M? CKO-
pOCTb J).p06u v 2 = 375 M/c.
1,33. noe3J). J).BULKeTCSI co CKOpOCTblO V = 36 KM/L[. noJ).
npSlMblM yr.'10M K HanpaBJIeHHIO J).BH>KeHHSI noe3J).a J).yeT BeTep co
CKOpOCTblO U = 10 M/c, OnpeJ).eJIHTb HanpaBJIeHUe P $naLKKa,
YCTaHOBJIelfliOrO Ha Kpblwe JIOKOMOTHBa.
1.34. JIOKOMOTHB J).BHLKeTCSI Ha BOCTOK co CKOpOCTblO V =
= 18 KM/Il. .l1.blM H3 Tpy6b1 nOJ).HHMaeTCSI BepTHKaJ1bHo. Onpe-
J).e.n:HTb CKOpOCTb H HanpaB..1eHHe BeTpa.
1.35. Kopa6JIb nJIbiBeT Ha lOr co CKOpOCTblO 42,3 KM/Il. 3a-
MeTHB B Mope KaTep, Ha6..'11O,!!.aTe.n:b, HaxoJ).SiIllHikSi Ha naJIy6e
Kopa6JISI, onpeJ).eJIlI.'I, L[TO KaTep J).BHLKeTCSi Ha ceBepo -BOCTOK co
CKOpOCTblO 30 KM/Il. KaKoBa CKOpOCTb Karepa H B KaKOM Ha-
npaB.'1eHHII OH lIJ).eT?
11

1.36. J1o;J.Ka Jl.BH}I{eTCH no)J. yrJloM a = f/i' K 6epery co
CKOpOCTblO v = 2,0 "tic. CKOpOCTb peKIi U = 0,5 r.fic. Onpe)J.e;
nI1Tb CKOpOCTb Jl.BIILKeHlUI JIOJl.KII OTHOCllTeJIbHO peKH.
1.37. 4eJIOBeK, e;tyuuIii B BarOHe
"'- ___ __ 8__ noe3;J.a B Jl.OLKJJ.JIHBYIO noroJl.Y Ha IOro a
 _ BOCTOR CO CKOpOCTblO V = 30 KM!IJ,
 aaMeIJaeT, rJlH}J.H B 6oKot3oe CTeKJIO, IJro
/J .ll.OLK;J.b na;J.aeT Bep1'liKaJIbHO BHII3. OlJ.e-
___ _(1_____ HliTb CKOpOCTb BeTpa.
A 1.38. KaTep Jl.BliLKeTCH OT nYHKTa .4
PHC. 15 K nYHKTY B (pHC. 15), .'I.epLKa KYpC .
CKOpOCTb TeIJemUI peKU u=2,O M/c.On-
peJl.eJIHTb CKOpOCTb KaTepa OTHOCHTeJIb-
HO 6epera li OTHOCIITeJIbHO pehH, ec.'m
a = 45°,  = 30°.
1.39. fpY3- nO)J.BeweH C nOMOIU.blO
Jl.BYX 6JIOKOB (pHC. 16). C KaKoA CKO-
pOCTblO )J.BHLKeTCH rpY3, eCJlli BepeBKY
TSIHYTb co CKOpOCTblO vo?
1.40. JJ.Be JIHHeHKli 06pa3YIOT Me}KJI.Y
co60ii yro.'1 a. (pHC. 17). OAHa .'1I1HeAKa
nOKoHTcH, a BTopaH Jl.BHLKeTCH co CKO-
pOCTblO V. C KaKoH CKOpOCTblO OTHOCli-
TeJlbHO HenOJl.BHLKHOH JlHHeHKli Jl.BliLKeT-
CH TOIJKa 0 nepeceIJeHHH JIHHeeK?
1.41. 06bHCHHTb, KalUlM 06pa30'\f HXTa MOLKeT )J.BHraTbCH
co CKOpOCTblO, npeBbiWalOIU.eii CKOpOCTb aerpa.
1.42. MoropnaH JlO}J.Ka Jl.BIILKeTCH nepneH}J.HKYJIHpHO 6epery
co CKOpOCTblO v = 10 ID.L'IJ. C KaKOU CKOpOCTblO )J.BIILKeTCSI
f
PHe. 16
Pile. 17
-
v,
A
PHe. 18
- ..
TCHb OT .'IO;J.KH no Jl.HY, cocTaB.'1HlOllleMY C nOBepXHocTblO BO,l:lbl
yroJI a = 30 0 ? eo.'JHl.le HaXo.'l.HTCH B 3eHHTe.
1.43. CTepLKeHb wapHHpHo coe)J.HHeH C MY<Prar.-IH A H B,
KOTOpbIC nepelelllalOTCH no Jl.BYM B3allMHO nepneH)J.HKYJISlpHblM
peHKaM (pHC. 18). .MY<Pra A Jl.BULKeTCH C nOCTOSlHHOA CKOpOCTblO
VA. HafITH CKOpOCTb MY4m>l B KaK «PYHK!.t1l1O yrJIa a.
12

 2. PalnfOnepeP,leHHoe npsblOnHHcHHce Asnm:.eHHe
2.1. Oxap?,lCTepll3yfiTe .ll.BmKel1.fH Te.n, rpa4>HKH CKopocTeii
KOTOpblX npeACTaBJleUbi Ha pliC. 19.
2.2. Ha pm:, 20 nOKa3aHa 3aBI1\:UMOCTb CKOpOCTH TeJIa OT
BpeMeHII. nOCTpOHTb rpa4>IIKH 3aBH\.IfMOCTeii YCKopenml H KO-
op.:\,HHaTbi Te.na OT BpeMellH, B MOMHT rJ
to = 0 KOOp;I.IIHaTa Te.na Xo = 0, non:a-
3aTI" tITO TaHrellC yr.'1a HaKJIOHa rpa-
<}JIIKa CKOpOCTH KOCH BpeMeHII IIHCJIen-
HO paBeli YCKopeHH10 re.'1a, a nJlOIWi.llb
no;I. rpa4>nKoM YCKopeHIIH OT BpeJeHH
'1l1c.neIiHO paBna 113MeHeHlllO CKOpOCTH.
2.3. nOCTpOIlTb rpa4>IIKH 3aBliCHMO-
cTen KOOp.llliHaTbI H YCKopemul Te.na OT
BpeMeilH. fpa<pHK 3aBliCUMOCTH CKOpO-
CTn OT BpeMelllf .llaH Ha pHC. 21. B MO-
MeHT BpeMeHH to = 0 KOOp.llllllaTa Te.na Xo = O. no rpa<pIIKY
x (t) nOKa3aTb, '1m TaHreHC yrJla HaKJIOHa KaCareJlbllOii K rpa-
q>HKY '1HCJleHIlO paBeH CKOpOCTIi TeJla B .:\,aHHI,lii MO\.eHT Bpe-
Menll, a nJloma.iI.b no;I. rpa<pHKoM v (t) IJHC.'1enHO paBHa _1I3Me-
JleHHIO KOOp.llHHaTbI. .
2.4. no rpa<}JHKY 33BHcn:.wcrll KOOpAlinaTbl TeJla OT Bpe-
MellH (pHC. 22) nocrpO!ITb rpa<puKH 3aBHcliMOCTeA YCKopeHHSI,
CKOpOCTli H nYTH, npOH..'I.eHHoro TeJrOM, OT BpeMeHH.

t
PHe. 20
Pile. 21
J
2
1
t
Pile. 19
JC
t
Pile. 22
2.5. fpa<}JHK 3aBl!CIIMOCTH CKOpOCTIi Te.'1a OT BpeMeHII JJ,aH Ha
pHC. 23. Ha'laJlbHaH Koop.llHllaTa Xo = o. nOCTpOHTb rpa4JHKJI
33BIICIIMOCTII YCKopeHIIH, KOOp.llHHaTbl H nYTH, npOA.lleillfOrO Te-
nOM, OT BpeMeHIf.
2.6. !laH rpa<}JHK 3aBllCliMOCTH CKOpOCTH Te.na OT BpeMeHH
(pHC. 24). nOCTpOHTb rpa<pHKH 3aBHCHMOCTH nYTH H Koop.llllna-
TbI OT BpeMeHII. OnpeJ1.e.'1HTb Cpe.llHIOIO CKOpOCTI, 3a nepBble 2,0 II
II 5,0 c. Ha'lIa.1bHaH l<oop.nHHaTa Xo = O.
13

2.7. no rpa4>HKY a (t) (pnc. 2a) nOCTpOHTb rpa4>HKH v (t),
x (I) If S (I), CCJI1I HatlaJIbHbIe YCJIOBJUI CJIe)l.YIOI.!.lHe: v (0) =0,
x (0) = O.
2.8. KaK H3MeHSlTCSI rpa<lJHI<H v (t), x (t) H S (t) (c.". 3a)l.a-
tlY 2.7), CCJlH HatlaJIbHbIe YCJlOBIiSI CJIe)l.YlOl.!.llfe: a) x (0) = X o ,
v (0) = 0; 6) x (0) = 0, v (0) = v o ; B) x (0) = 0, v (0) =
= - v o ?'
2.9. T e.'lO )l.BHLKeTCSI no np SlMOH C YKopcHlfeM a = 0,5 MI c 2 .
HatlaJIbllaSl CKOpOCTb TeJIa V o = - 5,0 M/c, Hatla.'IbHaSl KOOp-
U. MIC
"

2 -
J
2
1
o
-2
Pile. 24
)l.HHaTa Xo = 2,0 M. 3anlfcaTb ypaBHeHlfe )J.BHLKelllfSl TeJIa, 3a-
BHCHMOCTb CKOpOCTlf OT BpeMeHlI. Onpe)l.eJIHTb BpCMSI )l.BHLKe-
IIIfH TC.1a )J.O OCTaHOBKH If nYTb, npOH.3.eHHbIH TeJIOM Jl.O ,?cTaHoB-
RH.
2.10. npSlMOJIIlHeHHoe )J.BHLKeHHe TOtlKIf omfCbIBaeTCSI ypaB-
HeHHeM X = 1 + 3t - 2t 2 (x BblpaLKeHo B M, t - B c). r)J.e
lIa>"O;:l.lf.1aCb TOtlKa B UatlaJIbllbm MOMeHT BpeMelllf? KaK MeHSI-
eTCSI CKOpOCTb co BpeMeHeM? Kor)l.a TOtlKa OKaLKeTCSl B HatlaJIe
KooD)J.HHaT?
" h
L...--1 t
Pile. 25
Pile. 26
2.11. TOtlKa )l.BIILKeTCSI no 3aKoHY x = 2 - 12t + 2[2 (x
BbIpaLKeHo B M, t - B c). nOCTpOHTb rpa4>HKH 3aBlfcHMoCTeH
KOOp;:l.lfHaTbI, nYTH, CKOpOCTH H YCKopeHHSI TOtlKH OT BpeMeHIf.
2.12. TpaeKTOpHSI )l.BlfLKemfSl Te.n:a nOKa3aHa Ha pHC. 26.
YpaBHeliHe )J.BH}I{eHHSI TeJIa B)l.OJIb OClf Y 3amfCbIBaeTCSI B CJIe-
)l.YIOI.!.lCM BH)J.e: y = a u Fl2, f)J.e a y = 2,0 M/c z . YroJI a = 30°.
14

Onpe;J.e.1UTb YCKOpeHUe Te.'1a. KahYlo CKOpOCTb HMeer Te.'10
qepe3 i = 5,0 C nOCJIe HaQa.'1a Jl,BH>KII1UI, KaKOBbI ero KOnp;I.lI-
IlaTbI B 3TOT :lfOMeHT BpeMeHII?
2.13. lI.BU>KeHHe TOqKH 3a.'l.anO ypaDlIeHlleM x = 12 t-
- 2t 2 (x Bblpa>KenO B M, t - B c). Onpe.1.eJUITI? CpeJl,HIOIo CKO-
pOCTb ;I.BII>KeHIHI TOqKH B HHTepBa.'1e npeMeHII OT i 1 = 1,0 C Jl,0
i... = 4,0 c.
- 2.14. ABTOM06HJIb HaqaJI Jl,BuraTbCSI C YCKopelIlieM a=-I,5 M:C 2
U Qepe3 neKOTopoe BpeMSI OKa3a.'1CH Ha paccTOsnum s = 12 Pol
OT HaqaJIbHOH TOqKU. Onpe..'1.eJIHTb CKOpOCTb Te.'1a B 3TOT MO-
MCHT BpeMeHIf. 4eMY paBlfa CpeJl,HSIH CKOpOCTb?
A
-
D __
-- 
--
8
B
l
.
A
Pile. 27
PHe. 28
2.15. nOKa3aTb, QTO CpCJI,HSIH CKOpOCTb 3a npOH3Bo.'1bllbIii
MOMCHT Bpe:lfeHH 't = i 2 - i 1 npH paBHOnepe:llCHHOM Jl,BII>KeHIlIf
paBHa CKOpOCTH B MOMenT BpeMeHH t = i 1 +'t/2.
2..16. B MOMenT BpeMeHH io = 0 noe3J1, HMeJI CKOpOCTb.
V o = 10 M/C; B MOMeHT BpeMeHH t 1 = 5,0 c- CKOpOCTb VI =
= 18 KM/q. OnpeJl,e.n:uTb YCKopenlfe noe3J1,a U ero cpe;J.HlolO
CKOpOCTb.
2,17. Jth TOtIKIf C (pHC. 27) HalIllHaeT Jl,BUraTbCSI TeJIO I
C nOCTOSlHnoA CKOpOCTblO V = 2,5 M/C B,lJ.OJIb npSlMoH CA. B
TOT }l{e MOMeHT H3 TOIJKH B BJI,OJIb npHMOH BA HaIJHnaeT Jl,BU-
raTbCH YCKopeHHO 6e3 HaqaJIbHOH CKOpOCTU Te..10 I I. C KaKII\f
YCKopeHHeM .ll.BHraJIOCb TeJlO II, eCJIu B TOqKe A TeJIa BCTpenf-
JIHCb? Ha CKOJIbKO OTJIHIJalOTCH CpeJl,1lHe CKOpOCTH 3THX Te.'1?
4epe3 KaKoe BpeMSI TeJIa BCTpeTHJIUcb? 3aJl,aHO b = 10 M.
2.18. TeJIo HaIJIIHaeT Jl,BHraTbCSI H3 TOtJKU A (puc. 28) co
CKOpOCTblO V o H 'lepe3 HeKOTOpoe Bpet.1H nonaJl,aer B TOqKY
B. KaKoA nYTb npOllIJIO Te.n:O, eCJIH YCKopeHHe paBHo a? Ha-
npaBJIeHHe BeKTOpa nOKa3aHO Ha PHCYHKe. PaccTOHHue Me>K;l.Y
_ TotJKaMH A H B paBHO t. Onpe.lleJIUTb CpeJl,HlO1O II Cpe.1.HIOIO ny-
TeBYIO CKOpOCTIf.
2.19. Te.n:o HatJHHaer .ll.BHraTbCSI co CKOpOCTblO V o = 10 M/C
H .ll.BH>KeTCH C YCKopeHHeM a = - 2,0 M/C z . OnpeJl,CJUITb.
KaKOU nYTb Te.'10 npOH.lleT 3a BpeMH i 1 = 6.0 C H t s = 8,0 c.
15

2.20. ABToM06Hnb, J1By.raHCb pmmoycKopermo, qepe3 1= 10 C
nocne Halla,a J1I3H)KeHH}{ Jl.CCTUr CKopocnf v = 311 KM/q. 0:1-
pCJl.e.1HTb YCKopeHHe, C KOTOpb:M J1BHra.'CH aSTOMof\Hnb. KaKua
nyTb 011 nplf 3TOM nporr:en? KKOH nYTb aBToMo611nb npoillen
3a noc.le.n H10IO ceKYII.'1.Y?
2.21. C KaKlI:\1 YCKOrelllfc:\1 .ll.BH>KCTCH Te.!lO, eC.rtI1 33 BOCb-
MYIO ceKyH.1.Y noc::e Haqa.'1a J1BnjKCHIHI 0110 npOlllno n}Tb S =
= 30 M? Haihn nYT!> 3a 15-10 ceK}'H;J.Y.
2.22. .M3TepJlanbllaH TOQKa .!1.BH)KeTCfl C yc!"opeHucM a.
Onpe.J.cnllTb pa3HocTb nYTeii, npa-..oJ!.tiMbIX TOlIl\Oii B ]l.B3 nocne-
Ji,OBaTeJlbHbIX O;J.HllaKOBbIX npoMc:r.YTKa Bpe!<lcHIl 'to
2.23, Te.'1o, J!.BHraHCb Ge3 HattanbHOH CKOPOCTi{, npOllJ.lo sa
nepBYIO ceKYH,!{Y 1,0 :\1, 33 DTOp}"1O - 2,0 M, sa TpeTblo - 3,0 M,
3a tlCTl3epTYIO - 4,0 MilT. .n. ;,lo>KHO nil CtiHT3Tb TaKoe J!,BlD{{e-
IIl1e paBlloYCKOPCHllbIM?
2.24. .llna aBTOM06HnH BLIXOJ1flT 113 0J1110ro n} IIIcra B 0)1.110:\1
nanpaBJlCHliH. BTOpOH aBTO,106Hnb BblXOJ1I1t" Ha 't = 2D C n03>Ke
nepBoro. 06a J1BII>KYTCH paBHOYCKopeHIIO C O,!{JfllaKOBbIM YCKO-
penile:\{ a = 0,40 f.I/c 2 . 1.Iepe3 CKo.'1bKO BpeMelfJI, CqHTaH OT 113-
'Ia.13 Ji,BII)i{eHlffl nepBoro aBTO:\106H.'IH, paCCTOSlHlle Me>K)1,Y HII-
MH m::a)i{eTCH S = 240 M?
2.25. Or J1D!DKymerocSl noe3J1.a OTl.lennSlIOT nocneJl.!wA
DarOH. noe3!t npo..'1.0nJKaeT Jl.BllraTbCSI C TOll :me CI\OpOCTblO.
KaK 6}",.1.} T OTHOCIITbCSI nYTlI, npOfiJl.eHHble nOC3;J.OM H BarOHOM
Jl.0 MOMeliTa OCTaHOBKH BaroHa? ClUfTaTb, I,!TO BarOH Jl.BnrancSI
paBII 03aM eJlJIeHHo.
2.26. 1.Ie.'IOBeK, BLlii;t.H 113 .:meKTpOne>e3.1.a, nome.' no XOXj
cro Jl.BU)KCHIIH co CKOpOCTblO V = 4,5 KM!q. Kor.z;.a qe.lOBeK no-
paDllflJICSI C lIa'la.'10:\1 ::meKTpOn0e3J1.a, OH CT2n .ll.BHraTbCH paB-
1I0VCKope1i1l0. Onpe.J.e.'1HTb CKOpOCTb 3neKTponoe3;J,a, hOf.ll.a
011' nop3BlUleTcH C qCnOrleKmI.
2.27. PaccToHHHe Me>K;lY .lI.BYMH CTalll.lHSlMJI S = 3,Q K!>I
nOC3.!1. MeTPO npOXOJl.HT co cpe.ll.Heii CKOpOCTblO v cp = 54 KM'q.
npn 3TO'1 OH pa3roHSleTcH B TeqeHlle BpeMeHH 11 = 60 c, 3a-
TC;J. Jf;I.eT paBHOMepllO lIeKOTopoe Bpe'IH I, a SaTeM .lI.BmKeTCH
paBII03aJde.!1..'1eHII0 .lI.O nOJllloii OCTalfOBKH D Tc-qellHe BpeMelilf
t 3 = 40 c, nOCTpOHTb rpa<p uK CKOpOCTH .lI.BHJKellHH noe3.1a If
onpc;I.enJfTb lIaHoo.'1blll}'1O CKOpOCTb noe3.3.a.
2,28. Onpe.lJ.eJllI1'b, Ha CKonbKO nYTb, npOHJl.eHHblH CBOOOJl.-
110 na)l.alOW,H\I TeJlOf.f B n-JO ceKYH.lJ.Y, 6o.lbllle nYTH, npOHJl.eH-
1I0ro B npeJl.b!.ilymyJO ceKYII;J.Y.
2.29. Te.-10 cBo50.ll.1io na..'1.aeT C BLiCOTbI 270 M. Pa3J1.e.'IHTb
3TY BblCOTY H8 Tpn qaCTH hi, h 2 , h3 TaK, IJT06b1 Ha npOXo>K;J.eHu€'
IUUf(J!.OH 113 HHX nOTpe6c>B8.'1OCb O,'].HO H TO >Ke npel\fSl.
..
16

2.30. C BCpTOJi€Ta C6POCU.1If ()e3 HattanbHoH CKOpOCTH )l.Ba
rpY33, npHlJeM BTOpOH Ha 't = 1,0 C n03n<e nepBoro. Onpe.lle.
nllTb paccTOslIllfe MCn<,llY rppa1>HI lJepe3 Bpe\fH t 1 = 2,0 C H t 2 =
= 4,0 C nocne Haqana .llBUn<eHUH nepBoro rpY3a.
2.31. C B03;i.YllJIIOrO wapa, HaXO!l.HlllerOCH Ha BbiCOTe h =
= 240 M, C6POCH.'!I1 6e3 lIaqa.FIbuoH CKOpOCTiI OTIIOCHTeJIbHO
mapa l:!60.'IbWOi'I, HO TH>Ke.n:blii rpp. Onpe!l.CnHTb Bpe1>UI na-
.lleHHH rpY3a, eC.'II1 wap 6b1.'I Heno.nBH}I{HblM. To :me, eCJIIi wap
)l.BllranCH BHH3 co CKOpOCTbIO Va = 5,0 M'C, BBepx co CKOpOCTbIO
Va = 5;0 M/c. C IcaKHM YCICopeHHCM OTHOCH1'e.1bHO mapa )l.BH-
ra.'ICH rpY3 B Ka:m;I.Oo,f H3 CJIyqaeB?
2.32. Te.n:o najj.a.10 C HeKOTopoH BLrCOTbl H nocne.nHlle h =
= 1961>1 npowno 3a BpeMH 't = 4,0 c. CKonbKo BpeMeHH II C
KaKoH BbiCOTbI na.l1B.'IO Te.'10?
2.33. C OTBeCHoro 06pblBa yna., KaMeHb. qenoBeK, CTOH-
lllHll Y TOro MecTA, C KOTOpOro ynan KaMeHb, yc..1b1Wan 3BYK
ero na.lleHlfH QepC3 Bpe:\fH t = 6,0 c. HaiiTlf BblCOTY 06pblBa.
CKOpOCTb 3BYKa v aB = 340 WC.
2.34. LlBa Te.1a HallanH na.J.aTb C o;J.Hoii H Toli JKe BbiCOTbi tIe-
pe3 npm.If)KYToK Bpe\leHH 't O;l.HO noc.lJe .llPyroro. qepe3 CKD.'.;!b-
h.O ceKYH;{ nOCJIe Haqana na!l.CHlIH BToporo Tena paccToHIllle
Me:mlty HIfMlf 6Y.l1eT paBHO l?
2.35. C KpblWH na.l1aIOT KannH BC;l.bJ. npO:\tC>KYTOK BpeMe-
HII1>e:m.ll.Y 0'i'pl::3.m Kane.'Ib 't = 0,10 c. Ha KaKOM paccTOHHHIl
)l.pyr 01' .l1pyra 6Y.l1YT HaXO.1.UTbCSI qepC3 BpeMH t = 1,0 C noc.'1e
Haqana na;J.eHIlSi nepnoll Kanml Cne.l1YIOlltl:e TpH?
'2.36. LlBa Te.1a naIJIlH8.IOT na.li.aTb o;lHoBpe:\leHHo C pa3ublx
BbiCOT H H h H .l10CTllraIOT 3eMnH B O.ll.IIH H TOT:me Mo:o.:eHT Dpe-
MeHH. KaKYIO HaqanblIYIO CKOpOCTb cool5lltInu BepXlleMY Te.n:y.
ec.'H IUUKHee HaqanO na.llaTb 6e3 Haqa.1bHoii CKOpOCTII?
2.37. nOKa3aTb. tIro .l1ml Te.n:a. 6poweHIIoro BepTHKa.'1bIlO
Bsepx: 1) HalJanbHaH CKOpOCTb Va paBua KOneqHOH CICOpOCTU
ero npH conpHKocHoBeHlIH C 3e1>f.7Ieii; 2) BpeMH nO;J.'beMa paBHo
BpeMeHII na.l1eHIIH.
2.38. 'Te.lIo 6poweHo BepTHKanblIo BBCpX C naqa.lJbHoH CKO-
pOCTbJO Va. Kor!l.a OHO ,nOCTHrno BL!Cweii TOIJKU TpaeKTopHH, 113
TOro :me Hatta.'1bHOrO nYIUCTa C TOU }l{e CKOpO::TbIO Va 6poweHO
BTOpoe TeJIO. Ha KaKOM paCCTOHHHII OT HattanbllOrO nynKTa OHII
BCTpeTSlTCSI?
2.39. Te.'1o 6pocaIOT BepTIlKanbHO BBepX. HaMIO.J.aTe.'1b
3aMettaer npO\fe:mYTOK Bper,teHH to Me:m.ny JlBYMH MOMeHTaMIi.
KOr)l.a Te.n:O HaXO)tUTCH Ha BblCOTe h. HauTH Hatta.'Ib") 10 CKOpOCTb
TeJ!3 II BpeMH )l.BlfnieHHH.
17

2.40. C a3poCTaTa, onycKaJOlerOCSI co CKOpOCTbJO llo_ 6po-
caJOT BBepx TeJIO co CKOpOCTbJO V o OTHOCHTeJIbHO 3e\lJIH KaKoe
6y.neT paccToSlHHe [ Me>K.ny a3pocTaToM H TeJIOM K MOMeHTY Ha-
I!BblcllIero no.n'beMa TeJIa OTHOCHTeJIbHO 3eMJIH? KaKoBo HaH-
60JIbllIee paccToSlHlle [MaKc MC>K.II.Y Te..10M H a3pocT3TOM ? tIepe3
KaKoe Bper.m 't OT MOMeHTa 6pOCaJlHSI TeJIO nopaBHSlcTcSI (' a3po-
CTaTO'\! ?
2.41. nOKa3aTb, IJTO npll cBo60.nHoM na.neHHIl TCJI B6JIII3H
nOBepxHoCTH 3eM.'JH HX OTJlOCUTeJIbHaSl CKOpOCTb nOCTOSlHHa.
2.42. D.Ba KaMHSI HaXOJl,HTCSI Ha O.nHO" BepTHKaJIH Ha paccTO-
SlHIIH S = 10 M .npyr OT .npyra. B HeKOTOpblH MOMeHT npeMeHH
BepxHHH KaMellb 6pocalOT BJIIB co CKOpOc;rbJO V = 20 M/c, a
JIII>KHHii omycK3lOT. tIepe3 KaKoe BpeMSI KaMHH CTOJIKHYTCH?
 3. KpHBOJIlIHeHHOe .ll.BH>K.eHHe
3.1. C Bepxneii nOJIKII BarOHa paBHoMepHo .nBH>Kyw.erocH
noe3.na ynan npe.nMeT. KaKoB xapaKTep .nBH>KeHHH npeJJ,r.teTa
OTHOCHTeJIbHO BaroHa? OTHOCHTeJIbHO 3er.tJIH?
3.2. B KaKOM c.'1YlJae BbrnaBllIHH H3 OKHa BarOlla npe.nMeT
yna.neT Ha 3eMJIJO paHbwe: Kor.na BarOH CTOIIT Ha MeCTe UJIH
Kor.na 011 .nBlJ}KeTcSI?
3.3. TeJIo 6poweHo ropU30HTaJIbHO C HalJaJIbHOH CKOpO-
CTbJO Vo. nOMecTIIB HalJaJIO Koop.n1maT B TOqKY 6pocaHHSI H Ha-
npaBIiB OCb x B.nonb HalJaJIbHOH CKOpOCTH, a OCb Y - BepTH-
KBw'Iblio BHH3, nOCTpOHTb rpa<fJHK saBHCIiMOCTeii: ax (t), a y (t),
V x (t), V y (t), x (I), Y (I).
3.4. TeJIo 6pollIeHo ropH30HTanbHo C HalJaJIbHOH CKOpO-
CTbJO Vo. HaHTU: I) ypaBHeHHe TpaeKTOplfH rena y = f (x)
(nocTpoHTb COrJIaCHO 3TOMY ypaBHeHHIO TpaeKTopmo nOJIeT8
TeJIa); 2) 3aBllCIIMOCTb CKOpOCTH TeJIa OT BpeMeHH; 3) 3aBHCH-
MOCTb OT npe:'>teHII yr JIB a Me>KAY BeKTopOM CKOpOCTH TeJla H ro-
PU30HTOM.
3.5. KaMeHb, 6poilleHHblH ropH30HTanbHo C 06pblBa BblCO-
TOH H = 10 M, ynan Ha pacCToHHHH S = 14 M OT TOqKH 6poca-
HHH. 3anHcaTb ypaBHeHHe TpaeKTopHH KaMHH H H3 Hero onpe-
.neJIHTb HaqaJIbHYJO CKOpOCTb.
3.6. Onpe.neJIHTb CKOpOCTb Te.na qepe3 t = 3,0 C nocne TOro,
KaK ero 6pOCIIJIli ropH30HTaJIbHO co CKOpOCTbJO V o = 39,2 M/C.
3.7. tIeJIOBeK HbipHeT B BO.ny C KpYTOro 6epera BbiCOTOH
H = 5,0 M, HMeH nocne pas6era CKOpOCTb V o = 6,7 WC. Onpe-
.neJIHTb Mo.nynb H HanpaB.'1eHHe CKOpOCTU qeJIOBeKa npll .n.OCTU.
}l{eJllflf 11M BOJl,bl.
18

3.8. B KaKOU MoMeHT BpeMeHU Y Tena. t'ipoIlleHHoto tOPII-
30HTanbHO C Ha'lanbHOH CKOpOCTblO V o = 19,6 WC. hacaTe.'1b-
Hoe YCKopeHHe paBHO HopManbHoMY?
3.9. /I\s!1J 6poIlleH ropH30HTanbHo co CKOpOCTblO V o =
=9,8 M/c. t.Jepe3 CKOJIbKO BpeMeHH H B KaKOM Mecre HopManbHoe
YCKopeHHe MH"Ia 6Y,lleT B ,llBa pa3a 60JIbIlle KacaTenbHoro?
3.10. C 06pblBa B ropH30HTanbHoM HanpaBJIeHHH 6pocalOT
KaMeHb co CKOpOCTblO V o = 20 WC. Onpe,lleJIHTb TOIJKY TpaeKTo-
pHH, pa,llHYc KpliBH3HbI KOTOpOH B BoceMb pa3 OOJIbIlle pa,llllyca
B BepxHeH TO"lKe.
3.11. .lJ.anbHoeTb nOJIeTa TeJIa. 6poIlleHHoro ropH30HTanbHo
co CKOpOCTblO V o = 4,9 M/e. paBHa BbiCore, C KOTOpOH ero 6po-
cunH. t.JeMY paBHa ::ITa BbiCOTa H no,ll KaKHM yrnoM K ropH30HTy
Te.!JO ynano Ha 3eMJIIO?
3.12. C BepTOJIeTa, neTHlllerO Ha BblCOTe H = 125 M co CKO-
pOCTblO V = 90 KM/q. c6pocHnH rpY3. Ha KaKOH Bblcore ero
CKOpOCTb 6Y,lleT HanpaBneHa no,ll yrnoM 45° K ropH30HTY?
3.13. B MHIlleHb C paccToSlHHH S = 50 M C,lleJIaHO ,llBa BblCT-
peJIa B ropH30HTanbHOM HanpaBneIfHH npH O,llHHaKOBOH HaBO,ll-
Ke BUIfTOBKU. CKOpOCTb nepBoH nynH VI = 320 M/c. BTOpOH V 2 =
=350 M/c. Onpe,lleJIHTb paCCTOHHHe Me)K,lI.Y npoooHHaMli.
3.14. KaKoH cKopoeTblO 06na.nan nbILKHlfK npll npbILKKe C
TpaPommma, HaXO.llHlilerOCH lIa Bepumlle ropbI, HMelOllleH YK-
nOli a = 45." eCJHf OH npH3eMJIHnCSI lIa rope lIa paccToHHUH s=
= 29 M OT BepIllHllbI?
3.15. .lJ.epeBHHHblH Illap. CKaTblDaHCb C JIeCTIfHLlbl. IfMeJI ro-
pH30IfTaJIbilYlO lIa"lanbllYIO CKOpOCTb V o = 1.7 M/c. BbIcoTa h
H IlllipHua b Ka>K,llOH cTyneHH paBHbI no 20 eM. 0 KaKYIO no c"Ie-
TY CTyneubKY Illap y,llapHTCH BnepBble?
3.16. .lJ.nH TeJIa. 6poIlleHuoro no,ll yrnoM a K ropJl30HTY
co CKOpOCTblO Vo. nocTpoHTb rpa4>HKH 3aBucliMoCTeH: ax (t).
a y (t), v x , (t), VII (t). x (t). Y (t). Ha"lano KOop,llHHaT COBfeCTUTb
C lIa"lanbUbIM nO.!JOLKeHHeM Tena.
3.17. TeJro 6pocHnH co cKopoeTblO V o no,ll yrno1 a K ropl!-
30HTY, 3anHcaTb ypaBHeHHe Jl,BHLKeHHH Tena B .neKapToBbIX KO-
op.nHuaTax. Y6e,llHTbCH. "ITO TpaeKTopHH Tena npe.1.CTaBnHeT co-
OOH napa60ny.
3.18. TeJIO 6pocHnH co CKOpOCTblO V o no.!J. yrnoM a K ropl!-
30HTY. HaHTH: 1) BepTHKaJIbUYIO If ropH30HTanbilYl0 COCTaBJIH-
IOU{He BeKTOpa CKOpOCTH If 3aBHCHMOCTb CKOpOCTH OT BpeMetUf;
2) BpeMH no.1eTa; 3) 3aBHCH-.tOCTb OT BpeMeHH yrna <p MeLK.ny
BeKTopoM CKOpOCTH If ropH30HTOM; 4) MaKcHManbHYIO BblCOTY
noneTa; 5) ,llaJIbUOCTb noneTa, Y6e.llHTbCH. "ITO Bpe"fH nO.!l.'beMa
paBHo BpeMellH enycKa.
19

3.19. JJ.Ba Te., 6poweHll C O.ll.hH31<0BOH Ha'l3nblIoH CKO-
pOCTblO no,'t. yrJIa.1H a H (90 0 - a) K ropn30HTY. OnpeJJ.e,1IHTb
OTHOLUeHHSI HaHOOJIbWnX BbiCOT no.u.'b(':!\.Ia H .'I.a.iIbHOCTeH nOJIeTa
3THX Ten.
3.20. TeJIo 6poweHo no.u. yr.lOM a  60° K ropH30HTY co
CKOpOCTblO V o = 10 M/c. Onpe,'t.e.1HTb MOMeHThI BpeMeHH, Kor)J.a
CKOpOCTb HanpaBJIeHa no.u. yrJIOM p = 45° K ropn30HyY.
3.21. HallaJIbHaSl CKOpOCTb 6poweHHoro BBepx KaMHH V(I =
= 10 wc. CnycTSI BpeMH 't = 0,50 C CKOpOCTb KaMHH CTaJIa paB-
1I0H v = 7,0 M/c. Ha KaK)'1O BbiCOTY Ha)J. HallaJIbllblM ypoBHeM
nO)J.I1HMaeTCH KaMeHb?
3.22. JJ.Boe HrpalOT B MHIl,6pocaH ero )J.pyr Jlpyry. KaKOH
Han60JIbweH BblCOTbI )J.ocTUraeT MSl'l BO BpeMSI HrpH, eCJIH OH OT
O:UiOro IIrpoKa K )J.pyroMY neTHT B Te'leHlie BpeMeHH t = 2,0 c?
3.23. no.u. KaKHM yrJIOM K ropH30HTY HY}KHO 6pOCHTb C 3eM-
mf TeJIO, 'Iro6bI ero MaKCIIMaJIbHaSl BbICOTa no.u.'beMa 6bIJIa B .lI.Ba
pa3a 6o.'Ibwe ,'t.aJIbHOCTH nOJIeTa?
3.24. KaMeHb, 6poLUeHHbIH no)J. yrJIOM K rop1f30HTY, ynan
Ha seMJIIO 'Iepe3 t = 4,0 ell. t.JeMY paBHbI BbICOTa H )J.aJIbHOCTb
nOJIeTa KaMHSI, eCJIH H3BecTAo, qTO BO Bper.m ,lI,BH}KeHIISI ero MaK-
CIIMaJIbUaH CKOpOCTb 6b1JIa B)J.Boe 6o.1bUJe t.uIHHMaJIbHOiL
3.25. KaMeHb 6pOCIIJIli co CJ<OpOCTblO V o = 19,6 M/C no,'t.
yrJIOM a=60° K rop1l30HTY. Onpe)J.e.1HTb pa)J.IIYc J,pHBH3HbI ero
TpaeKToplfH: 1) B BepxHeH TOIlKe; 2) B MOMeliT na)J.eHIUI Ha 3e.\{-
JHO,
3.26. KaMeHb 6pOCIIJIH no)J. yr.lOM 60° K ropH30HTY co CKO-
pOCTblO 19,6 M/ c . KaKoBbI 6Y)J.YT HOpMaJIb1Ioe H KacaTe.lbHoe
YCKopeHHH KaMH? IJepe3 0,5 C nOCJle Ha'lana .ZI.BH}KeHIIH? t.Jepe3
CKOJIbKO BpeMeH.. nOCJIe HallaJIa .lI.BH}KeHml HOpMaJIblIOe K
TpaeKTopHH YCKopeHHe KaMHH 6Y)J.eT MaKCHMaJIbHbI?
3.27. KaMeHb, 6poUJeHHblH no)J. yrJIOM a=60° K ropll30HTY
co CKOpOCTblO V o = 30 M/C, IJepe3 t = 2,0 C ynaJI Ha KPbllllY )J.O-
Ma. Onpe.u.eJIHTb BbiCOTY )J.OMa H paccToHHHe )J.O Hero.
3.28, MOTOLUfKJIIfCT B'be3}KaeT Ha BbICOKHH KpaH pBa. KaKYIO
MlllfHMaJIbHYIO CKOpOCTb )J.OJIiI\eH UMeTb MOTOlUfKnHCT B MOMeHT
OTpblB OT KpaH, IJro6bI nepeCK01J:IITb pOB (pIlC. 29)?
3.29. MrpoK nOCbIJIaeT ilfSlIl C BblCOTbI h = 1,2 M Ha;J. 3eM-
neH TaK, 1J:T06bI yroJI 6pocaH:ul 6b1n paBeH a = 45°. Ha pac-
CTOHHIUI S = 47 M OT MeCTa 6pOC2HlfH paCno.'IO>KeHa ceTKa BH-
COTOH H = 7,3 M. KaKoBa )J.OIDKHa 6b1Tb MHHHMaJIbHaH CKG-
pOCTb, 1JT06b1 MSIIJ nepeCKO'lHn ceTKY?
3.30. <1>YT60JlbHblH MHIl nOCbIJIaeTCH C HaqanbHOH CKOpO-
CTblO V o = 10,7 M/C no)J. yrnoM a = 30" K roplf30HTY. Ha pac-
CTommH S = 6,0 M OT TOtIKH y)J.apa naxo.u.IITCSI BepTilKaJIbHaH
20

CTeHKa, 0 K01'0PYIO MSlIl ynpyro y,napSiercH. HauTH paCCTOg-
HHe 01' TOqKH y,napa no MSlIlY ,!I.o TOqKH ero npH3eMJIeHHH.
3.31. Ha rope C YKJIOHOM ex = 30° 6pocalOT MSlIl C HaQaJIh-
HOU CKOpOCTblO V o = 9,8 M/c nepneH)1.HKYJIHpHO CKnOHY ropbl.
HauTH BpeMSI nOJIeTa MSlqa. Ha KaKOM paccTOSlHHH O1'TOqKH 6po-
caHHSI yna,neT MSlq?
3.32. MHQ 6pocalOT BBepx B)1.OJIh CKJIOHa XOJIMa noon yrJIOM
p = 60° K ropH30HTY. Ha paccTOSlHHU S = 30 M 01' TOqKH 6po-
caHHH OH na,naeT Ha 3eMJIIO. YroJI HaK.'IOHa XOJIMa ex = 30°.
-
tJ
A
H
PHe. 29
PHe. 30
Onpe;J.eJIHTh HaqaJIbHYIO CKOpOCTb MSI'ia. CKOJIhKO BpeMeHH
npollIJIo Me>K,ny .lI.BYMH no..10>KeHJlSlMH MSlqa Ha TOH Bbicore, Ha
KOTopa OR ynaJI?
3.33. MSlq 6pocalOT ropH30HTaJIhHO co CKOpOCThlO V o =
= 14 wc C ropbl, COCTaBJISlIOw.eu yroJI ex = 45° C ropH30HTOM.
Ha KaKOM HaH60JIbllIeM paCCTOSlHHH 01' nOBepXHocTH ropbl OKa-
;)KeTCH MSiIl BO BpeMSI nOJleTa? f.u.e OH npH3eMJIHTcSI?
3.34. .lJ.Ba TeJIa 6pollIeHbI noon pa3HblMH yrJIaMH K ropu-
30HTY H C pa3JIU'iHblMH Halla.'IbHblMH CKOpOCTSlMH. TIoKa3aTb,
'lTO BO BpeMH ,nnH>KeHHH HX OTHOCHTeJIhHaSl CKOpOCTh nOCTOSlH-
Ha no MO,nYJIIO H HanpaBJIemllO.
3.35. 113 TOIlKH A cBo60,nHO na,naeT TeJIO, O,nHoBpeMeHHo H3
TOIJKH 8 noon yrJIOM ex K rop!f30HTY 6pocalOT .n.pyroe TeJIO
(pHC. 30) TaK, IlT06bI o6a Te.TIa CTO.1h.HYJIHCh B B03,nyxe, TIoKa
3aTh, liTO yroJI ex He 3aBHCHT 01' Hall3JIbHOH CKOpOCTH TeJIa, 6po-
llIeHHoro !f3 TOQKH 8, H onpe,neJIHTh 31'01' yron, eCJIH HIl= 1,6.
3.36. TOIlKa H>KeTCH B nJIOC, KOCTH npHqeM ee npSlMo-
yronhHbIe Koop,nHHaThi onpe,ne.I1S1IOTCH ypaBHeHHSlMH x =
= A cos rot, y = A sin rot, r,l:le A H ro - nOCTOHHHble. KaKoBa
cfx>pMa Tpa-eKTOpHH TOqKH?
3.37. TOQKa .aBH>KeTCH no OKPY>KIIOCTH C nocToSlHHOH CKO-
pOCTblO v =50 cM.'c. BeKTop CKOpOCTH H3MeHSleT HanpaBJIeHHe
Ha 1\cp = 30° 3a BpeMH 1\t = 2,0 c. KaKoBo HOpM3.'lbHoe YCKO-
peHHe?
21

3.38. KOHen MlfHYTHOH CTpeJIKH qaCOB Ha CnaccKoH oouIHe
KpeMJul nepeJl.BHHYJICSI 3a 1 MHH Ha 37 CM. KaKOBa )J.JIHHa
CTpeJIKU?
3.39. MHHYTllaH CTpeJIKa tIacon B TPH pa3a JI..1IHHHee ceKYHk
HoiL KaKoBo OTHOllIeHHe Me>K.n.y JIHHeHHblMH CKOpOCTSlMH KOH-
nOB 3THX CTpeJIOK?
3.40. KaKoBo YCKopellHe TOqeK 3eMHoro 3KBaTOpa, o6yc-
JlOBJIeHHoe CyroIJHblM BpallI.elllleM 3eMJIH? Bo CKOJIbKO pa3 .nOJUI{-
Ha 6blJIa 6b1 YBeJIHtIHTbCSI yrJIOBaSl CKOpOCTb 3eMJIlI, tIT06bl 3T0
YCKopeHHe CTaJIO paBHblM g?
3.41. Onpe.n.eJIHTb JlHHellHYiO CKOpOCTb H }CKOpelllle, KO-
TOpblMH 06JIa.nalOT TOIJKH 3e"HloH nOBepxHocTH Ha llIHpOTe JIe-
IIHllrpa.n.a (60 0 c. 1lI.) 3a CIJeT CYTOqHOro 0PaIl.leHHSI 3eMJIH.
3.42. TOIJKa .n.BH>KeTCSI no OKPY:H<HOCTH pa.nHyca r = 20 CM
C nOCTOSlHHblM KaCaTeJIbHblM YCKopeHHeM a't = 5,0 cM/c 2 .
1.Jepe3 CKOJIbKO BpeMeHH noc.'le HaIJaJIa .nBH>KeHHSI HOpMaJIbHoe
YCKopeHHe 6y.ner paBHO KaCaTeJIbHoMY?
3.43. BaJi HaIJHHaeT BpallI.eHHe H3 COC10SlHHSI nOKOSl H B
nepBble t = 10 C cOBepllIaeT N = 50 060pOTOB. CIJIITaSl BpaIlle-
HHe Ba.la paBlloycKopellllblM, onpe.n.eJIHTb yrJIOBoe YCKOpe-
Hlle.
3.44. HeKoTopoe Te..lO HaIJIIHaeT BpaIllaTbcH C nOCTOSlH-
IIblM }' r JIOBblM YCKopeHlleM £ = 0,04 pa.n!cl!, Qepe3 CKOJIbKO
BpeMeHlI nOCJIe HaIJa.'Ia BpallI.eHHSI nOJIHoe YCKopeHHe KaKOH-JIII-
60 TOIJKII Te.'Ia 6y.!1.CT lIanpaBJleHo no.n yrJIOM p = 7ft K lIanpaB-
.'IeHliiO CKOpOCTH 3TOH TOIJKH?
3.45. lI.HCK HaIJHHaer .n.BH:H<eHHe H3 COCTOSlHHSI nOKOSl H
BpallI.aeTCSI paBlloycKopeHllo. KaKHM 6y.n.eT yrOJI Me>K.ny BeKTO-
pOM CKOpOCTH H BeKTOpOM YCKopeHIISI npOH3Bo..lbHOH TOIJKH .nIlC-
Ka, Kor.n.a OH c.n.eJlaeT O.n.HH o60pOT?
3.46. noe3.n B'be3>KaeT Ha 3aKpyrJleHHblH YIJacToK nYTH C
HallaJIbHOii CKOpOCTbiO V o = 54 KltI/IJ H npoxo.n.IIT nYTb S =
= 600 M 3a opeMSI t = 30 c, .nBHraSiCb
paBHoycKopeHHo. Pa.n.HYc 3aKpyrJIeHHSI
paBell R = 1,0 KM, Onpe.neJIHTb CKO-
pOCTb H YCKopeHHe B KOHne 3Toro nYTH,
3,47. CTyneHIJaTblH llIKHB C pa.n.HY-
caMH r = 0,25 M H R = 0,50 M npH-
BO.!1.IITCSI BO BpallI.eHHe rpY30M, onyc-
KaiOllI.HMCSI C nOCTOSlHHbIM YCKopeHHeM
a = 2,0 cM/c 2 (pHC. 31). Onpe.n.eJIHTb
MO.nYJIb H HanpaBJIeHHe YCKopeHHSI roq-
KH M B TOT MOMeHT, Kor.na rpY3 npOH.neT
PHe 31 nYTb S = 100 CM.
22

3,48. KOJleco BeJlOCHne.n.a H\feeT pa..1.HYc R = 40 CM. C Ka-
Koii CKOpOCTbiO e.l!.eT BeJlOCHne.l!.}fCT, eCJlH KO.'Ieco ,!I.eJlaeT n =-
= 100 06/MHH?
3.49. Kor.n.a KOJleCO KaTHTCH, TO BepXHHe CnHlI.hI qaCTO C.11I-
BaiOTCH, a HH}!{HHe BH.D.HbI OTqeTJlHBO. 06"bHCHHTb 3TO SIBJleIlHe.
3.50. KOJIeco pa.ll.Hyca R = 0,50 M KaTHTCH 6e3 CKOJIblKe-
I1HH no ropH30HTa.'IbHOH .n.opore co CKOpOCTbiO v = l,OM/c.On-
pe.n.eJIHTb CKOpOCTb H YCKopeHHe TOlleK JlelKaw.HX Ha KOHu.ax
BepTIfKaJlbHoro H ropH30HTaJlbHoro .n.HaMeTpOB,
PHe. 32
Pac. 33
3.51. TOqKa A, .'IelKaIllaH lIa nepeceqeHlIII pe.'1bCa C BHCllI-
JlJIM o60;J.oM KOJleCa noe3,na, .lI.BHlKeTCH B .n.aHHblH MOMeHT Bpe-
MeHlf co CKOpOCTbiO U = 5,0 M/C (pIlC. 32). Onpe.n.e.'1HTb, C Ka-
KOH CKOpOCTbiO H B KaKOM HanpaBJlellHH .lI.BH}!{eTCH noe3.l1.. eC.111f
, = 50 CM. R = 56 CM.
3,52. MaJlbllHK Bpaw.aeT KaMeHb, npllBH3aHlIblii K BepeBKe
JI,J1I1HOH 1 =0,50 M, B BepTIIK3J1bHOH nJlOCKOCTH C qaCTOTOH: n =
= 3,0 c- I . Ha KaKYiO BbICOTY B3J1eTeJI KaMeHb, eCJIH BepeBKa
OOOpBaJlaCb B TOT MOMeHT, Kor.n.a CKOpOCTb 6b1J1a HanpaBJICHa
BepTHKaJlbHO BBepx?
3,53. KpHBolliltn OA, Bpaw.aSIcb C yr.'IOBOH CKOpOCTbiO CI) =
= 2.5 pa.n/c, npHBO.ll.HT B .l!.BH}!{eHHe KOJIeCO paAHyca , = 5,0 CM,
KaTSIw.eecSI no HenoJJ.BH)f{HOMY KOllecy pa.n.lfyca R = 15 CM.
HaHTIf CKOpOCTb TOqKH B (pHC. 33),
3.54. ll.HJIHH.D.PHqecKHH KaTOK pa.ll.Hyca R = 10 CM nOMe-
w.eH Me}!{)J.Y .l!.B}'MH napaJlJleJIbHbIMII peHKaMH. PeHKH .l!.BIIIKYT-
CH B o.n.HY CTOPOHY co CKOpOCTHMH VI = 6,0 wc H v 2 =4,0 M/C.
KaKoBa CKOpOCTb ero u.eHTpa, ecJIH npocKa.'Ib3bIBaHHe OTCYT-
cTByeT? KaKoBa yrJloBaH CKOpOCTb Bpaw.eHHH KaTKa? PellIHTb
3a.u.aqy J1.IIH CJlyqaH, Kor,na CKOpOCTH peK HanpaBJleHbl B pa3-
Hhle CTOpOHhI.
3.55. KpyrJIaH ropH30HTaJibnaH n.'IaT<t>oPMa Bpaw.aeTCH
BOKpyr CBoeH OCH C qaCTOTOH n = 30 !>fHn- I .11Iap KaTHTCH B Ha-
npaB'1eHHH AO co CKOpOCTbiO V = 7,0 Mfc (pIlC. 34). HaHTH
23
.

CkOUOCTb mapa OTHOCJlTeJILIIO nJIaT<t>oPMbl B MOMeHT, Kor.na
1.401 = 8,0 M.
3.:'i6. ABTOM06HJIb A ltBInheTCH no 3aKpyr.'ICHHIO pa.nuycoM
0.,1 = 0,5 KM, a aBTOM06UJIb B - npS!lo.:I11l1erfHO (pilC. 35).
PaCCTOHl1ne AB = 200 M, CKOpOCTb KalK,:J;oro aBTOM06HJISI'
v = 60 KM/IJ. HaiiTJI CKODOCTb aBTO:\106nJISI B OTHOClfTeJIbHO aB-
TOM0611JIH A. -
GJ- -----B
Pile 31
o--t--$-f
/ I
Pile. 35
3.57. npOnCJIJIep CaMOJIeTa pa.nHYCOM R = 1,5 M Bpa-
IllaeTCS! C lIaCTOTOii n=2,O, 10 3 MUll-I, npH'lC\1 noca.nOlJllaSl CKO-
pOCTb CatO.1eTa OTHOCHTeJIbllO 3e!\f.'lH paBlia V = 161 KM/'l,
KaKoBa CKOpOCTb T01JKJI 113 KOHlle npone.1JIepa? KaKOBa Tpa-
CKTOpUSI .nBIDKeIlHH 3TOii TOIJKU?
3a.ll.a'l" K"r.'JaBe 1
I. 1. PaCCTOSIHJle s = 360 K:\1 lelK.ny nYIIKTaMU A H B ca-
MO.'ICT npo.leTeJI 3a /1 = 30 MIIII. Bo BpeMH nOJIeTa .nYJI BeTep
no.1 Yf1O:\I ex = 30" K JIHHIIH AB co CKOpOCTblO U = to M/c.
OnpC;I.c.ll1Tb KYpC l CatOJIeTa npn nOJIeTe OT A K B, BpCMSI /2
nO.1CTa Ca:\10,leTa !.I hYpC 2 np" nO.'JeTe OT B K A npll TOM lKe
BCTpe?
1.2. KaTep, .nBHraSiCb OTIIOCIITeJIbHO peKU co CKOpOCTblO
V = 9,0 KftI'l, .nepIKUT KYpC nepneH.!].III<YJIHpIlO 6epery. no.!]. yr-
1ml ex = 45° K 6epery ,lI.YeT BeTep co CKOpOCTblO UI = 3,5 "tlc.
CKOpOCTb TelleHHH peKII U 2 = 2,5 M/c. O!1pe.n.eJIHTb, no.n KaKHM
yr.'JoM K 6epery HanpaBJIeH clJJIlOrep, YCTaHOBJIeHHbIil lIa KaTe-
pe.
1.3. no ;I.B}M nepeceKalOIllu:'lcSI no.!]. yr.'JoM ex = 30° ,lI.OpO-
ra1 ,lI.mllKYTcH ,lI.Ba aBTOM06IlJIH: O,ll.IIH - co CKOpOCTblO VI =
= 54 KM,'lI, BTOpOli - co CKOpOCTblO v z . 26 WC. lIepe3 Dpe-
!\fSl t . 1,0 MHH nOCJIe nepeCelJeHlfSl nepBblM aBTOM06HJIeM nepe-
KpccTKa no ,lI.pyroll .nopore ero ncpcccK BTOpOH aBTOM06HJIb.
Onpc;J.CJIHTb MUHlI:\JaJIbHOe paccToflHHe SII!n MCIK,lI.y 8BTOM06H-
.1H!>fIf nOCJIe ncpeKpccTKa.
1.4. .lI.Ba TCJIa HaXO,ll.IIJ1HCb Ha oJJ:HHaKoBoH Bblcore H8 pac.
CTOS/HlIII S = 20 "I ,lI.pyr OT ,lI.pyra. B HCKOTOpblH MO\feHT Bpe-
24

MCHH O.'l.HO TeJIO OTnYCTH.lIJl, a BTOpC'e 6pOCII.lIJi noJl. yr.10\! a.=
= 30° K ropIl30HTY. Onpe.Zl.eJIlITb. 113 Kahoe MHHHM::JJIbHoe
paCCTOSlHlie C6JIII3J1JIHCb TeJIa.
1.5. C KaKOH: BbiCOTbl HaltO 6pOCHTb Te"10 B ropll30HTaJIb-
HO"I Hanp2B.1eHIIH. IIT06b1 ono CTO.1JKHYJIOCb B B03,'lyxe C .il.Py-
fll:\1 TeJIO:\l, 6porncHHbIM noJl. yr.10M a. = 60° K ropH30HTY C TOU
>Ke nallaJIbHOil CKOpOCTblO H3 TOIIKH, OTCTOHl.l.1.eH Ha paccToH-
HHIi 5 = I,D M no ropli30HTaJIII OT Me-
CTa 6pocamm nepBoro Te"1a?
1.6. Ha H3KJIOHIIYlO !':..iOCi\OCTL,
;r.B11 n<YI.l.1.YlOC5! co CKOpOCTblO VI =
- = 1,0 M/c. na.1aeT C HCKOTOpoil BbiCOTbi
6e3 HallaJIbHOH CKOpOCTII IIJapuK. npo
.1eTeB paccToSlHlle h = 5.0 nl, IIJapllK
KOCHYJICH nJIOCKOCTH,OTCKOIIll.1 H BHOBb
: na:J Ha Hee. HaiiTH paCCTOHUJle Men<Jl.Y
TOIIKaMII nepBoro II BToporo y.n.apOB Ha nJlocKOCTH. Y;J.ap
a6COJ1IOTUO ynpyrv.iL HaKJIOH n.'10CKOCTII a. = 45°.
1.7. nOCTpOIlTb rpa<l>HK 3aBJICIIMOCTII CKOpOCTli TC.lJa OT Bpe-
HeHII no rpa<l>uhY YC'Kopemm (pIlC. 36). HallaJIbHaH CKOpOCTb
e'Ia V o = O.
1.8. oac KeTUo.'I I:CT, UaXO..1.HCb Ha paCCTOSIJIIUI 51 = 10 M
OT I.l.1.IITa, 6pocaeT MRII noJl. )'fIJOM a. = 45" K ropIl30H-
TY co CKOpOCTblO V o = 11 M/c. .MHII Y.'1apSieTCR 0 I.l.1.IIT II ynpy-
ro OTCKaKIJBaer, Ha KaKoM paccToSlHl1II OT I.l.1.lIra 6aCKeT60JIIICT
ncpe>"BaTIIT MHII? COnpOTIJB.1eHlleM B03J1.yxa npeHe6pellb.
1.9. C KOJIeCa aBTmr061!.IJSI, Jl.BII>KYl.l.1.erocSi co CKOpOCTblO
t'c, C'IeTaeT' KOM rpSl311. Pa.n.nyc KOJIeCa R. Ha KaK)1O BbiCOTY H
P1.'1. ,noporOli 6YJl.eT oT6pacbIB3TbCH rpSl3b? J.h:\leHllTcSI JIll BbI-
Cf)Ta H, eC.1J1 KOJIeCO 6y,neT F:aTJlTbCH C npo6YKcoBImH?
r.IJABA 1I.1-lHHAMltKA
dl .
VI
t,
t z
t
Pile. 36
 4. JI.HHaMHKa npHMOJIHHeUHOro .ll.BH>KeHHH
4.1. nOlleMY rpY3, C6pOIIJeHHbJii C rOpJl30lITaJIbHO JIeTHl.l.1.ero
ca:\IO,'IeTa, He na.n.ae-r BepTHKaJIbHO Blllf3?
4.2: nOqe"IY paCmaTaBIIJHHCSI MOJIOTOK H.rm Tonop nJIOTJIee
HaCa>KJlBaeTCSI Ha PYKOSITKY, eCJIJI cBo60,nHbIM KOHlI.ml 3TO"
:'1KOSlTKII CTYKllyrb 0 KaKoH-HlI6y,nb TBep,nblil npe.u..'Ier?
4.3. KaKHM cnoco60"f MO>KHO onpe,neJIliTb. HaXOJl.llTCH ;I.aH-
Hoe TC'IO B JIHCPlI.llaJlf,HOji V.,IIll HeIIHCplI.na.'1bHQH CHCTeMe OTC-
qeTa? .
25

. 4.4. K TeJIY npllJIOlKeHl.l .nBe CHJIhl (pIfC. 37): FI = 15 H 11
F 2 = 10 H. Onpe.rr.eJIHTb CYMMY CHJI, .neHCTBYIOIllHX B.nOJIb
OCH x If B.nOJIb OCH y.
, 4.5. CHJIa F 3 = 10 H COCTaB.'ISleT C OCblO X yrOJI ex = 30 0 ,
CHJIbI FI 11 F'I. nepneH.nHKYJISlpHbI OCH X (pIfC. 38). Onpe.neJIlfn-
CHJIY F 2, eC.'lH 113BeCTHO, liTO CHJIa F I = 5,0 H, a cYMMa CIi.'l
B.!10.'lb OCH Y paBHa O. lJeMY paBHa CH_'la, .neHCTBYIOIllaSl B.nOJIlt
OCIi x?
. 4,6. no ropl130HTaJIbUOH nJIOCKOCTIl .nBHlKeTCSI rpY3 Mac-
COH nz = lU Kr no.n .neHCTBHeM CHJI F =50 H. nanpaBJIeH-
y --
U ct; ¥'
;, -
Fz
x
X
PIIC. 37 Pile. 38
HO" no.n yrJIOM ex = 60° K ropIi30HT}'. Onpep.eJIHTb, C KaKH\f
YCKopeHHeM .!1.BHlKeTCSI rpY3. C KaKOH CHJIOH OH .naBHT Ha nJIOC-
KOCTb? TpeHlleM Me>KJ1.Y rpY30M H nJIOCKOCTblO npcHe6pellb.
. 4.7. C KaKOM CHJIOH .naBHT 'ieJIOBeK MaCCOM 70 Kr Ha no.'1
JIllqrra, .nBHIKYIllerocSi C YCKopeHHeM 0,8 M/C 2 : 1) BBepx; 2) BHH3.?
C KaKHM YCKopeHHeM .nOJIlKeH JlBHraTbCSI JIHqrr. llro6bl lIe.'IOBel\
He JlaBHJI Ha nOJl?
4.8. .lI.JISI 3a.nallH 4.7 BhlllHCJIHTb CHJIY HaTSIlKeHHSI KaHaTa,
y.nep)f{HBaIOIllero JIHqrr npH no.n1>CMe: 1) YCKopeHHoM; 2) paBHo-
MepHOM; 3) 3aMe.nJIeHHOM. .Macca JIHqrra 300 Kr.
- 4.9. Ha rJIa.ll.KYIO HaKJIOHHYIO nJIOCKOCTb C yrJIOM ex = 30°
npn OCHOBaHHH nOCTaBHJIH TeJIeIKKY. Onpe.neJIIfTb CKOpOCTb Te.
Jlen<KH nOCJIe Toro. KaK OHa onYCTHJIaCb Ha BblCOTY h = 245 CM.
4.10. Onpe.ll.eJIHTb. KaKoH yrOJI C BepTHKaJIblO COCTaBJISIeT
HHTb C rpY30:.f, no.nBerneHHaSl Ha TeJIelKKe, JlBlflKYIlleHCSI C yc-
KopeHileM a.
r 4.11. l1Ba rpY3a MaccaMH m l = 200 r H m 2 = 300 r CBH-
3aHhl HHTblO H JleIKaT Ha rJIa.D.KoH ropH30HTaJIbHOH nOBepxHo-
CTH CTOJIa (plfC. 39). C KaKHM YCKopeHHeM 6YD.YT .lI.BHraTbCSI rpy-
3b1, eCJIH K rpY3Y m l npHJIOIKHTb CHJIY F = 1,5 H, HanpaBJIeH-
HYIO napaJIJIeJIbHO nJIOCKOCTH CTOJIa? KaKYIO CHJIY HaTHlKeHHH
6YJleT HcnhlThlBaTb nplf 3TOM HHTh. CBSl3hlBalOIll8H Te.'l8?
26

4.12. 1I.Ba rpY3a MaccaMII m! = 1,0 Kr H m 2 = 2,0 Kr
nO.!I.BellIeHbl Ha HHTH, BTOpoii rpys TSlHYT C CHJIOH F = 3,0 H
(pHC. 40). B HeKoTopblH MOMeHT BepXH1OiO HHTb nepe>KHraJOT.
Onpe.n.eJIHTb, C KaKlfM YCKopeuHeM HaqHyr .n.BHraTbCSI rpY3bl.
4eMY paBHa CHna HaTSI>KeUHSI HHTH, CBSl3b1BaJOllI.eH rpY3b1J H 2?
4,13. TeJlo MaccoH M = 2,0 Kr JleJKHT Ha rna.nKOM roPH-
30HTaJibUOM CTOJle (pHC. 41). C KaKHM YCKopeHlleM HaqUeT .nBH-
raTbCSI TeJIO, eCJIH: I) HHTb nOTSI- ,
Hyrb C CHJIOH F =- 9,8 H; 2) no.n-
BeCHTb K HIfTH rpY3 Maccoii m =
1,0 Kr .
Pile. 39
-


4,14. K KOHl.laM llIHypa, nepeKHHy enO >K-
Hbl" 6J10K, no.nBellIeHbI rpY3b1 l = 0,10 Kr H m 2 -
= 0,15 Kr. npeHe6peraSl TpeHHeM H CIJHTaSl llIHYP H 6J10K He-
BeCOMbI'dH H llIHYP HepaCTSI>KHMblM, onpe.n.eJIHTb YCKopelllle, C
KaKHM 6y.nyr .lI.BHraTbCSI rpY3b1, CHJlY HaTSI>KeHHSI wHypa H
nOKa3aHHSI JllmaMOfeTpa, Ha KOTOpOM BHCHT 6J10K.
4,15. lI.Ba o.n.HHaKOBbIX rpY3a MaccaMH M CBSl3aHbi Me>K.n.y
co60H HlfTbID, nepeKHHYToii tIepe3 MOK C HenO)l.BIf>KHOH: OCbID.
Ha O.n.HH H3 rpY30B KJIaJlYT neperpY30K MaCCOH m. Onpe.n.eJIHTb,
C KaKOH CHJlC)ii 6y.n.eT .n.aBIITb neperpY30K Ha rpY3.
--.--CJ
 / //
/1

Q
Pile. 41
PHe. 42
4,16. fpY3 Maccoii In l = 3,0 Kr Haxo.n.IfTCH Ha HaKJIOHHOii
nJIOCKOCTH C yrJIOM HaKJIOHa ex = 30° H CBSl3aH C rpY30M m 2 =
--= 2,0 Kr HepaCTSI>KHMOH nerKoii HHTbID, nepe6pollIeHHoii lJepe3
HeBeCOMblii H Heno.n.BH>KHblii 6noK (pHC. 42). Onpe.neJIlITb YC-
KopeHHe rpY30B, cHny HaTSlmeHHSI HHTH, cHny .n.aBneHHH Ha
OCb 6J10Ka.
· 4.17. HaiiTH CHJlY HaTSI>KeIlHH HHTeii H YCKopeHHe rpY30B
B CHCTeMe, nOKa3aHHoii Jla pliC. 43. TpeHHeM npeHe6peqb.
27

4.18. HaiiTH YCKopeHHSI a l H a 2 Te.'I Macca.UI m l H m 2 H
CMY HaTSDKeHHSI HHTe B CHCTeMe, nOKa3aHHoii H8 pHC, 44.
Macco 6JIOKOB H HHTe H TpeHHeM npeHe6pe'ib.
4.19. HaTH YCKopeHHe rpY3a MaccoH m H cH;ny HaTSUKe-
HHH HHTeH B CHCTeMe, nOK83aHHoii H8 pHC. 45. Macco 6noKoB
H HHTe H TpeHHeM npeHe6pe'ib.
,
PHC. 43
PHC. 44
Pile. 45
4.20. Onpe.n.enHTb YCKopeHHe rpY30B, nOK838HHbiX na
pHC, 46. M8CCbl rpY30B M = 5,0 Kr, m = 1,0 Kr. TpeuHeM,
MaccaMH 6JIoKOB H HIlTe npeHe6peQb.
4.21. KaK}TJO nocToSlHHYIO ropH30HTanbHYlO cHny (out. 4. J
HY>KHO npHnO>KHTb K Te.ne>KKe Macco M = 1,0 Kr, QT\J6bl rpy-
3bI MaccaMH m 1 = 0,40 Kr H m z = 0,20 Kr OTHOCIlTe.lIbHO Bee
He )1BllranHCb?
..  '
M rn z
-
 .
,
Pile. 46
PHe. 47
4.22. JIollIa;I.b paBHOMepHO TSlHeT caHH. PaCCMCTpeTb B3aJ(-
Mo.n.eiicTBHe Tpex Te.n: JIow.a.n.H, CaHe" H nOBepXHOCTH 3eMnu.
Ha'iepTHTb CHJIbl, .n.eCTBYIOw.He Ha Ka>K.!l,oe H3 3TIIX Te.n B CT-
.n.e.nb, HOCTH H YCTaHOBJlTb COOTHOllIeHlIe Mejf{l{Y HHMH.
4.23. Ha KnHH, KOTOpblH MO>KeT .ZI.BHraTbCSI no ropH30H-
TanbHoH nOBepxHocTH, nOJIO>KHJIH He60nbllIoe TeJIO. BCH CHC-
TeMa OK83anaCb B paBHoBecHH. Ha'iepTHTb CHJIbl, .neiiCTBYIO- .
lIJ,He Ha Te.lIO, K.rmH H ropH30HTanbHYIO nOBepxHocTb, II YCTa-
HOBHTb COOTHOllIeHHH r.te>K.ZJ.Y HHMH.
28

4,24. TIoJl. Jl.eHcTBHeM KaKoH BHel1IHeii CHJILI Jl.DH>ke'1'C ao-
'I'o!of06liJIb?
4.25. Teno Macco m = 1,0 Kr JIeJi<lIT Ha rop1l30HTa.r.bHO
nJIOCKOCTH. K03<lxl)lfD.HeHT TpeHHH .... = 0,10. Ha Te.'IO Jl.ecTBY-
eT ropH30HTa.'IbHaH CHJIa F. OnpeJl.enHTb CHJIY TpeHHH JI..TIH Jl.BYX
CJlYllaeB: I) F = 0,50 H; 2) F = 2,0 H. M306pa3HTb rpa<lJH'lec-
KH, KaK MeHHeTCH CHJIa TpeHHH npH H3:\feHeHHH CUJIbI F.
4.26. BpYCOK Macco m = 2,0 Kr HaXOJl.HTCSI Ha ropH30H-
..,.aJIbHO nOBepxHoCTH. K03<M>HD.lleHT TpeHHSI .... = 0,20. TIOCT-
pOHTb rpal}>HK 3aBHCHMOCTH YCKopeHHH 6pycKa OT BHel1IHe
ropH30HTaJIbHO CH F.
4.27. Ha TeJIO Macco m = 0,50 Kr Jl.ecTByeT ropH30H-
TaJIbHaH CHJIa f = 0,20 H, B npOTlIBOnOJlO}KHOM HanpaBJIe-
HHH Jl.eHCTByer CUJIa F, K03<M>HD.HeHT TpeHHH Me1KJI.Y Te.'IOM H
rop1I30HTaJIbHO nJIOCKOCTblO .... = 0,10. l'b06pa3l1Tb rpal}>Hllec-
KH 3aBHCHMOCTb CHJlbI TpeHHH OT CHJIbI F.
4.28. EpYCOK HaXOJl.HTCH Ha nJIOCKOCTH, yroJI HaK.'IOHa KO-
TOpOH Mo:mer MeHSlTbCSI OT 0 Jl.0 90". TIOCTpOHTb rpa<lJHK 3aBH-
CIIMOCTII CIIJIbi TpeHuH 6pycKa 0 nJIOCKOCTb OT yrJIa HaK.'IOHa
nJlOCKOCTII K ropH30HTY. K03<M>HD.HeHT TpeHHH paBeH ..... KaK
C nOMOIIJ.blO TaKo nJIOCKOCTH onpeJl.eJHITb K031}><lmD.HeHTbI Tpe-
HIiSl MeJKJl.Y n.'IOCKOCTblO H pa3JIHIIHm TeJIal\lH?
4.29. Teno MaccoH m, HaX0Jl.SlIIJ.eeCH Ha ropH30llTaJlbHo
n:IOCKOCTH, THHYT C cunoH F < mg, Km<M>HD.HeHT TpeHIlSI Me}K-
Jl.Y TeJIOM II nJIOCKOCTblO ..... TIOCTpOHTb rpa<}JHK 3aBHCHMOCTil
CH.'IbI TpeHHH OT yrJIa ex MeJi<Jl.Y CHJIO F H BepTHKaJIblO.
4.30. Ha TeJIO Macco m = 1,0 Kr, HaXOJl.H1.1.1.eeCH Ha ropu-
30HTaJIbHOH nJIOCKOCTif, .IleCTByer rCpU30HTaJIbHaH CHJIa F=
= 3,0 H. C KaKoH MUIIUMaJIbHOH ropH30HTaJIbHOM CHnon F MnB
Ha.IlO nO.IleHCTBOBaTb B nepneHJl.HKYJIHpHOM HanpaBJIeHHH, 'lTO-
6b1 TeJIO HallaJIO CKOollb3HTb? Ko3C}xPHD.neHT TpeHHSI TeJIa 0 nJIOc.
KOCTb .... = 0,50.
4.31. EpYCOK Maccoif m = 0,50 Kr JIe}KIIT Ha mepoxoBa-
Toif nOBepxHOCTIf (PHC. 4i HaKJIOHeHIIOii K ropH30llTY nor'(
}r.'IO'f ex = 30°. C KaKoif MHHHMaJIbllOif
ropH30HTaJIbJloif CHJIOH F, napaJI.'IeJIb-
HO pe6py.AB lI.ByrpaHHoro yrJIa, CJle-
.Ilyer nOTHHYTb- 3a HliTh, npu-
BH3aHHYIO K 6pYCKY, 1ff06b1 Ha'laJIOCb
ero CKOJIb}KeHHe? Ko*l>HD.HeHT TpeHHH
6pYCKa 0 nOBepXHOCTb .... = 0,70.
4.32. ECJIH KOJIeCO KaTHYTb ropH-
30HTa.'IhHO BJl.OJlh HaK'IOHHOH nJlOCKOCTIf,
0110 6YJl.er .IlBHraTbCH no npSlMoii, eCJlH
j'
arP
'" 8
Pile. 48
29

e l'OJIKIIYTb rOpH30H'raJIbHO ,nOCJ<y, TO OHa 6y,ne:r CKaTbIBaTb-
CSI BHlI3, 06'bSlCHHTb 3TH SlBJIeHHSI.
4.33. .MarHHT l.IaCCOH m = 50 I' npHJIHn K )KeJIe3HOH BepTH-
KaJIbHOH CTeHKe. 1l.TlSI paBHoMepHoro CKOJIlUKeHHSI MarHHTa
BHH3 npHKJIa.ll.bIBaiOT cnJIY f = 2,0 H. KaKYiO CHJIY Ha.ll.O npH-
JIO)KIfTb, 'lT06bl MarHHT Ha'laJI CKOJIb3HTb BBepx?
4.34. EpYCOK MaccoH m = 3,0 Kr C nOMolllbiO npY)KHJlbI
TSlHYT paBHoMepHo no .lI.OCKe, pacno.'Ion<eHHoH ropH30JlTaJIbHo.
-
F
m z

Pile. 49
Pile. 50
KaKOBa )KeCTKOCTb npY)KHllbl. eCJlH olla Y.lI.JIHJlHJI3Cb npH 3TOM
H3 l = 5,0 CM? KO$lJHlI.HeIlT TpellHSI 6PYCI;:3 0 nJIOCKOCTb Jl =
= 0,25.
4.35. KaKoBa Ha'laJIbHaSi CKOpOCTb rnaii6bl, n}lllellHOH no
nOBepxHocTH JIb.ll.a, eCJlH OHa OCTallOBHJI3Cb 'lepe3 40 c? Ko3<lJ-
$1flI.UeHT TpeHHSI rn3ii6bl 0 JIf.lI. J.1 = 0.05.
4.36. Onpf.ll.eJIHTb YCKopellHe TeJI3, COCK3.'Ib3blDaiOlllero
C H3KJIOHHOH nJIOCKOCTH, eCJIH ee yroJI H3KJIOHa ex = 30", a
K03<M>HlI.HeHT TpeHHH Me>K.!\Y TeJIOM H HaKJIOHHOH nJIOCKOCTbiO
J.1 = 0,30.
4.37. lIeJIOBeK nOTSIHY.'l caHKH MaccoH m = 8 Kr C CHJIOH
F = 100 H 3a BepeBKY no.ll. yrJIOM ex = 30" K ropH30HTY. Ko-
$lJHlI.UeHT TpeHHH caHOK 0 cller J.1 = 0,10. Onpe.ll.eJIIITb YCKO-
peHHe, C KOTOpblM Ha'lHYT .lI.BHraTbCSI callKH.
4.38. 3a KaKoe BpeMH TeJIO MaccoH m COCKOJIb3HeT C Ha-
KJIOHHOH n.'IOCKOCTH BblCOTOH h, H3K.110HeHHOH no.ll. yrJIOM ex K
ropH301lTY, eCJlH no HaKJIOlIlIOH nJIOCKOCTH C yrJIOM HaKJIOHa f\
OHO .lI.BH)Ke:rCSI paBHoMepHo?
4,39. Onpe.ll.eJIHTb YCKopCHHe TeJI B cnCTeMe, nOKa3allllOH
Ha pHC. 49. KO$lJHlI.HeHT 'tpeHHH MeJK.llY TeJIOM m 1 H nJIOCKOC-
TbiO J.1 = 0,10. TpeHHeM B 6JIoKe, MaccaMH 6JIOKa H HnTH npe-
He6pe'lb. Macca m 1 = 1,5 Kr, ms = 0,50 Kr, CHJIa F = 10 H.
YroJI ex Me)K.llY CHJIOH F H ropH30HTOM paBeH 30°.
4.40. no HaKJIOHHOH .llopore C yrJIOM HaKJIOHa ex = 30° K
roplf30HTY (pnc. 50) onYCKaercSi BaroHeTKa MaceOH M = 500 Kr.
30

OnpCJl.eJIHTb CHJIY H3TSDKeHlUi KaHaTa npn TOpMO}f{eHlfH Baro-
ueTKH B KOlllle cnYCKa, CC.'1H ee CKOpOCTb nepe.n TOpMO}f{CHHeM
6blJIa L'O = 2,0 M/c. a BpeMH TOpMO)f{eHHSI t = 5,0 C. K03<}xlJH-
UHeUT TpeHHSI npHHSlTb paBHbIM II = 0,010.
4.41. 4epe3 JIerKHH Bp31lI.alO1lI.HikSi (5ea TpeHHSI MOK nepe-
KHHYT umypoK. Ha OJlHOM KOHl.le U1HypKa npHBSl3aH rpY3 M3C-
coii mI' no JlPyroMY KOHLlY U1HypKa MO)f{eT CKOJIb3HTb KOJIbLlO
MaCCOH m 2 (pHC. 51). C K3KHM YCKopeHHeM .nBH)f{eTCSI KOJIbLlO,
eCJIlf rpY3 MaCCOH m i Heno.nBH)f{eA? 4eMY
paBua CHJIa TpeHHSI KOJIbLla 0 UJUYPOK?
4.42. Ha BepxHeM Kpae HaKJIOHIIOH nJIOC-
KOCTIf YKpenJIeU MOK, 'Iepe3 KOTOpblii nepe-
"HHYTa IIHTb (CM. pHC. 42). K O.nHOMY KOHLlY
IIHTH npHBSl3aH rpY3 MaccoH m i = 2,0 Kf, JIe-
)f{a1lI.Hii Ha HaKJIOHHOH nJIOCKOCTH. Ha .nPY-
roM KOHue IIHTH BHCIIT rpY3 MaCCOH m2 =
= 1,1 Kf. HaKJIOHHaSl nJIOCKOCTb 06pa3YeT C
ropH30HTOM yro.'1 a. = 30°, Ko3<}xPHLlHeHT
TpeHHSI Me}f(llY rpY30M H HaKJIOHHOH nJIOC-
KOCTblO II = 0,10. HaHTH YCKopeHHe, C KOTO-
pbIM .nBH)f{YTCSI rpY3bI, H CHJIY H3TH)f{eHHSI
HIITH.
4.43. J1.ocKa MaCCOH M MO)f{eT .nBllfaTbCSI 6e3 TpemlSl
no HaKJIOHHOH nJIOCKOCTII C yrJIOM a. K fOPH30HTY. B KaKOM Ha-
npaBJIemfH H C KaKIfM YCKopeHHeM .nOJI)f{Ha 6e)f{aTb no .nOCKe
c06aKa MaccoH m, 'IT06b1 .nOCKa He COCKaJIb3b1BaJIa C 113K.'10H-
HOH nJIOCKOcTH?
4.44. 4epe3 HenoJlBlDKUbIH 6JIOK nepeKHHYTa BepeBKa, K
OD.HOMY H3 KOHLlOB KOTOpOH npHBH3aH rpY3 MaccoH m 1 = 60 Kr
Ha .nPyroM KOHLle nOBHCJIa 06e3bHHa MaccoH m, = 65 Kr, KO-
TopaH, BbI6HpaSl BepeBKY, nOJlHHMaeT rpY3, OCTaBaHCb npH 3TO:\1
Ha OD.HOM H TOM }f{e paCCTOSlHHH OT no.'13. 4epe3 CKOJIbKO Bpe-
MeHH rpY3 OY;I.eT nOJlHHT Ha BbICOTY h = 12 M? .MaccaMH BepeB-
KII H MOKa npeHeOpe'lb.
4.45. nO'IeMY CKOpOCTb aBTOMOOHJISI npH ..I.BH)f{eHIIII no ro-
pH30HT3JIbHOMY nYTII lie B03paCTaeT 6ecKOHe'lHO, XOTSI CIIJIa TH-
rII MOTopa .neHcTByeT nocTOSlHHO?
4.46. ABTOM06HJIb Ha'laJI .nBHraTbCSI C }CKOpeHHeM a1 =
2,0 M/c 2 . npll CKOpOCTH v = 70 KM/q YCKopeHHe CTaJIO pan-
IIbIM a 2 = 1,0 wc'. Onpe.neJIHTb, C KaKOH YCTaHoBHBUJeHcSI CKO-
pOCTblO 6y.neT .nBHraTbCSI 3BTOM06HJIb, eCJIH CHJI3 TSirH MOTOpa
OCTaeTCSI nocTOHHHoit, a CH,,1a conpOTHBJJeHJiSI nponopLlIIOHaJIb-
Ha CKOpOCTII. .
PHe. 51
31

 5, ,D.HJfaMHKa KpHBOJllfHeHHOro JJ.BI1}!eHIUI
5.1. rJlaJI.KIIH ropH30HTaJlbHblH ,nIlCK paBHoMepHo BparnaeT-
CSI BOKpyr eepTHKaJlbHOH OCH. Ha nOBepXHOCTH ,nIlCKa Haxo-
,nSlTCSI rpY3bl 1 H 2, y,nep)f<IlBaelbIe ,nBYMSI HHTSlMH (pIlC. 52).
Macca rpY3a 1 e ,nBa pa3a MeHbwe MaCChi rppa 2, a paccToSI-
HHe OT OCH eparneHHSI B ,nBa pa3a OoJlbWe, lleM y rpY3a 2. a-
.  KaSi H3 HIITeH HCnbITbIBaer OOJlbllJYIO
 CIIJlY HaTSI)f{eHIISI II eo CKOJlbKO pa3?
. 5.2. rJlaJ1.KIIH ropH30llTaJlbHbIii lI.IICK
2, BpalllaeTCSI BOKpyr BepTHKaJlbHOii OCII C
llaCTOTOH If = 480 MIIH- 1 . Ha nOBI!O-
CTH .nHcKa Jle)f{IIT llJap Maccoii m <=
= 0,10 Kr, npllKpenJleHHhlH K lI.eHTpy
,nllcKa npY)f{HIIOH, )f{eCTKOCTb KOTO-
 pOH <'(paBHa k = 1500 HIM. KaKYIO MII-
HY vYll.er IIMeTb npY)f{IIHa npH epallle-
Pile. 52 III1H ,nIlCKa, eCJIH ee .nJlIIHa B HeJ1.e<Pop-
MHpoBaHHoM COCTOSlHHII 10 = 20 CM?
5.3. rOpIl30HTaJlbHO pacno.'10)f{eH-
L  LJa HbIH ,nHCK epalllaeTCH eOKpyr BepTII-
 KaJlbHOH OCH C llaCTOTOH n = 30 r.mH- l .
HaHOoJlbllJee pacCToSllllle OT OCII epaw.e-
HUH. Ha KOropOM y,nep>KIIBaeTCSI Te.'10 Ha
Pile. 53 ,nIlCKe, 1 = 20 CM. 4eMY paBeH K03<l>-
<}JlIlI.lleHT TpellllSI TeJIa 0 .nIlCK?
 5.4. Ha HaKJIOHHOH nJlOCKOCTII, COCT3BJIHIOllleH yro.rI a. C ro-
pIl30HTOM. JI(-')f{HT MOHeTa. Eii COOOllllI.'1H CKOpOCTb V napaJl-
JIeJIbHO OCHonaHHlO HaKJlOHHOH nJlOCKOCTII (pIlC. 53). Onpe,nc-
JIIITb KPllBH3HY TpaeKTOpllH. no KOTOpOH J!.BII>KeTCH MOHeTa,
B H31laJIbHblH MOMeHT BpeMeHIl.
5.5. lllap MaccoH m nOJ1.BellJeH Ha HHTH MUHOH I. Ha
pliC. 54. a. 6 nOKa3aHbI .lI.Be pa3JIHIlHblX J1.BH)KCHHSI llJapa no
OKPY>KHOCTII: a) B ropIl30HTa.'IbHOH nJlOCKOCTH (panHoMephoe
epallleHHe); 6) s eeprllKa.'IbHoH nJIOCKOCTII (J.!ep3BHOMepHoc
epallleIlHe). lI.JISI K:.!toro nOJIO)f{eHIIH llJapa HaHTH CIIJIY HaTH-
}f(eHIIH HUTH. MOll.YJIb U J:anpaBJleHHe YCKopeHIlSi mapa. JIII-
HeiiHytO H yr.oBYIO CKOpOCTH llJapa.
1/ 5.6. Ha pllC. 54, a 11300pa)f{eH TaK Ha3blBaet.IbIii KOHltlleC-
KUH MaSlTHHK. COCTOSIiH 113 llJapm<a, npllKpenJIeHHoro K HHTIt
H omiCblBalOlllero OKPY)KHCCTb B ropH30HTabHOH nJIOChOCTII.
MaCC3-11JapIlKa m = 100 r. ,nnHH3 :mTH 1 = 40 CM, yrOJI OTK.'IO-
HeHUSI OT l3epTHK3'111 a. ::;;:: 60°. HaHTH yr.'1oBylO CKOpOCTb illa-
pltKa Ii CI_f.'IY HaTSl>KeHlfSi IIHTU,
32

5.7. MaTeM3TnqeCKnii MaHTHHK JlMeeT !\faccy m H ,n.'1HHY 1.
B MOMenT, KOrJ1.a OH 06pa3YeT yro.1 a c nepTHKaJIblO, ero CKO-
pOCTb paBHa v. KaKoBa B 3TOT MOMeHT CHna HaTIDKeHlU1 HHTH?
J" 5,8. rpp, nOJ1.BCWeHHbIH Ha HHTH .D/IHH(lH 1 = 98 CM, paB-
HOl\lepHO BpaI.l.l.aerCSI no OKPY}KHOCTH B ropH30HTaJIbllOH n.rIOC-
KOCTH. HaHTH neplio,n BpaI.l.l.eHIfSi rpY3a, eCJIH npn ero BP3I.l.l.e-
HHII HHTb OTK.'IOHeHa OT BepTllKaJIU lIa yroJI a= 60 0 ?
5.9. Ha HIITH ,nJIHIIOH 1,0 M nO;J.BcwellO TeJIO MaccoH 100 r
KaK OTIIOCSITCSI YCKopeHHH, C KOTOpbll\fH 6Y.AeT BpaI.l.l.aTbCH Te-
il 5/ m
. 

10: i1 W]
- I
'_J__
PHC. 54 PIIC. 55
.'10, B c.'1yqaSlx, eCJIH HHTb 06pa3"yeT C BepTHKa.'1blO yrJIbI al =
= 30 0 H a 2 = 60 0 . KaKoBo npH 3TOM OTIIOweHHe JIllHeiiHbIX
CKopocTeH TeJIa? .
tI' 5.10. rOpHJOHT3JIbHbIH BaJI npaI.l.l.ae1CH C yroBoii CKOpO-
CTblO ffi (pHC. 55). lllapHK MaCCOH m npIlKpen.'IeH K BaJIY C no-
MOI.l.l.blO ,nBYX IIIiTeii J1...1HHOii 1. HaihH CliJIY HaTH}KeHUH HIITCH,
npeHe6peraSi CIIJIOH TH}KeCTH wapHha.
5.11. HaihH CHJIY, C KOTOpOH MoroLlUKJIHCT )\facco" m, ,nBII-
>KYI.l.I.Hi'ICSl co CKOpOCTblO v, ,naBHT Ha cepC,!{III1Y MOCTa B CJIyqae:
1) ropH30HTaJIbllOrO rJOCTa; 2) BbInYKJIOrO !\fOCTa pa;J.Hycor.1
R; 3) BorHYToro MOCTa pa,nllycoM R.
5.12. KaK OTHOCSITCH ,npyr K ,npyry CHJIhI, C KOTOpbIMH aB-
TO\10611JIb ,naBHT Ha cepe,nHHY BbmYKJIOrO H BOfHYTOro 1.lOCTon?
PaJ1.HYc Jo..PUBU3HbI MOCTa B o60ux CJIyqaHX paBeH 40 M. CKO-
pacTb J1.BH}KeHIISI aBTOM06HJIH 36 KMI'I.
5.13. no BblnYKJIOMY MQCTY, pa){HYc KpHBII3Hb1 KOTOpOro
R = 90 M, co CKOpOCTblO V = 54 K.Wq ,nBH}KeTCH .aBTOM06HJIb
Maccoii m = 2,0 T. Onpe;J.e.1I1Tb, B KaKoH TO'lKe CHJIa ,naBJIe-
HUSI aBTOt.mOHJIH Ha MOCT paBHa F --= 5,0 KH.
5.14. ABTOI061IJIb ,nBIUKeTCSI no BbmYK.i10MJ MOCTY pa;J.uy-
eO:.1 R = 40 M. KaKoe MaKCHMaJIbHOe ropH30HTaJIbHOe YCKO-
pf"H!Ie '.iO}KeT pa3BlfTb aBToM06H.1b B BbIcmcH TOqKC, ee.IIII CKO-
t: :Tb ero B 3TOH TOqKe v = 50,4 KM!Il, a h034xPIlUlleHT TpeHHH
It JIec 3BTOMOOU.'1H 0 MCCT f.I. = O,60?
2 311K. 18'.;7
33

5.15. CaMOJIeT C peaKTHBHblM J].BHraTeJIeM JIeTHT co n:opo-
CTbJO v = 1440 KMI'1.. OUlTaf/, llTO lle..10BeK MO}KeT nepeHocHTb
nSlTIIKpaTlloe YBeJIHlleHHe Beca, onpeJ].eJIHTb paJ].HYc OKPY>KJlO-
CTIt, no KOTOpOH MO>KeT J].BHraTbCSl CaMOJIeT B BepTHKaJIbllOii
nJIOCKOCTIl.
.. 5.16. noe3J]. J].BH>KeTCSl no 3aKpyrJIeHlU0 paJ].HycoM R'=
= 765 M co CKOpOCTblO V = 72 KM/'1. OnpeJ].eJIHTb, Ha CKOJIbKO
BHeilIHIIH peJIbC J].OJI>KeH 6bITb BblllJe BHYTpeHHero. PaCCTOf/-
Hlte Me}KJ].y peJIbCa!\tH npHHSlTb b = 1,5 M.
5.17. C KaKoH MaKCUMaJIbllOH CKOpOCTblO MO>KeT exaTb no
ropu30HTa.'IbIlOH n.rIOCKOCTH MOTOllHKJIHCT, onHCblBaSl J].yry pa-
;.
I
li
I
,
I
I
I
1«
--- - --
o
Jj
PHe. 56
PHe. 57
J].HYCOM R = 90 M, ecJIH K03(MmllHeHT TpeHHSl pe3HHbI 0 J].OpO-
ry f1 = 0,40. Ha KaKOH yrOJI OT BepTHKaJIH 011 J].OJI}Kell nplt
3TOM OTKJIOHHTbCf/?
\I 5.18. C KaKOH CKOpOCTbJO J].O.'I>KeH J].BHraTbCSl MOTOlllfKJIHCT
no rJIa.!l.KoMY TpeKY C yrJIOM lIaKJIOHa a. = 30° H paJ].HycoM 3a-
KpyrJIeHHSl R = 90 M? C KaKOH MaKCHMaJIbHOH CKOpOCTbJO I\tO-
)l{eT ..'UmraTbCSl MOTOllHK.'IHCT no TpeKY C TeM }Ke yrJIOM JlaKJIOHa
H TeM )l{e paJ].HycoM 3aKpyr.iIeHHSl, eC.1H Ko3<fxtJHllHeuT 7peHHSl
f1 = O,40?
5.19. llIapHK MaccoH 100 r, nO.D.BellJellHbIH Ha JIerKOll liliTH,
06pa3}'1Oll1.ell yroJI a. = 3(f' C BepnlKaJIblO, JIeJKlIT lIa rJIa;:U<011
nOJIyc<t>epe paJ].IIYcor.{ R = 10 CM (pHC. 56), TpeyrOJIbHIIK ABO
npSlMoyro.iIbllbIH. llIapHKY COO6ll1.HJIH CKOpOCTb v = 0,50 M/C
nepneH.!I.HKYJIf/pnO nJIOCKOCTIl llepTC)Ka, H 011 CTaJI CKOJIb311Tb
no nO.'Iyc<t>epe, onHCbIBaSl OKPYLKHOCTb. 4eMY paBlla CIIJIa J].aB-
JIeHUSl rnapHKa na nOJIycll>ePY BO BpeMfl J].BHLKenHSl? npn Ka-
KOM 3l1a'leHlm CKOpOCTH OHa CTaneT paBHOH HYJIIO?
,,5.20. r.'Ia.J,KHH crepLKeHb HalUIonell noJ]. yr.'1o!\f a. = 30° I-.
ropH30HTY (pHC. 57) H MOif<eT Bpall1.aTbCSI BOl.pyr DepTlfKaJIbHOH
OCH, npOXO;I.Slll1.eH '1epe3 HH}KHHH KOHell CrepLKI!f/ O. Ha CTCp-
}KeHb Ha:z.eTa 6yclfHKa, KOTOpaf/ ynHpaeTcSl B Orpaml'lUTe.'1b
Ha pacCTvHllllu l = 6,0 C\1 OT TO'lKH 0 C Kal-.OH yr.1oBoH Cf"o-
34

pOCTblO H8)J.O BpaU{aTb CTep>KeHl>, qTOUbl 6YClfIIKa CJleTe.'1a C He-
ro?
5.21. Ha KpalO HaKJIOHHOH nJIOCKOCTII C yrJIOM HaKJIOHa a
JIe>KIIT TeJIO. fIJIOCKOCTb paBHoMepHo BpaIllaeTCSI BOKpyr nep-
TIIKaJIbHOH OCH C yrJIOBOH CKOpOCTblO ro. PaccTOSlHlfe OT TeJIa
JJ.O OCII npaU{eHHSI nJIOCKOCTII paBHo R. HaHTH HaHMellbwIIH KO-
3<JxI>1I1I.lleHT TpeHHSI fl, npii Y.OTOpOM TeJIO y)J.epLKIITcSI Ha BpaU{a-
lOU{eikH HaKJIOHHOH nJIOCKOCTII.
 6. 3aKoH BceMupHoro TJlrOTeHIIR
6.1. IlBe TOllellHble MaCCbl m l = tOO r II m 2 = 500 Kr na-
XO)J.flTCSI Ha paccTOSlHIIH r = 20 M JJ.pyr OT JJ.pyra. OnpeJJ.eJIlITb
cHny B3aHMo)J.eHCTBHSI y HIIMII.
6.2. OnpeJJ.eJIIITb CHJIbl, C KOTOpblMII )J.eHCTBYfOT JJ.pyr Ha
JJ.pyra BCJIe,!l;CTBlle TSirOTeHHSI ,ABa conpHKacalOU{lIxcH CBHHlI.O-
BblX wapa JJ.llaMeTpoM D = 1,0 M KIDKJJ.bIH.
6.3. nOIleM}' TeJIB, HaXO)J.H1lI.HeCH B KOMHare, HecMOTpH Ha
IIX B3allMHoe npIlTSI>KeHHe, He npH6JIII>KaIOTCH JJ.pyr K 1l.Pyry?
6.4. B O)J.HOH 83 YCTaHOBOK OnbITHOH npOBepKII 3aKOHa
BceMllpHoro TfirOTeHIISI CHna npHTIDKeHHSI MeJKJJ.Y CBIIHlI.OBbI\I
wapOM MaccoH 5,0 Kr H wapHKoM MaccoH 10 r Ha paccTOHHHII
7,0 CM 6bIJIa paBHa 6,8 HH. 4eMY paBHa, Ha OCHOBaHIIII 3TItX
JJ.aHHbIX, rpaBHTall.HoHHaSi nocToHHHaH?
6.5. B CBHHlI.OBOM wape pa)l.HycoM R CJJ.eJIaHa c<t>ePIl'IeCKaSi
nOJIOCTb, nOBepxHocTb KOTOpOH KacaeTCH nOBepxHOCTH wapa H
npoxoJJ.HT qepe3 ero lI.eHTp. Macca wapa M. C KaKOH CHJIOH
CBHHlI.OBblH wap 6YJJ.er npHTHfllBaTb wapHK MaccoH m, HaXOJJ.H-
U{HHCSI Ha pacCTOSlHHII d > R OT lI.eHTpa CBHHlI.OBOrO wapa Ha
npHMoH, coe)J.IIHfllOU{eH lI.eHTpbl w.apa H nOJIOCTH, co CTOpOllbl
nOJIOCTH?
6.6. B 6e3rpaHlI'iHOH cpe)J.e nJIOTHOCTblO Po = 1,Ox
X lOS Kr/M s HaXO)J.HTCSI Ha paccToSlHHH r = 20 CM OT lI.eHTpOB
JJ.pyr JJ.pyra ,ABa wapa oOO,eMaMH VI = 30 CM s H V 2 = 40 CM 3 ,
nJIOTHOCTblO P =2,O.IOS Kr/MJ. Onpe)J.eJIIITb CHJIY B3aHMoJJ.eHc1-
BHH Me}f{)J.y wapaMH.
6.7. OnpeJJ.eJIHTb YCKopeHHe CBoOO,'J.HOro na,!l;eUHH TeJI Ha
BbICOTe h = R 3 OT nOBepXHOCTII 3e!.IJIH, eCJIH Ha 3eMJIe YCKO-
peHHe CBOOO)l.HOro na)l.eHHSI go = 9,8 Mlc 2 .
6.8. 3HaSi Cpe)l.Hee 3HaqeHlle YCKopeHItH CBoooJJ.Horo na)J.e-
HHH, onpe,'J.eJIHTb Maccy 3elllJIH.
6.9. Ha KaKOU Bl:lCOTe OT nOBepXHOCTH 3eMJIII CtfJIa TfI>KeC-
Tit YMeHbWlfTCH B)J.Boe?
2-
35

6.10. C KaKoH clIJIofi 6y.neT npHTSlrHBaTbcSI K JJYlle rHpSl
Maceoo m = 1,0 Kr? Macca JJYHbl M = 7,3.102 Kr.
6.11. npe.ncTaBHM,l1TO K neHTpy 3eM.'m npopwUI lUaxTY.
Onpe.neJIHTb, KaK 6y.neT H3MeHSlTbCSI CHJIa TSI>KeCTH B 3aBHCH-
MOCTH OT paccTOSlHHSI r .no l.{eHTpa 3eMJIH, eCJIH Te.'10 Maccoll m
nepe.ll.BHraTb B.llOJIb lUaXTbl.
6.12. C KaKoH ropH30HTaJIbHoH CKOpOCTblO Ha,no 6pOClITb Te-
JIO, IlTo6bl OHO CTaJIO HCKyccTBeHHblM cnYTHHKoM 3ellfJIn?
6.13. B KaKOM HanpaBJIeHlIH H C KaKoH ropH30HTaJIbHOlf
CKOpOCTblO ,nOJI>KeH JIeTeTb B.llOJIb sKBaTOpa CaMOJIeT, l1To6b1
cKoMneHcHpoBaTb YMeHblUeHHe Beca, 06YCJIOBJIeliHoe BpaJ.l.le-
HHeM 3eIlfJIH? ;
6.14. nOlleMY KOCMHl1eCKHe paKeTbl 3anycKalOT B HanpaBJIe-
HHH C 3ana.na Ha BOCTOK? nOl1eMY HaH60JIee Bblro,nHO 3anYCli:aTb
paKeTbI B nJIOCKOCTH 3KBaTopa?
6.15. Onpe,neJIHTb nJIOTHOCTb lUapoo6pa3Hoii nJI8HeTbI, ec-
JlH Bec TeJla Ha nOJIlOce B n = 2,0 pa3a 6oJlblUe, IIeM Ha SKBa-
Tope. nepHO.ll BpaI..U.eHHSI nJiaHeTbI BOKpyr CBoell OCH T = 2 11
40 MHH.
6.16. HaHTH yrJloByro H JlHHeHHyro CKOpOCTJf Op6HT8J1b-
HOro Jl.BH>KeHHSI HCKyccTBeHHoro cnYTHHKa 3eMlm, eCJIH ero
nepllo,n BpaI..U.eHHSI BOKpyr 3eMJIH T = 4,0 IJ,
6.17. Ha KaKYIO BblCOTY Ha.n nOBepxHocTblO 3eMJlII CJIe-
,nyeT 3anycTHTb cnYTHHK, IIT06b1 OH OCTaBaJiCSI HenOABH>KHblM
OTHOCHTeJlbHO ee nOBepxHocTH?
6,18. 51,npo MaccoH m = 8,0 Kr 6pOCHJlH BepTHKaJlbHO
BBepx. Onpe.neJIHTb, C KaKHM YCKopeHHeM .llBH>KeTCSI Sl,npO H C
KaKIfM YCKopeHHeM Jl.BH>KeTCSI 3eMJlSI no.ll ,neiicTBHeM CHJIbI HX
B3alfMHoro npHTSI>KeHHSI.
6.19. n0K33aTb, lITO KBa,npaTbI nepHo,nOB BpaIlleHIlSi pa3-
JlJlIIHblX nJiaHeT "BOKpyr CO.'1HI.{8 OTflOCSlTCSI, KaK Ky6b1 pa,nJlY-
COB op6HT BPaJ.l.leHHSI. ,
6.20. PaAHYc Op6HTbI HemYHa B n = 30,0 pa3 60JIblUe pa-
.nHyca Op6HTbI 3eMJlH, KaKOIa npo,nOJl>KHTeJlbHOCTb ro.na }fa
HemYHe?
 7. KOJIH'ieCTBO ,nBH}KCHHSI. 3aKoH coxpaHeHHH
KOJIHIJCCTBa ,nBH>KeHHH
7.1. <I>YT60JlHCT, y,napSiH MSlII MaCCO" m = 700 r, C0061l.l8-
eT eMY CKOpOCTb v = 15 Mfc. OmTaSl .nJlHTeJlbHOCTb y.n a -
pa p8B1JOii t = O,OO c onpeJI.e.'1HTb Cpe;I.HfOlO CH.'1Y
};I.apa.
36

7.2 KaKona CpeAHSUI CIIJIa AaBJIeHHSI F Ha nJIelJO npH
CTpe.'1b6e H3 aBTOMaTa, ec.7JH Macca nYJI1I m = 10 r, a CKOpOCTb
nYJIlI npH BblJIeTe H3 KaHa.na CTBOJIa v = 300 wc? ABToMar .ne-
JIaeT n :.- 300 BblCTpeJIOB B MUHYTY.
7.3. .lI.Ba o.nHHaKoBblx rnapHKa MaccaMH m = 2,0 r .nBII-
>KYTCSI B ropH30HTaJIbHOH nJIOCKOCT1I C o.nHHaKOBbl!>Uf CKOpOCn!-
MH v = 4,0 M/C: 1) B,Z/.OJIb o.nHoil npSlMoH HaL':TpeIJY APyr .nPyry;
2) B,nOJIb O.nHOH npSlMoH OAHH 3a .nPynIM; 3) nOA yrJIOM a. = 120"
.npyr K .npyry. 4eMY paBHo c}"MMapHoe KOJUllJeCTBO .nB1I}f{eHHSI
3THX rnapHKoB BO Bcex CJIYlJaSlx?
7.4. TeJIO MaccoH m paBHoMepHo ABH}f{eTCSI no OKpYn<HO-
CTH co CKOpOCTblO v. HaHT1I 1I3MeHeHHe KOJIHlJeCTBa .nBH>KeHHSI
TeJIa np1l nOBopare Ha 50, 90, 180
11 360°.
7.5. lIlapHK MaccoH m = 10 r
na.nae:.r Ha ropH30HTaJIbHYlO nJIOC-
KOCTb C BblCOTbl hi = 22,5 CM.
Haihll Cpe.nHIOIO CHJIY YJI.apa B
CJIe.nYlOlII.HX CJIYlJaSlx: 1) capHK
n.7JaCTHJIHHOBbIH, npHJIlmaeT K
n.7JOCKOCTH; 2) rnapHK cTa.1!>I10H, nOCJIe y,Z/.apa OTCKaKIiBaeT Ha
B1>1COTY hi; 3) rnapHK nJIacT:,laccoBblii, nOCJIe y.napa OTCKaKH-
BaeT Ha BbICOTY h 2 = 11 C!>I, D.JIHTe.7JbIlOCTb y.napa BO Bcex
CJIYlJaHX CIJHTaTb o.nHHaKo!::>a 11 paBHoii t = 0,030 c.
7.6. D.Be lJaCTHbI MaCC:':.::1 m If 2m .nBIDKYTCH BO B3aHMHO
nepneH,'I.HKYJISlpHblX Hanpan.'1eHHHX co CKOpOCTHMH COOTBeTCT-
BeHHO 2v II v (pIiC. 58). Ha lJaCTIfbl HalJHHaeT .neiicTBoBaTb O;l.H-
HaKOBaH CIiJIa. Onpe.n.eJIlfTb MO.n.YJIb H HanpaBJIeHUe CKOpOCTH
qaCTHb1 Maccoii 2m B MOMeHT BpeMeHH, Kor.n.a CKOpOCTb lJaCTII-
1U>1 l\aCCOH m CTaJIa TaKoii, KaK nOL{a3aHO nyuKTHpO!>I: 1) Ha
pHC. 58, a; 2) Ha pHC. 58, 6.
7.7. KOJIeco MaccoH m = 3,0 Kr KanITCS! 6e3 npOCK3.'1b3LI-
BaRIIS! no rO;:l130HTaJIbHOii nJIOCKOCTlI co CKOpOCTblO v =
= 5,0 M/C. Onpe!I.e.llITb KO.1HIJCCTBO .n.Bun<:eHIISI KO..'Ieca.
7.8. no YCJIOBHIO 3a)J.a1J1I 4.44 paCCIJHTaHTe KOJIIIlJeCTBO
.D.BH}f{eHHS!, KOTOpoe 6Y,Z/.eT IIMeTb CHCTe\la rpY3 - o6e3hSlHa
lJepe3 t = 1,0 C noc.1e HalJaJIa ;I.BH}f{eHIISI.
7.9. nO}f{apHbIH HanpaB.'1S1eT CTPYIO BO,J,bI 113 6paH.lI.CnoiiTa
Ha orOHb. CKOpOCTb HCTelJeHHSI BO;J.bI V_ = 16 M/c. nJIOlIl.3.l1.b OT-
BepcTHSI 6paH,Z/.cnoiiTa S = 5,0 CM 2 . HaiiTIl CIIJIY, C KOTOpOH no.
)f{apHblil y.n.cp)f{IIBeT 6paH.lI.cnoiiT.
7.10. Te..l0 Maccoii m 1 = 100 r CKOJIb3HT 110 aOCOJIIOTHO
r."Ia.nKoii ropH30HT3 '!bHDH nJIOCKOCTIl co CKOpOCTblCJ tJ = 3,0 M/c.
Ha CBoeM nYT!f OHO BCTpeIJaeT HenO,'I.BH>KHoe TeJIO MaCCOH m1.'=
a}
2u .m 2u
-----
I;
61
-
2u
m
,
,
Izu
t
.
I;
PHe. 58
37

= 200 r, Onpe.neJUITb CKOpOCTb TeJl, ec.nH nocJle y.napa OHII
.nBHIKYTCSI KaK O.nHO ueJloe. 11306pa3HTb CHJlbI, .neiicmYIOIl.I.He lIa
TeJIa BO BpeMSI y.napa. KaKHe CHJIbI SlBJlSlIOTCSI BHYTpeHIIHMH,
KaKHe - BHelllHHMH AJISI ::IToii CIlCTeMbI .nBYX TeJl?
7.11. IlBa Te.1Ja, .nBHraSiCb HaBcTpellY APyr .npyry co CKO-
pOCTb1O V = 3,0 M/C KalK,lJ.oe, nOCJle coy.napeHHSI CTaJlH .nBII-
raTbCSI BMeCTe co CKOP0C:Tb1O U = 1,5 M/C. Onpe.neJlHTb OTIIO-
llleHHe Macc 3THX Ten, TpelmeM npeHe6pellb.
7.12. TenelKKa C neCKOM KaTHTCSI co CKOpOCTblO VI =
= 1,0 M/C. HaBcTpellY TenelKKe JleTHT 1113p Maccoii m =
= 2,0 Kr C ropH30HTaJIbHOii CKOpOCTb1O V2 = 7,0 M/C. C Ka-
KOH CKOpOCTb1O (H B KaKOM nanpaBJleHHH) 6y.neT npOAOJl/KaTbCSI
.nBHlKeHHe TeJlelKKH C 3acTpSlBlllHM B neCKe 1113pOM? .Macca Te-
JlelKKH C neCKOM M = 10 Kr,
7.13. no aoco.rnoTHO rJla.nKoii nOBepXHOCTH .nBHlKeTCSI co
CKOpOCTblO v = 6,0 M/C SlIl.I.HK C neCKOM Maccoii M = 9,0 Kr.
B neCOK nona.naeT rHpSl MaCCO" m = 1,0 Kr, OTnYIl.l.eHHaSi 6e3
HallaJlbHOii CKOpOCTlI C IO-MeTpOBOif BblCOTbI. Onpe.neJlHTb CKO-
rOCTb SllUllKa nOCJIe nona.naJIIISI B Hero rHpH.
7.14. C KaKoH CKOpOCTblO v nOCJIe ropH30HTa.'IbHoro BblcTpe-
Jla 1f3 BHHTOBKH CTaJl .nBHraTbCSI cTpenoK, CTOSlIl.l.IIH Ha rJla.n-
KOM JIbJlY? .Macca CTpeJIKa C BHHTOBKOH COCT3BJISIeT M = 70 Kr,
a Macca nYJIH m = 10 r H ee HallaJlbHaSl CKOpOCTb Vo =
= 700 M/C.
7.15. I1CnOJIb3YSl YCJloBlle 3aAatlH 7.14, on pe.B,eJIHTb , C Ka-
Koil CKOpOCTblO CTaJl JlBHraTbCSI CTpeJlOK, eCJlH OH c.ne.rIaJl .nBa
Bl>1<.TpeJla: J) B OJlHOM H TOM lKe HanpaBJIeHHH; 2) BTOpOH BbICT-
peJl B HanpaBJleHHH, nepneHJlHKYJlSlPHOM nepBoMY.
7.16. )Kene3110JlOpOIKHaSl nJlaT<t>opMa Maccon M = 20 T
.nBIIlKeTCSI co CKOpOCTblO VI = 9,0 KMlIl. 113 0pYIKHSI, YCTaHOB-
JICHIIOro Ha nJIa$pMe, BblnYIl.I.eH.CHapSl.n Maccoii m =25 Kr
co CKOpOCTblO V 2 = 700 M/C OTHOCHTeJIbHO Opy.nHSI. OnpeJle-
.'lHTb CKOpOCTb nJIaTq;opr.1bI U nOCJIe BblCTpeJIa: 1) Kor.na BblCT-
pen npoll3Be.J,eH B lIanpaB.'leHHH .nBH>KeHHSl nJIaTItx>PMbI; 2)
Kor.na J3bICTpeJl npoH3Be!l.eH B npOTlIBOnOJIO/KHOM HanpaB.le-
HIIII.
7,17. 113 CTapHllJloif nYlllKH, He mlelOIl.I.eii npOTHBOOTKaT-
lIoro }CTpOHCTBa, CTpeJISlJOT SI.J,pOM no;!. yrJIOM IX = 40 0 K ro-
PH30HTY .Macca SI,!I.pa m = 10 Kr, Hall3JIbHaSi CKOpOCTb V o =
- 200 M/C. KaKoBa 6YJleT CKOpOCTb OTKaTa nYlilKH, eCJIII ee
Macca M - 500 Kr? TpeHlle He YIHlTblBaTb.
1.18. Te.'1o Maccoii M = 300 r na.!l.aeT cBo6o.nHO C J3l>ICOTW
Ii = 10 M. Ha BblCOTe H.'2 B TeJIO nona.!l.aeT II 33cTpeBaeT B He\!
nyJISI r.1accoil m JO r, .1eTeBwafl ropll30HT3JIbll0 co CKO-
38

pOCTblO Vo = 400 M/c. HaitTH CKOpOCTb TeJIa If yroJl, KOTOpblH
06pa3ye-r BeKTOp CKOpOCTH C ropH30HTaJlbIO B MOMeHT noc-
.'Ie cOY,D.apeHHSI.
7.19. TpH JlO,D.KH OJl.HHaKoBoH MaccoH m H,D.YT B KHJIbBa-
Tep (Jl.pyr 3a ,D.pyroM) C O,D.HHaKoBoH CKOpOCTblO v. 113 Cpe,D.Hei'r
JlOJl.KH OD.HOBpeMeHHo B nepeJ!,HIOIO H 3a,D.HIOIO JlOJ!,KH 6pOCaJOT
co CKOpOCTblO II OTHOCHTeJIbHO JlO,D.KH rpY3b1 Macco. mI' KaKo-
B 6YD.YT CKOpOCTH JlO,D.OK nOCJIe nepe6pocKH rpY30B?
7.20. CHapSl,D. B BepxHeH TOIJKe TpaeKTopHH pa3pblBae-rcSI
Ha ,D.Ba OCKOJlKa paBHoii MaCCbI. O,D.HH OCKOJlOK nOCJIe B3pblBa
B03Bpal.l.l.aeTCfI K 0PYJ!,HIO no np>KHeii TpaeKTopHH. r,D.e yna;J.eT
BTOpOH OCKOJIOK? ConpOTHBJleHHe B03,D.yxa He YIJHTbIBaTb.
7.21. CHapSl,D. pa3pblBaeTCSI B BepxHeii TOIJKe TpaeKTOpHH
Ha BbICOTe H = 15.9 M Ha ,D.Be OJ!,HHaKOBbIe lJaCTH. 4epe3 Bpe!o!:Sl
t = 3,00 C nOCJIe B3pblBa O,D.Ha lJaCTb na,D.aeT Ha 3eMJlIO no,D.
TeM MecTOM. r,D.a npOH30WeJI B3pblB. C KaKOH clmpoCTblO H no,D.
KaKHM yrJloM K ropH30HT)' HalJa.1a .IumraTbCSI BTopaSl lJaCTb
CHapSl,D.a nOCJIe 133pblBa. eCJIH nepBaSl ynaJla Ha paccTOSlHHH I =
= 636 1.1 OT MeCTa BbICTpeJIa? ConpOTHBJleHlle B03J!,yxa He
YIJHTbIBaTb,
7.22. no HaKJlOHHOM n.1OCKocTH. COCTaBJISllOl.l.I.eii yroJl a.
C ropIf30HTOM. HaIJHHae-r CKOJIb3HTb 6e3 TpeHHSI fll.l.I.HK C necKoM
MaCCOH M. B TOT MOMeHT. KOr,D.a HI.l.I.HK npOWeJI nYTb I. B Hero
nonaJIO TeJIO MaCCOH m. J!.BHraBweecH ropH30HTaJlbHO, }lI.l.I.HK
npH 3TOM OCTaHOBHJlCSI. C KaKOH CKOpOCTblO J!.BHraJlOCb TeJIO?
7.23. no HaKJIOHHOR nJlOCKOCTH C yrJIOM a. = 30° npH OC-
HOBaHHH paBHOMepHO CKOJlb3HT fllItHK C necKoM Maccoii M =
= 10 Kr co CKOpOCTblO v = 1,0 wc. Kor,D.a B HI.l.I.HK nonaJ!,aeT
nYJlfl MaCCOH m = 10 r. JleTeBWafi ropU30HTaJlbHo. SlI.l.I.HK
OCTaUaBJIHBae-rcSI, Onpe,!l;eJIHTb CKOpOCTb nYJIH.
7.24. 4eJIOBeK MaccoH m = 70 Kr HaXO,D.HTCSI Ha KopMe
JIO,D.KH, Haxo,WIl.l.l.eiicfI B o3epe, IlJIHHa JlO,D.KH I = 5.0 M. Mac-
ca ee M = 280 Kr. 4eJIOBeK nepeXO,D.HT Ha HOC JIO,D.KH. Ha
KaKoe paCCTOSlHHe lJeJIOBeK nepeMeCTHTCSI OTHOCHTeJIbHO ,D.Ha?
ConpOTHBJleHHeM BO.lJ,bl npeHe6pelJb,
7.25. C BepwHHbI KJlHHa C yrnoM a. = 45° npH OCHOBaHHH C
BbiCOTbi H = 20 CM HalJHHaeT CKOJlb3HTb TeJIO MaccoH m =
= 0.50 Kr. KJIHH JIe>KHT Ha a6COJIIOTHO rJlMKoii nOBepxHocTH,
On peJl.eJIHTb. Ha KaKoe paccToSlHue nepeMecTHTcSI KJIHH. KOrJl.a
Teno OKa>KeTCSI y ero OCHOBaHHSI. Macca KJlIIHa M = 1.5 Kr.
7.26. 4enoBeK 3aXOTeJI cnycTHTbCSI no BepeBOIJHOH JIeCT-
HHIe 113 CB06oAHO BHCflI.l.I.ero a3pOCTaTa. MaCCOH M = 350 Kr.
KaKOH MHHHMaJIbHOH J!,JlHHbI BepeBOIJHYIO JleTllHuy off ,D.OJI>Kf'1I
39

npllBSl3aTb K rOH){0.1e a3pOCTC3Ta, 'lT06bl, cT}'naSi H3 nocJlen;
111010 CTyneHbKY, Of!: KOCHYJJCSl 3e"It? Macca 'leJJOBeKa m =
= 70 Kr. PaccT01Hule OT 3e".'m ,lI.O a3pocT3Ta H = 10.
 8, PaooTa. MOIllHOCTb. 3HeprHR. 3aKoH
coxpaHcHHHSHeprH"
8.1. KahYIO pa60TY COBepJlJHT CH.1Ia F = 20 H, KOr,ll.a Te.10
npOiin;eT n}Tb S = 5,0 \f (puc. 59, a-z)? Yro.., a. = 30".
8.2. Te.no Maccon m = 2,0 Kr Jl,BH>KeTCSl paBHoepHO DO
ropH30HTa.1lbHOii nOBepXHOCTIl nOn; ;J.eikTBlleM CHJJbI F, HanpaB-
JJellHOH non; yrJJOM a. = 60"
K ropH30HTY. Ko3<fxPlIlllleHT
TpeHHH Me>K)l.y Te.nmf If
nJJOCKOCTblO f.I. = 0,20. On-
pe..'1€JJlfTb, KaKYIO pa60Ty
COBepJlJaT CH.na TSI, >KeCTH
clI.na peaKllltll onopl>l, ClfJJa
TpeHIfH, CIIJJa F, Kor.aa TeJJO
npoii..'1eT paccToSlHue s =
= l,OM.
8.3. JIH4rr Maccou 300 Kr
nOJ1.HIf:\laeTCSI Ha 10 M. Ka-
KYIO pa60Ty conepllilfT clma HaTHn<eHUSl KaHaTa, nOJ1.HU!llalO-
lli.ero JJH4JT? KaK}1O pa60TY cODepnlllT Clf.'la TSl>l{eCTH?
8.4. .MoropHaSl JJOJ1.K3 n;BH>KeTCSI npoTIlB TelleHHR ropHOIi
peKH. CH.1Ia THrH MOTopa 2,0 KH. JIo;J.Ka OTIIOCHTe..1bHO 6eper8
OCTaeTCR HenoJI,BH>I!Hoii. CKOpOCTb TelleHHSl peKH paBHa 5,0 M/c,
Q
/""" "
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Pile. 59
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8J
f,H
2
X,eM
5 10 I, CM
PHC. 60
COBepJlJ3e-r .1IH pa60T}' CII;18 TSirH MOTopa? ECJm COBCpJlJaeT,
TO qey paDHa 3T3 p60Ta 3a 5,0 c? KaKoca MOlli.IIOCTb MOTopa?
8.5: no rpa(tJ:iKa1 38BHCmtOCTIf C".lbl f OT nepe'-lelli.€HIIR
lIa1iT" pa60TY 3TOii cmlLl (rllc. 60, a-li) npll neper.e!lJ.c:', a"ft'.8
Ha 5,0 If to CM.
40

8.6. J{ocKa MaccoH m = 3.0 Kr JI ;I..'IHHOH I = 1,0 \1 Jle»{lfT
Ha paCCTOflHJfJf x OT .n,BYX conpIfKaCaK>Il\IJXCH no.'1ynJlocKocTeI'i
"3 pa3HblX \laTepHaJlOB (pIiC. 61). KaKYIO pa60TY Ha.n,o cOBep-
lllHTb, QT06b1 nepe.n,BHHYTb .n,OCKY Ha BTOpylO nO.lynJlOCKOCTh,
B CJlYlJaH:.x: I) x = O. J.Ll = J.L2 = 0.10; 2) x = O. J.Ll = O.
JLI = 0,10; 3) x = 10 CM, J11 = 0.10. J.L2 = O,20?
I..
I
I
 /$ /,
..,
IX
. I I.
I I
,  l "m' "

PHe. 61
PIIC. 62
8.7, Ha ropH30HTaJlbHOH nJlOCKOCTH Jle}l{HT rpY3 MaccoH
m= 100 r Ha paCCTOJlHJfH x OT nppKuHbI JKecTKOCTblO k= 100 H/\I
(puc. 62). K034$HLlueHT TpeHJlH Me}l{.n,y TeJIOM If n"IOC-
KOCTblO J.L. KaKYIO pa60TY Ha.n,o COBepIlJJlTb. IJT06b1 nepe,'I,BlI-
HYTb rpY3 na Xo= 3,0 CM, B CJIYlJaHx: 1) x = 0, J.L = 0; 2) x =
= 1,0 CM. J1 = 0,10.
8.8. KaKaH pa60Ta npoH3Be.a.eHa npJl C}I{aTHH 6Y4>ePHOii
npYJKHHbl JKeJIe3lfo.n,opO}l{HOrO BarOHa Ha 11 = 5,0 CM. eCJIJI
JlfI C}I{aTJfH npYJKHHbI Ha I. = 1,0 CM Tpe6 y eTcH CJfJla F =
= 30 KH?
8.9. npe.n,cTaBHM, qTO K LleHTPV 3eMJlIf npopblJlJl llJaxTY.
KaKYIO pa60Ty Ha)l.O COBepIlJHTb, qr06b1 BblT311UITb TeJIO Mac-
coil m = 1,0 Kr Jf3 LleHTpa 3eMJlJf Ha nOBepXHOCTb?
A
t
t
PIIC. 63
PRC. 64
8.10. nOCTOflHHaSi CHJla COBepllJae-r pa6OTy. fpact>JlK 3aBJI-
CH\!OCTU pa60Tbi OT BpeeHJf .n,aH Ha pHC. 63. KaKOB xapaKTep
.lI.Blf}l{eHHH B Ka}K)10'd H3 .n,Byx CJlYlJaen? nOCTpOHTb rpact>HI<Jf
3aBHCII\IOCTII MOlllHOCTJI OT Bpe\leHJI.
8.11. Ha rpaqmKe (pHC. 64) npeJl.cTaBJleHa 3aDHCJfMOCTb
pa60Thl nOCToHHHOH CHJlbI OT BpeMeHH. nocrpOJfTb rpact>HKlf
33BUCU'dOCTU MOlllllOCTH H CKOpOCTJI TeJIa OT BpeeIIH.
41

8.12. npH HcnblTaHHH aBTo06HJ1bHOrO .n.BHraTeJJH nOJlY-
qlfJIIf 3aBHClfMOCTb ero M01l\.HOCTH OT BpeMeHH (pHC. 65). no
rpaqmKY onpe.n.eJUITb pa60TY 3a Becb nepHO.n. HcnblTaHHH.
8.13. ABTOMoOHJlb MaccoH M = 1,0 T TporaeTcH C MeeTa
H, )1BHra HCb paBHoycKopeuHo, npOXO)1HT nYTb 5 = 50 M 3a
t = 5,0 c. KaKYIO M01l\.HOCTb pa3BHBSeT aBTOMoOHJIb?
8.14. .lI.Ba aBTOMoOHJIH O.ll.HOBpeMeHHo TporalOTcH C MeCT(.i
H .n.BH}KYTCH paBHoycKopeIlHo. Maces aBToM06HJIeH O.ll.HllaKOB8.
Bo CKOJIbKO pa3 M01l\.HOCTb nepBoro aBTOM06HJIH 60J1bllle MOll\.-
HOCTH BToporo, eC.'Il1 3a O.ll.HO H TO iKe BpeMH nepBblH aBTOM06HJlb
pa3BHBaeT CKOpOCTb B.n.Boe 6oJIblllYIO,
'IeM BTOpOH? ConpOTlfBJIeHHeM Jl.BH-
}KeHHIO npeHe6pe'lb,
8.15. Onpe.n.eJIHTb cpe;J.HIOIO no-
Jle3HYIO M01l\.HOCTb npH BblCTpeJIe H3
rJla.ll.KOCTBOJIbHOrO PY}KbH, eCJIH H3-
BecTHo, 'ITO nYJIH MaccoH m BblJIe-
TaeT 83 C'fBOna co CKOpOCTblO V o , a
.n.:IHHa KaHaJIa CTBOJIa I (.n.aBJleHHe
nopOXOBblX ra30B Cl1HTSTb nOCTOHH-
HblM BO Bpe\Ul HaXO}K)1eHHH [1YJIH B KaHaJIe CTBOJIa) ,
8.16. MOTopbl meKTpOB03a npn )1BH}KeHHH ero co CKOpo-
CTblO V = 72 KM/IJ nOTpe6JIHIOT M01l\.HOCTb N = 800 KBT,
K03<l><PHllHeHT none3Horo .n.eHcTBHH CHJIOBOH YCTaHoBKIf 3JIeK-
TpoB03a '1 = 0,80. Onpe.neJIHTb CHJlY THrH MOTOpOB.
8.17. MaxoBHK pa.n.HYCOM R Bpaw.aeTCH C lJaCTOTOH n,
nepe.n.a13aH peMHeM npHBO.ll.Y MOlllftOCTb N. HaHTH CH.IJY HaTH-
>KeHHH T peMHH, HJl.YIlI.ero 6ea CKOJ!b}KeHHH.
8.18, no.n. .n.eHCTBHeM nocToHHHOH rOPI!30HTaJIbHOH CHJ1b1
F = 10 H )1BH}KeTCH TeJJO MaccoH m = 5,0 Kr. K03<l><PHll HeIlT
TpeHHH Me}K)(Y TeJIOM H nJIOCKOCTblO J.L = 0,10. KaKYIO pa60ry
COBeplllaT CHJIa TpeHHH H CHna F, Kor.n.a TeJIO npOHJl.eT nyTb
5 = 10 M?
8.19. nOqeMY paCXO)(yeTcH 60JIbWe 6eH311Ha B TOM cnyqae,
Kor.n.a aBToM06HJIb ,ABH}KeTCH C YCKopeHHeM, 'IeM npH )1BH}KeHHH
C nocToHHHOH CKOpOCTblO?
8.20. TOpM03HOH nyTb aBToM06HJIH, Jl.BHraBlllerOCH co
CI<OpOCTblO VI = 30 KM/IJ. paBeH 51 = 7,2 M. I.J:eM}' 6YJl.eT
paBeH TOpM03HOH nyTb, eCJIH CKOpOeTb aBToM06H.'IH YBeJIH'lHTCH
)10 V 2 = 50 KMI'I?
8.21. Ha Teno MSCCOH m = 10 Kr )(ei1CTnyeT nOCTOHHHaH
CnJIa F = 5,0 H. Onpe.n.eJIHTb KHHeTH'IecKYIO 3HepriflO Te.'Ia
IJepe3 t = 2.0 C nOCJIe HSIJaJIa AEIf}KeHlfH. ConpoTHB.lJeHHeM
npeHe6pe'lb.
11, KBm
JO
PHC. 65
42

8.22. KaKYIO pa60Ty HaAo cOBeplllHTb, 'lT06b1 3aCTaBHTb
aBTOM06HJIb MaccoH M = 1,5 T: I) YBeJIHIJHTb CBOID CKOpOCTb
OT 0 11.0 36 KM/IJ; 2) OT 36.11.0 72 KM/IJ? ConpOTHBJIeHHeM npeHe6-
pelJb.
8.23. MeTaJI.'IUttecKHH lllapllK Maccoi'! m = 100 r paBHoMep-
HO J1.BH.meTCH B ropIl30HTa.'IbHOH nJIOCKoqH no OKPY*HOCTH
p3,ll.HYCOM R = 50 CM C lJaCTOTOH nl = 3 c- 1 . KaKYIO pa60Ty
HY}I{HO cOBeplllHTb, ttT06b1 yBeJIH'lHTb lJaCTOTY JJ.O ns = 5 c-I?
8.24. KaKYIO pa60ry HY}I{HO 6b1JIO 6b1 coBepwHTb, qr06b1
BblBeCTH cnYTHHK MaccoH 500 Kr Ha KpyroBYIO Op6HT)', npo-
XO.ll.H1l.lYIO B6JIJl3H nOBepXHOCTJI 3e\tJlH, ecJIli 6b1 conpOTHBJIeHlle
B03xa OTCYTCTBOBaJIo?
8.25, OnpeAeJIlITb KHHeTllqecKYIO 3HeprHIO TeJIa MaccoM
1,0 Kr, 6pollleHHoro ropH30HTaJlbHO co CKOpOC:fb1O 2(hf/C, B
KOHl..le qeTBepToH ceKYHAbl ero ABJI}I{eHHH,
8.26. Onpe.ll.eJIHTb KHueTHtJ:ecKYIO 3HeprHIO KOJIeca, ABlI-
*YllI.erOCH 6e3 npOCKaJIb3b1BaHHfl co CKOpOCTblO v = 5,0 M/C.
Macca KO.'Ieca m = 2,0 Kr cOCpe11.OTO'leHa B o60.l1e.
8.27. TeJIo, 6pollleHHoe nepTHK3.'IbHO BBepx, ynaJIo 06paT-
HO qepe3 4,0 C nOCJle HatJ:aJla ;J.BH>KeHHH. Onpe;J,eJIHTb KHHeTH-
qecKYIO ::meprHlO B MOMeHT II3AeHHH H nOTeHl..lnaJIbHYIO 3HepruIO
B BepxlIeH TOtJ:Ke, eCJIH Macca TeJIa 200 r.
8.28. 00 KaHaTHoH }l{eJl€3HOH Aopore, U11.YllI.eH C yrJIOM
lIaR.'IOHa a = 45° K rOpIf3QHTY, n011.HHMaerCH BarOHeTKa Maccoll
m = 500 Kr. Haihn pa60TY, KOTOPYIO coBepruaeT MOTOp noJJ.'b-
eMHIIKa, npH nO..'l.HHTUH BarOHeTKU Ha BblCOTY h = 10 M. K034>-
IJJIIl..lHeHT TpeuHH npHHHTb pa3HbI\f !1 = 0,10.
8.29. Te.1e}l{Ka 11.Bu*eTCH no rOpH3OHTaJlbHoi'! JJ.opore co
CKOpOCTblO 18 KM/IJ H B'be3>KaeT Ha nOA'beM. Ha KaKOU BblCOTe
113.!1, ypOBHeM AOpOfH OCT;iHOBIITCH TeJle*Ka? COnpOTHBJIeJUle\f
npeHe6pelJb.
8.30. KUHeTllqeCKaH 3HeprHH Te.1a B MOMellT 6pocaHHH paBfla
200 !I.iK. OnpeJJ.eJUiTb, JJ.O KaKoH BblCOTbl OT nOBepXtiOCTII
3eMJIU MO>KeT nOJJ.HHTbCH TeJIO, eCJIII ero Macca paBHa 800 r.
8.31. Ha HlITH A.1HHOH l nO,'I,BerneH wap. Kal\YIO ropH30H-
TeJIbHYIO CKOpOCTb v HYiKHO co06I1.lHTb lllapy, qTo6b1 OH OT-
KJlOHM.'ICH AO BblCOTbl TO'lKli nO;J,neca?
8.32. fIpYiKHHa }l{ecTKOCTblOk = 100 KH. .1 Iaccoif m =
= 400 r na;J,aeT l!a 3e.f.'110 <; BbiCOTbl h = 5,0 M. Ha CKOJIbKO
(OMMeTCH npY>KHHa, eCJIH lipH YAape ee OCb OCTaeTCH Bepnl-
K3J1bHOil?
8.33. TeJIo 6pornello noJJ. yr.'IOM K rOpJl301lT)' co CKOpOCTblO
tI" nOJIb3YHCb 33KOnO\f coxpaHeHIIH MeXaHH'leCKOH 3HepnUf,
onp e .l1e.nuTb CKOpOCTb TCJla !fa Bblco'!e h HaA ropu30HTOM.
43

8.34. TeJlo 6pollleHo BepTIIKaJIbHO BBepx co CKOpOCTblO 00 =
= 20 M/C, Ha KaKOH BblCOTe It OT TOqKH 6pocaHluI KHHeTH-
qecK8H :meprHH Te.'Ia paBHa ero nOTeHl.lHaJIbHOH 3HeprHH?
8.35. HUTb c nO)I,BeWeHHbI.M Ha HeH rpY30:\t OTK.'IOHIIJIH Ha
yrOJI a IJ oTnycTHJIH. Ha KaKoH yrOJI  OTKJIOHIITCH HHTb C
rpY30M, eCJ1H npH CBoeM Jl.BH}KeHHH OHa 6YJl.eT 3a.ll.ep}KaHa lllTII<p-
TO:'.f, nOCTaB.'IeHHbl\f Ha BepTHKaJIH. nocepe)J:HHe JI..1IHHI>l HHTH?
8.36. MHq Maccoil 50 r npH na)l.eHHH C BblCOTI>l 3.0 M noJl.-
, CKOqllJI lIa BbiCOTY 2,0 M. Ha CKOJIbKO YMeHblllHJIaCb MeXIDUI-
qecKaH 3HeprHH? KaK cornaCOBaTb 3TO C 3aKOHOM coxpalleHIIH
:meprllll? B KaKoH BH)I. 3HeprllH npeBpaTHnacb B 3TOM CJIyqae
MeXallllqeCKaH ::meprHSI?
8.37. TeJlo MaccoH m = 100 r. 6pollleHHoe BepTHKaJIbHO
DHH3 C BbiCOTI>l It = 20 M co CKOpOCTblO VI = 10 M/C. ynaJIo
Ha 3e:\f.lIlO co CKOpOCTblO V 2 = 20 M/C. HaHTH pa6o-ry no npeo)l.o-
.'IeHUIO conpOTIIBJIeHHH B03J1.yxa.
8.38. rOpHblii pyqeH C CeqeHHeM nOTOKa S 06pa3yeT BO.ll.Ona)l.
BblCOTOii It. CKOpOCTb TeqeHHH BO)l.bI B pyqbe v. HaiiTH MOlU,H<?CTb
BO)J:ona)l.a. .
8.3. OnpeAe.'IIITb nOJIe3HYIO MOlU,HOCTb BOJl.HHOrO ,ABHraTe-
JIH, K03qxpHI..lHeHT nOJIe3HOrO )l.eiiCTBHSI KOToporo 1) = 0.80.
eC.'I1i H3BecTHO. qTO BO)l.a nocTynaeT B Hero co CKOpOCTblO VI =
= 3,0 M/c. a OCTaBJISleT ero co CKOpOCTblO V s = 1,0 M/C Ha
ypoDHe, HaXOJl.SllU,CMCSI HH}Ke YPOBHSI BXOJl.a Ha It = 1,5 M,
Pacxo.n;. BO)l.bI Q = 0.30 M 3 /C. .
8.40. MOlU,HOCTb rIf)l.p03JIeKTpocTaHI..lHH N = 73,5 MBT. KO-
3qxpUl..lHCHT nO.'IC3HOrO )l.eHCTBHSI 1) = 0,75. Onpe)l.eJlHTb, Ha
KaKOH ypoBeHb nJIOTima nO)l.UHMaeT BOJl.Y. ecJIH pacxo,':l BO.ll.bl
Q = 1,0 . 10 3 M 3 :C.
8.41. HaHTU MOIl.lHOCTb B03;I.YlllHoro nOTOK8, IIMeJOlU,erO
nOnepeqHOe CCqeHUe B BH;J.e Kpyra .ll.llaMeTpo:'wf d = 18 M II
:I.BII}KYll1.erocH co CKOpOCTblO v = 12 M/C (B03..'1.YX HaXO)l.UTCH
npu 1I0pMa.'IbHbIX YC.lIOBl1S1X).
8.42. Teno COCKaJIb3bIBaeT C HaKJIOHHOH nnOCKOCTH BblCOTOH
It = 2,0 M H yr.'IM Hal\.'10Ila a = 45°. Onpe.n;enHTb K03cIxlm-
I..lUeHT TpeHlfH Me}KJl.Y TeJlO:\f H nJIOCKOCTblO, eCJIH H3BecTHO. qTO
Y OCHOBaHHH CKOpOCTb Tena V = 6,0 M/c, 4e:\lY paBeH K034>-
iplll..lUellT nOJIe3l1oro .n.eHcTBHSI HaKJIOHHOH nJIOCKocTII?
8.43. C JIe.n;HHoH ropbl BblCOTOH It = 1,0 M H OCijOBaHUeM b =
= 5.0 M C"be3aJOT caHKH, KOTopbIe OCTaHaBJIlmalOTCH, npoii-
Jl.SJ ropU30HT8JIbllblH nYTb't- = 95 M. HaHTH Ko3<txPHlI.llellT
TpeHHH U Ko3<MmI..lUeHT nOJ"le3HOrO .n.eHcTBHH.
8.44. C BepwlIHbI ropKH (pIlC. 66) CKaTbIB8e-rCH TeJlO II OCTa-
l&nJIUBae-rcSI .B TOqKe, 113 hOTOpoii BepUHIHY BII)l.II0 noJl. } rJIOlot
44

a. = 6,0°. Onpe.a.eJUlTb Ko3<!xPHl.lUeH1' TpeHHSI, €CJIH oM ua Bce1C
Y1J3CTKaX nYTli o.n;UHaKOB.
8.45. KaKYIO ropH30HTanbHYIO CKOpOCTb Ha.n.o co06lU,I1Tb
llJapuKY, 1JT06bI OH C;I,eJIaJI nOJIHblH 06opoT B BepTHKaJlbHOii
nJIOCKOCTH, ecJIH OH B'HCUT: I)
Ha nerKoH HUTH )J..'IIIHOH l; 2)
118 }KeCTKO1 HeBeCOMOM CTep}K-
He Jl../IUHOH I?
8.46. Onpe.n.eJIHTh YCKO-
peHlle 06pY1Ja, CKaTblB8IOlU,e-
rocSi 6e3 npocKa.1b3b1BaHHSI C HaKnoHHoH nnOCKOCTH C
yrJIOM a npu OCIlOBaIlHH. BcSI Macca 06PYQa cocpe.n.oT01Je-
Ha B 06o.n;e. -
8.47. He60.'IbllJoe TeJIO COCKaJlb3b1BaeT BHH3 no HaK.'10HHo-
MY CKaT}', nepexo)l.SlIll.eMY B MepTBYIO neTJIIO pa)tuYCO\1 R =
=20 CM (puc. 67). KaKoBa AOn}KHa 6blTb HaUMeHbllJaSi BbiCOTa
CKaTa, IIT06bl TeJIO c.D.eJIaJIO nOJIHYIO neTJIIO He Bblna;I.aSl?
TpeHHeM npene6pelJb.

 A -------.1
B <8'
.. --r--
.\' '"
-- ---
Pile. 67 PHe. 68
8.48. He60JIbllJOe Te.'10 HalIUHseT COCKa.'1b3b1DaTh C BepllJlIHbl
cq,epbl BHU3. Ha KaKoH BbicOTe h OT BepllJHHbI TeJIO OTopBeTcSI
OT nonepxHocTH Cq,epbl PaAHYCOM R? TpeHHeM npeHeOpelJh.
8.49. C BepllJUHbI A rJI8)l.KoH nOJIY- A
Ccpepbl paAHycOM R (pUC. 68) 6e3 lIa-
llaJIbHOH CKOpOCTH COCKaJIb3blBaeT OIJeHb
ManeHbKHH llJapHK. nOCJIe OTpblBa OT
nOBepXIIOCTH B TOIJKe B OH IIcnblTblBaeT
a6COJllOTHO ynpyroe cOY.D.apeHHe c rna.n;-
KHM ropll30flTaJlbHblM nOJIOM. npeHe-
6perM TpeHHeM, OnpeAeJIHTb, Ha KaKYIO
BblCOTY OT nOBepXHOCTH no.'Ia no.n;CKO-
IIHT llJapHK.
8.50. Teno COCKaJIb3bIBaeT 113 T01JKH A B TOqKy B no Jl.BYM
HaKJIOHHbThl nOBepXHOCTIl, npOXOASllU,IIM IJepe3 TOllKU A H B,
0;I,11H pa3 no BblnYKJIOH .D.yre, BTOpOH pa3 no BorHYToH (pllC,
69). K03qxpUl.lHeHT TpeHH'I B 060Hx CJIYlIaJIx O;I.HH II TOT }Ke.
n KaKOM CJIytJ:ae CKOpOCTb Ten3 B TOllKe B 6oJIbllJe?
n
-
Pile 66
B
Pile. 69
45

,
 9. 3aKoHbI coxpaHeHHH B MeXaHIIKe
9.1. TeJIO COCKaJIb3blBaeT 6e3 TpeHlUt C KnlfHa, JIe>KalU,ero
Ha ropH30HTa.1bHoH nJIOCKOCTH, .l1Ba pa3a: nepBblH pa3 KJIHH
3aKpenJIeH, BTOpOO pa3 KJIHH MO>KeT CKOJIb311Tb 6e3 TpeHHH.
BY.l1.eT JIll eKopOCTb TeJIa B KOHl.le COCKaJIb3blBaHHH C K'IHHa
omlaKoBoH B OOOIlX CJIyqaHX, eCJIII TeJIO 06a pa3a eOCKaJlb-
3bIBaJIO e OAHOH II TOH >Ke BbiCOTbl?
9.2. no yeJIOBHK> 3a.l1aqH 9.1 onpe.l1.eJIHTb, BO CKOJIbKO H3-
lJaJIbHan BbleOTa Te.rla 60JIbllJe BO BTOpOH p33, lJeM B nepBblii, eCJIII
.
KOHCIJHaH cKopoeTb TeJIa B 060HX .CJIYQaHX O.l1I1HaKOBa. .Maeea
re'lam = 2,O.Kr, Maeea KJIIIHaM = 10 Kr, HaKJIOHUaH rpaHb
KJIHila nJIaBHO nepexO.l1HT B ropH30HTaJIbHYK> n.rloeKOCTb (pile.
70).
9.3. TeJIO MaeeoH m = 500 r .l1BH>KeTCS1 co cKopoeTblO
v o = 3,0 M/e no ropH30HTaJlbHOH nOBepXHOCTH II B'be3>KaeT H3
I10KOH1l.lY10eH lIe3aKpenJIeHHYK> ropKY MaeeO" M = 7,5 Kr
(pHe. 71). Onpe.l1.eJIlITb, Ha
KaKYK> BbleoTY nO)lHHMeTeH
TeJIO no ropKe H C KaKoH
CKOpOCTbK> OHO e'be.l1eT e Hee.
9.4. qeJIOBeK crOIlT Ha
HenO)lBH>KHOH TeJIe1KKe H
tSpoeaeT ropH30HTaJlbHO Ka-
MeHb MaceoH m = 8,0 Kr
co eKOpOCTbK> v = 5,0 M/C.
Onpe.l1.eJIHTb, KaKYIO npH
3TOM lIeJlOBeK COBepllJaeT
pa60Ty, eCJIH Maeea TeJle>KKH BMecTe C QeJIOBeKOM M = 160 Kr.
npOaHam-l3HPYHTe 3aDHeHMOCTb pa60Tbl OT Maeebl M.
9.5. BHHToBKa MaceoH M = 2,8 Kf nO)1BeIlIeHa ropll30H-
Ta:IbUO Ha .l1.Byx napaJIJIeJIbHblX HHTHX. npn BbleTpeJIe B pe-
3YJIbTaTe OT.l1aQH OHa OTKalJHYJIaCb BBepx H3 h = 19,6 CM
(pHe. 72). .Maeea nYJIII m = 9,8 f. Onpe.l1.€.1HTb eKopoeTb, c'
KOTOpoii DbI'IeTe'Ia nYJIH.
Pile. 70
I
I
I
I
I
I
I
/
r L ___
L__--
Pile. 72
46
- d
m u
/// ,,, .
Pile. 71
.c:

9.6. .D.JIS! onpeJl.eJIeHHH CKOpOCTIf nYJIH HCnOJIb3YIOT 6a.n-
JIHCTHQeCKHH MaHTHHK. OnpeJl.eJIlITb CKOpOCTb ropH30HTanbHo
JIeTeBllJeH nynH nepeJl. nOnaJl.aHHeM B MaHTHHK, eCJIH OH
nOCJIe nonaJl.aHHH ny.'IH OTKnOHHncSI Ha yroJI a = 15°. .D.JIHHa
HHTH 1 = 4,0 M. Macca nYJIH m = 20 r, 6a.nJIHCTlflJeCKOrO Ma-
HTHHKa M = 5,0 Kr,
9.7. Ha TeJIKY MaccoH M, JJ.BmKY11l.YlOcH co CKOpOCTblO v,
onycK8IOT C HroOJIbllJOH BblCOTbi KHpnHIJ MaccoH m. HaihH 1f3-
MeHeHHe BHYTpeHHeH ::meprHH TeJIe2KKH.
9.8. CKOpOCTb TeJ1a nepe,lt 'aoconlOTHo ynpyrHM y,ltapoM 0
BTopoe Heno,ltBH2KHOe TeJIO 6blJIa paBHa VI = 3,0 M/C, nOCJIe
YJJ.apa CTaJIa paBHoH UI = 2,0 M/C, Onpe.I!.e.'1HTb CKOpOCTb BTO-
poro TeJIa nOCJle YJJ.apa.
9.9. .D.Ba TeJIa JJ.H2KYTCH ropH30HTaJIbHO HaBCTpelJY Jl.pyr
.lI.pyry B,lto.'Ib OJJ.HOH npSlMoH. nOCJle CTOnKHOBeHHH TeJ1a CJIH-
naIOTCH. OnpeJJ.eJIHTb CKOpOCTb TeJ1 nOCJle CTOJIKHOBellllSl, ecnH
ml = 0,50 Kf, m z = 0,90 Kr, VI = 20 CM/C. CpaBHlITb 3HeprHIO
TeJI .11.0 H noc,,1e YJJ.apa. 06"bHCHHTb, nOQey npOHCXOj),HT H3-
J,leHeHHe 3HeprHH.
9.10. .D.Ba llJapa MaccaMH ml = 1,0 Kr, If m 2 = 2,0 Kf
,ltBHLKyTCH nocTynaTeJ1bHO BJl.OJIb ropH30HTanbHoH npHMoii B
O.D.HOM HanpaBJIeHHH co CKOpOCTHMH VI = 7,0 M/C H V 2 = 1,0 M/C.
Onpe.ll.eJIHTb CKOpocru llJapOB nOCJle aOCOJIlOTHO ynpyroro Y.ll.apa
9.11, llIapHK MaccoH ml' JJ.BlffaBIlJHHCH nOCTynaTeJIbHO co
tKOpOCTblO Vb HaneTaer Ha HenO.ll.BmKHblH mapHK Maccoil
m 2 . OnpeJJ.eJIHTb CKOpOCTH llJapHKOB nocne a6conIOTHO ynpy
roro neHTpanblloro Y.I!.apa. npOaHaJIH3HpOBaTb 3aBHCHMOCT
CKopOCTeH mapHKOB OT COOTHOllJeHHSI HX Macc. nOKa3aTb, (no
B cnYllae a6conlOTHO ynpyroro y,ltapa 0 MaCCHBHoe TeJ10 Ha-
npaBJIeHlle CKOpOCTH llJapHKa MeHlleTCSI Ha 06paTHoe.
9.12. ..1erKHH llJapHK lIaQHHaeT cB060,ltHO na,ltaTb H, npo'Ic-
TeB pacCToHIIHe I, CTaJlKlfBaerCH ynpyro C TSl2Ke.'IOH nJIHTOii,
.D.BH}f{)'11I.eHCH BBepx co CKOpOCTblO u. Ha KaKYIO BbiCOTY noJl.-
npLIrHeT llJapHK nocne YJJ.apa?
9.13. llIapHK MaccoH m = 100 f, .I!.BH2KY11l.eHCH co CKOpO-
CTblO v= 1,0 M/C, ynpyro Y.ll.apHeTCH 0 nJIOCKOCTb. OnpeJl.enHTb
H3MeHeHile KonHllecTBa .lI.BlUKeJIIUI llJapHKa H MaKCH\fanbHYIO
3HeprHIO ynpyroH .lI.OpManHH, ec.11f HanpaBneHHe CKOpOCTH
COCTaBnSleT c nJIOCKOCTblO yron a, paBHblH: 1) 90°; 2) 30°.
9.14.. llIapHK nOJl.JIeraer K HenO.ll.BH)KHOH CTeUKe cBepxy co
CKOpOCTblO V = 10 M/C noJl. yrJIOM a = 45° K CTeHKe. Haunl
yroJI, noJl. KOTOpbl llJaplfK OTCKOIJHT OT CTeHKlI. LlmlTeJILIIOCTb
ynpyroro y,ltapa 't = 50 MC,
47

9.15. TeJIO noc.'Ie a6COJIIOTHO lIeynpyroro Y.l1apa 0 He-
nO.J..DII>KHOe TeJIO CTa.'IO .l1BllraTbCSI B n=4 pa3a Me.'1.JIeHHee. Onpe-
.l1e.'IIITb .11.0.'110 ::meprull, nepeweAweH BO BHYTpeHulO1O mepnllO
TeJIa.
9.16. .lI.Ba wapllKa Macca!>!H ml H m 2 nO;J.BeIllCHbI: Ha HIITSIX
OJl.IIUaKOBoil .l1J1I1HbI: TaK, "ITO conpII KacaIOTCSI. OJl.IIU wapHK
OTBO.l1S1T B nnOCKOCTII HIITeH Ha yroJI a H omycKalOT. npollc-
XO;J.IIT l.leHTpa.'Ibllbl:H Y.l1ap rnapllKoB. Ha KaKlle yrnbl a l II all
OTHOCIITeJIbHO OTBecllOH JIIIlIlfH OTKnOHSlTCSI wapllKH nOCJIe
YJl.apa (yrnbl: C"IIITaTb Manbl:MII, Y.ll.ap - ynpYrllM)?
9.17. Ha KaKoH yroJI  OTK.'IOHSlTCSI mapllKII (CM. 3a)l.811)'
9.16), eCJIII y;I.ap lIeynpYrHH?
9.18. .lI.Ba H.II.eaJIbllO ynpyrllx !llapllKa Macca!>!11 ml H mil
.l1BII>KyTCSI B.l10nb 0.'1.1I0H H TOU >Ke npSlMoH co CKOPOCTSI\IH VI
H v'z' Bo npeMSI cronKHoBellllSi mapllKII lIaQll1l8lOT JI.OpfHpO-
BaTbCSI II "IaCTb KlilleTlI'IeCKOH 311eprHII nepeXo.l1I1T B nOTeHI.lII-
aJlbH)'1O 3HeprllIO .l1eq>OpMaI.lIlH. 3aTeM .l1eq,opMal.lHSI YMeHbma-
eTCH II 3anacellHaH nOTeHUllaJIbHaH 311eprllH BHOBb nepeXOAHT
B KHHeTHtlecKYlO, HaHTII 3HaQeHlle MaKCII\la'IbHOH 9neprHH
.l1op:\lal.lllll,
9.19. nOKa3aTb, "ITO npH ynpyroM Y..1ape mapa B TaKoil >Ke
lIeno..1BII>KHbIH map lie no JlIIIIIIH ux I.lCHTpOn wapbl pa3JIeTa-
IOTCH no"" yr.'IOl\l 90° Jl.pyr K .D.Pyry,
11.1. Maccbl TC'I lIa pHC. 73 paBHbI: mo, ml .. m 2 . TpeHlle\l,
MaccaMII 6noKoB H HIiTeH npeHe6pe"lb. Haiiul YCKopeulle TeJla
mI' Hccne.l1onaTb B03MO>KIlbl:e CJIYQall.
11.2. Ha CTOJle Jle>KIIT .l1OCKa MaccoH M = 1,1 Kr, alia .l10C-
Ke - rpY3 MaCCOH m == 1,9 Kr. KaKYIO cnny F "Y>KHO npn-
JlO>KIITb K .l1OCKe, IJTOt)bI: OHa Bbl:CKOJIb3I1YJla 113-no.l1 rpY3a?
K03<l><tmI.lIlCHT TpCIIIIH MeiK;J,y rpY30M H .l1OCKOH III = 0,23, a
Me>KJI.Y Jl.OCKOH H CTO.-W:'.I III = 0,52,
11.3. Ha TeJIO !'.IaCCOH m = 2,0 Kr,
HaXO.l1HIaeeCSI lIa lIaKJlOHHOii nnOChO-
CT,I C }'rnoM HaKJIOna a = 30°, .l1eHcT-
ByeT CIIJIa F = 12,5 II napaJlnenbIlO
lIaKnOllIloii nJIOCKOCTII (pIlC. 74). Ko*
4JIIl.llleHT TpeHiUl MCiKJl.Y TcnOM II II a-
KnoHHoii nnOCKOCTblO l = 0,20. On pc-
.l1CmfTb YCKopeHllc Te.1a II CII.1Y TpC-
II11H.
/
Pile 73
48
3aJJ.a"lH K r JJaBC II

11.4. )l(ecTKHH HeBeCOMblH CTepJKeHb C ManeHbKIIMH wapl!-
KaMH MaCCaMH m 1 H m l Ha KOHl..laX HaXO;!.HTCR BHYTPH r.lJa)l.KOH
c<t>cPU'leCKOH nO.IJOCTH H COCTaBnReT yron a < 11./2 C ropU30HTOM.
5ylI.)"lH OTnyxnell, crepJKeHb )l.BHJKeTCR B BepTHKanbHoH n.1OC-
KOCTH TaK, 'lTO wapHKH Bce Bpe:m KacalOTCR CTeHOK nonOCTH.
PacTRHYT H.1H CJKaT CTep}l{eHb B MOMeHT, KOr)l.a 011 ropll30H-
TaneH? C KaKOH CHJlOH? .l1.nHHa CTepJKHR paBHa pa,'T.uycy nO.lJo-
CTII. JpeHHR HeT.
n.5. TeJIO CKarbIBaeTCH no BIlYTpeHHeH nOBepxHocTH no-
nyc<t>cPbl C BblCOTbl R (pHC. 75). OAHa nOJlOBIIHa nonyapePLl
a6COJIIOTHO rJla.zI.KaH, BTopaH - wepoxoBaTaH. Ko3<M>lfl..llleHT

I I
::L/ I I' I I
Pile. 74
Pile i5
TpeUHH Me}K.l!.Y TeJIO:\I H nOBepxHocTblO .... = 0,15, Onpe.lleJlHTb
yeKopeHue Te.na, KaK To.1bKO 0110 KOCHerCH WcpoxoBaToli no-
BepxHocTH.
11.6. lIlapHK MaeeOH {Tl = 50 r BblJleTaer 113 CTBOJIa Hrpy-
We'lHOH nYWKJf, H8KJlOHeHHOrO K ropH30HTY nq.n; }TJlO:\1 a =
,--: 45°, co cKopoeTblO V o = 5,0 M!C OTHoeHTe.'1bHO nywKH, BHa-
qane nOKOIIBWeH:CR Ha r.'1a..'l.KO1 no.'1Y. no;!. KaKIIM yr nOM f3
K ropH30IlTY BblJlCre.n wapllK? KaKO-
Ba CKCpOCTb oTAa'HI nYWKH, Macca
KOTOpOll M = 150 r?
11.7. H a nYTH Te.na Maccoii in =
= 2,0 Kr, CKOJlb3Rxnero no rna)l.KOi\ty
rop30llTanbHoMY CTOJlY, HaXO)l.lfTCH
He3aKpenJleHHaH cropK<U BblCOTOH
H = 2,0 M. np<>4>Hnb ropKH H306pa>l\eH lIa pHe, 76. npll
KaKoH MHHIIMa.1bHoH CKOpOeTiI Te.nO CMOiKeT oeTaTbCR Ha rop-
Ke? .Maeca ropKH M = to Kr. C'lHraTb, 'ITO TCJIO Jl,BH}KeTCH,
Ha OTpblBaHCb OT cropKII». Te.no Ha cropKe», a T8KJKe crop-
K-» no CTOJlY CKO.lJb3RT 6e3 TpeHHH.
II.S. K Te.1Y MaeCO" m b pacnOJlOw.eHl=aMY na rJla.'1.KO\f ro-
pH30HTanbHO:\I CTo.'1e, nplf!3R3aHa BepeBKa, nepe6poweHHaH
'lepe3 HeBeeO:\lb!ii 6noK. 3a CBHC8IOlilliH KOHel..l nepeBKII l..lell.1R-
eTCS! 06c3bHHa Maecoa m z , KOTOpast, nepe6HpaH BepeBKY,
L1"pe.\fHTCH CCTaBaTbCR H3 O;1.HOrl BLIeOTe. !aK }l.onro eil 3T0 YJl.a-
A--
Pile. 76
49

eTCH, eCJIH MaKCHMaJIbHaH MOrn.HOCTb, pa3BHBae\laH OOe3bHHOH,
paBHa P?
11.9. KocoHaBT MaccoH M = 100 Kf HaXO.D.HTCH Ha no-
BepxHocTH acrepoJl.D.a, HMelOrn.ero cJ>oPMY wapa pa)tHycoM R =
=1,0 KM, H .D.ep>KHTB pYKax K8MeHb MaccoH m = 1,0 Kf. C
KaKOH MaKCHMaJIbllOA ropH30HTanbHoH CKOpOCTblO OTHOCH-
TenbHO acrepoJl.D.a KOCMOHaBT MO>KeT t>pOCHTb KaMeHb, He pHC-
KYH, "ITO ca\l CTaHeT cnYTHHKOM acrepOH.D.a? nnOTHOCTb Bew.e-
CTBa OJl.HOpO.D.HOro aCTepOH)1a P = 5,0 r/CM 3 .
f J1 A B A III. CTATHKA
 10. PaoHooecHe MaTepHaJTbHOH TO"lKH
10.1. Ha pHC. 77 nOKa3aHbI nHTb pa3Hblx CJIY'laeB nOKOH-
rn.erOCH TeJIa: a) TeJlO nOKOHTCH Ha ropH30HTaJIbHOA nOBepxHo-
CTH; 6) TeJlO nOKOHTCH Ha HaKJIOHHOH nJIOCKOCTH; B) TeJlO nOA-
BeweHO na HHTH; r) TeJIO nO)1,BeWeHO Ha .nByx HHTHX; JI.) Teno
nO.ll.BeWeHO Ha KpOHwTeHHe. B K8>K)l.OM CJIYlJae YKa3aTb H Ha-
pHCOBaTb CHJIbI, npHnO>KeHHble K TeJlY. YKa3aTb npOHCXO>K.D.e-
HHe Ka>K)l.OH CHJIbl.
- 10.2. K .D.BYM .D.lrnaMoMeTpa\! nO.D.BeweH rpy3 MaccoH m =
= 1,0 Kr (pHC. 78), qro nOKa>KeT Ka>K)I.blH H3 .D.HHaoMeTpoB?
.Maccy HH>KHerO )l.UHaMOMeTpa He YIJHTblBaTb.
01
o

,'/Q;:0' 
M  m
Tv
PHe. 77
m
PHC. 78
- 10.3. fpY3 MaccoH 2,0 Kr nOABeweH H3 .D.HHaMOMeTpe.
CHJl3Y rpY3 THHYT C cnno" 10 H. qTO nOKa3bIBaeT Jl.HHaMO-
MeTp?
10.4. Ha ropH30HTaJIbHOH nJIOCKOCTH ne>KHT rpY3 MaccoH
ml = 5,0 Kr, CBH38HHbIH C nOOIl\blO BepeBKH, nepeKHHYToli
llepC3 MOK, C rpY30\! MaCCOH mz = 2,0 Kr (pHC. 79). Onpe,!le-
nHTh CUJIY HaTH>KeHHH nepeBI<H H cuny .D.aBJIeHlUi rpY38 "fac-
COH ml H3 n.'IOCKOCTb.
50
1-.__

- to.5. Onpe.lle.rIHTb CHJ1Y HaTst>KeHlfst BepeBKIf, CIIJ1Y .113BJ1eHllst
rpY3a lIa lIaKJlOllllYIO nJ1OCKOCTb. CHJIY TpellHH Mf)K){y rpY30M H
nnOCKOCTblO (pHC. 80). m 1 = 2,0 Kf, m z = 1,0 Kr. a1 = 30",
a l = 90 0 .
10.6. K KOHLI.aM HHTII, nepeKHHYToH 'lepe3 J],Ba 6noKa, no.ll-
BellleHbI rpY3b1 MaCCaMlI m 1 = 60 f H m. = 80 r (pHC. 81).
KOf.lla K HHTH nOJ],BecHJIH TperHH rpY3, TO yrOJI, 06pa30BaHHblif
HHTHMH, CTan a = 90 0 . Onpe.lleJIHTb Maccy TpeTbero fpY3a.
10.7. K KOHLI.aM HHTlI, nepeKHuYToH 'lepe3 .llna 6JloKa, no.J..
BeCHnH .llB3 O.llHHaKOBblX rpY3a MaccoH m1 = m. = m = 5,0 Kr
KIDK.llbIH (pHC, 81). KaKou rpY3 HaAo nOJ],BecHTb K HHTH Me>K){y
6JIOKaMH, 'lT06b1 npH paBHoBecHH YfOJI a 6blJI paneH 120"?
_ 10.8. rpY3 MaCCOH 15 Kf, nOJ],BeWeHHblH Ha npoBoJl0Ke, OT-
KJlOHSIeTCH Ha yron 45 0 OT BepTHKaJlbHOrO nOJImKeHHH CHJIOH
F, .lleHcTBYIOLLI.eH B ropH30HTanbHoM
HanpaB.'leHliH. Onpe.lleJIliTb 3T}' CliJIy H
CHJlY T HaTSIeHIiSi npOBOJIOKH.
\( 10.9. npOBOJIOKa, Ita KOTOpOH BH-
CIiT rpy3 MaccoH m = 20 Kf, OTBO-
.llI1TCSI B HOBoe nOJIO)!{eHlie CHJIOH
F = 147 H. .lleHcTBYIOLLI.eH B ropH30H-
TanbHOM HanpaBJIeHHH. Onpe.lleJIliTb
CliJIY HaTSI>KeHHH npoBonoKH Ii yroJI OT-
KJIOHeHHH npOBOJIOKH OT BepTHKaJIli.
- 10.10. rpY3 MaccoH 10 Kf nO.llBeuIeH H3 KpoHwTei'me ABC
(pRC. 82). Yron Mf)K.ll}' fOpR30HTaJIbHblM CTep>KHeM AB H no.ll-
KOCO:\I BC paneH a = 60 0 . Onpe.lleJIlITb CIIJIbI, .lleHcTBYIOLLI.Re
Ha CTep>KeHb II nO.llKOC.
'. 10.11. 4e\1Y paBeH Bec rpY3a, BnCSlLLI.erO Ha KpoHllITeHHe,
ec.nH CHJIa, C KOropOH paCTSlrHBaerCH ropn30HTanbHblii cTep-
)ReHb, F = 90 H. YfOJI Me>K){y CTep>KHe\l If nO.'J,KOCC\t a =
= 45 0 (CM, pHC. 82).
PIIC. 79
PIIC. 80
m,
Pile. 81
51

1..12, YnHIlHblH q,oHapb MaccoH 20 Kr BUCliT Ha .lI.BYX
CTep)KHHX, npHKpenneHHblx K creHe, H3 paccToHHUU 60 C'd
.1.pyr OT .D.pyra (pHC. 83). .lJ.mma CTep>KHeit: AC = 90 CM,
BC = 120 CM. OnpeAe..1lfTb CH.'IbI, .n.eiiCTByro1.U.He Ha CTep>KIIH.
1'.13. K KOHLI.aM HHTH. nepeKuHYTOH Qepe3 .D.Ba 6noKa. no,'{-
BellleHbI rpY3b1. Kor.n.a MeJK.n.y 6nOKaMH (puc, 84) nO.D.BeCUnH
rpY3 MaCCOH 150 r, yro:r ABC CTaJI paBeH 30° II yrOJI BAC paBeH
yrny BCA. Onpe..1e.'IHTb MaCCbI rpY30B ml H mz.
PIIC. 82
PHC. 83
PHC. 84
"
1'.14. rOpJf30HTa.'lbUaH aHTeHHa npuKpenneHa K MaqTe
(pllC, 85), Ha KOTOpyro OHa .n.eiICTBYeT c cunOH 750 H. no.ll
KaKUM yrnoM K ropu30HT}' .n.OJI>KHa" .n.eHcTBoBaTb OTTSI.>KKa C
.il.pyroH CTOpOHbI MaQTbl, IlTo6b1 MaqTa He my naCb U CU.1a
.llaBneHUH Ha ee OCHOBaHJfe COCTaBJIHna 1,0 KH?

PHc.85
A
20l(z
PHC. 87
11.15. rpY3 J,faccoil 60 Kr BHCUT Ha .D.BYx TPocax (pllC, 86),
npulle'd yrOJI ACB paBeH 120°. Onpe.ll€.'!uT CHJIbI, .lleHcTBYIOe
Ha TpOCbI. YroJI OBC paBeH 90°.
1'.16. BepeBKa npnBSl.3aHa K KplOllK}' A If nepeKIiHyra qe-
pe3 6JIOK C (puc. 87). K BepeBKe B TOqKe D npuKpenneH rpy.J
Maccoii 20 Kf, npHqeM TOqKa D He MO>KeT nepeMC1.U.aTbCSI. no
BcpeBKe. KaKoH MaCCbI rpY3 CJIe,n.yeT npHKpenUTb K KOHLI.Y
Bepel3KH, qTo6b1 CIIJIa lIaTHlKeHUH BepeBKU H3 YllaCTKe -AD
52
PHC. 86

6b1J1a B .l1Ba pa3a OOJlblUe, lie\! B OCTanbHOU ee qaCTH, H yrO.'1
ADC = 90°?
1'.17. C KaKoH MHHHManbHoH CHJlOH F, HanpaBneHHOH
ropH30HTanbHo, HY>KHO npH>KaTb nnocKHH 6PYCOK K CTeHe,
QT06b1 OH He COCKonb3HY.'I BHH3? Macca 6PycKa m = 5,0 Kf,
Ko3<W>HllHeHT TpeHHH MeJK.u.y CTeHKOA H 6PYCKOM J.L = 0,10.
1'.18. <l>oHapb MaccoH M = 10 Kr nO.l1BeWeH HCIA cepeJ1.H-
HOH ynHllbI WHpHHOA 1 = 10 M Ha Tpoce, .l\OnYCTHMaH CHna Ha-
TH>KeHHH Koroporo T = 500 H. KaKoBa .u.OJl>KHa 6b1Tb BbiCOTa
KpenneHHH KOHllOB Tpoca, ecJIH TOIIKa
KpenneHHH 40HapH HaXO.l\HTCH Ha BbI-
COTe h = 5,0 M?
I.. IS. MO>KHO nH H3THHYTb rOeH-
30HTanbHblH TpOC TaK, IIToObi OH He
npOBHcan?
1..2.. .lJ.Be npY>KHHbI C K03<lxlJUllHeH-
TaMH ynpyrocTH k 1 H k l Coe.u.HHHIOT O.l\IiH
pa3 nocne.u.oBaTeJlbHO, .u.pyroH pa3 na- PHe. 88
panneJlbHO. KaKoH .l\o.'DKHa 6b1Tb :>Ke-
CTKOCTb npY:>KHHbI, KOTOpOH MO>KHO 3aMeHHTb 3TY cHcTeMY
H3 .u.BYx npY>KHH?
k 1'.21. Ha HaK.llOHHOH nnOCKOCTH C yrnoM a = 30<' npH
OCHOBaHHH nOKOHTCH TeJIO MaCCOH m l = 2,0 Kr, CBH3aHHoe
C nOMOlllblO HHTIf, nepeKHHyrofl Qepe3 o.nOK, C TeJIOM Maccoil
m z (Cf. pHC. 42). TpeHue OTC}'TCTBYeT. Onpe.l\eJlHTb Maccy
BToporo rpY3a H CHJlY, .l\eHcTBYIOll{YIO Ha OCb 6J10Ka.
'"Ll'.!I. CllcTeMa rpY30B MaccaMH mlo ml H m3 (pHC. 88)
HaXO.l\HTCH B paDHoBecHH. HaHTH Maccy m3 H CHJIY .u.aBnellHH,
apOll3BoJI.HMoro MaCCOH ml Ha HaKnOHHYIO nnOCKOCTb, eC.;m Mac-
CbI ml' m l H yroJl a, KOTOpblH COCTaBJ1HeT HaK.1l0HHaH n.IlOCKOCTb
c ropH30llTOM, H3BecTUbi. TpeHHe OTCYTcTByeT,
 11. PaBHoseclle TBepJi.OrO Tcna
11.1 Ha CTCp>KeHb .lleHCTB)'IOT .u.Be napan.'IeJlbHble clf.'Ibi
F] = 10 H H F z = 20 H. PacCToHHHe MeJK.I\y .1lHHHHMH .u.eiI-
CTBHH CHn 1 = 1,2 M. Onpe':;;eJIIITb, B KaKOM MecTe H KaKYIO
cuny HY>KHO npHnmKHTb K CTep>KHIO, IIT06b1 OH Haxo.u.HnCH B
paBHoBecHH.
11.2. OnpeJ.eJlHTb paBHo.u.eHCTBYIOIj(YIO .l1Byx aHTlmapan-
JIeJ[bHbIX CHJI FI = 15 H H FI =c6QH. PaCCTOHHlte Me>K.n.y JIII-
HHRMH .u.eikTBHH CHn 1 = 90 CM':\ '-"
11.3. K CTep>K1l1O WIHHOH I = 120 C\I npHnO>KeHbI TPH
napa.'I!Ie.'IbHblX CHJIbI O.l\ltHaKOBOro Han3BJIeHlHl: y JIeBOra
53

J<OHua FI = 30 H, B cepe.n.IIHe FI = 80 H, Y npaaoro KOHua
F 3 = 90 H. LIe\1Y paBHa paBHo.n.eHcTBYIOll{.aH 3THX CHJI? r.n.e
JIe>KIIT TOl/Ka ee npHJIO>KeIlIlH?
11.4. 113.n.BYX aHTHnapaJIJIeJIbllblX CIIJI OOJIbllJaH CH.IIa paBHa
30 H. HaUTIi MeHbWYIO CHJIY H paBHo.n.eiiCTBYIOll{.YIO CIIJIY, eCJIIi
OTIlOllleHlle paccToHHHU TOl/eK npHJIO>KeIlHH COCTaBJIHlOlllHX
CHJI OT TOIJKII npHJIO>KeHHH paBHo.n.eHcTByro'u.eii paBHo 0,4.
11.5. Ha nOBepxHocTH BO.zu,r nJIaBaeT ,l\epeBHHHaH nJIac-
TIIHKa, K KOTOpOH npHJIaraeTCH napa CIIJI B ropll30HTaJIbHOM
lIanpaBJIellllll. OTHOCTe.nbHO KaKoii TO'lKH nOBOpalJHBaeTCSI
nJIaCTIIHKa?
11.6. ABTOM06I1JIb Maccoii M = 1,0 T B'be3>KaeT Ha ropll-
30HTaJIbHblU MOCT .n.JIIiHoA L = 10 M. Onpe.n.eJIHTb, C KaKHMH
CIiJIaMIi aBToM06HJIb .n.aBHT Ha onopbl MOCTa, Haxo.n.HCb Ha pac.
CTOHHHII I = 1,0 M OT onopbl. nOCTpmlTb rpaqJIIK 3aBllCliMOCTII
H3MeHellllH CIIJIbl .n.aBJIeHHH HB OJlHY 113 onop OT paCCTOSlHHH .n.o
Hee.
11. 7. Tpy6a Maccoii M = 1,2 . 1 Q3 Kr JIe>KHT Ha 3e),tJIe.
KaKoc YCIiJIlie lIa)l.O npllJIO>KIITb, 'lT06b1 npllno.n.IIHTb KpanoM
Tpy6y 3a O.n.HH H3 ee KOHUOB? C KaKOH CHJIOH .n.eikTByeT .n.py-
rOM Koneu Tpy6bl lIa 3eMJIIO?
11.8. ABTOM06HJIb MaCCOH M = 1,35 T H\leeT KOJIeCHYIO
6a3Y .n.JIHIIOii L = 3,05 M. ll.eHTp TH>KeCTH pacnOJIo>Ken Ha
paCCTOflHIIII I = 1,78 M n03a.n.H nepe.n.lleii OCII. Onpe.n.eJIIITb CH-
JIY .n.CiiCTBY10Ill.YIO Ha Ka:>K..1.oe 113 nepe.n.HIIX KOJIeC H Ha Ka>K}lOC 113
33}lHIIX KO.T\CC CO CTOpOHbl ropll30HTaJIbHoi'1 nOBepXHOCTII
3e\tJIIi. . I
11.9. CTep>KeHb .n.mtHoi'1 I = 10 CM nOJ],BeWeH 3a KOHU 1 .>! lIa
}lBYX npY>KHHaX >KeCTKOCTblO k 1 = 98 H/cM H k 2 = 3k l . Ha
KaKOt pacCToHHIIH OT uellTpa CTE:p>KHH II KaKOU MaCCbl lIa}lO
nO.iJ.BCCHTb K CTep>KHIO rpY3, 'lTOObl CTep>KeHb CMeCTIiJICH Ha
BblCOTY t!!h = 1,0 CM II OCTMCH BliceTb rop1l30HTaJIbHO? Mac-
coo CTCP}!(HH npeHe6pe'lb.
11.10. H:1. .n.OCKe }lJIIiHOH I = 4,0 \t II MaccoH M = 30 Kr
Kal/aIOTCH }lBa MaJIbl/IIKa MaCCaMIt ml = 30 Kr IJ m2 = 40 Kr.
f.n.e }lO'l:>Klla 6blTb y }lOCKIi TOl/Ka onopbl, eCJIIi MaJIbl/IiKII CH.llHT
Ha KOHuax }lOCKH?
11.11. no HaKJIOnHOii n.'IOCKOCTH J!..tlllHOii I = 5,0 M H Bbl-
COTO}i h = 3,0 M nO}lHlt\faIOT rPY3 Maccou m = 200 Kr, npn-
KJI8,.'l,bIBaH CIIJIY F = r,5 KH. Onpe.n.e.nHTb KnJI. HaKJIOHHOii
IlJIOCKOCTIt. LIetY 6blJI ObI paBeH DbIllrpblW B clI.'Ie B CJIYl/ae OT-
CYTCTBIIH TpeHlIH?
11.12. O.n.UH KOHeu TBep.n.oro CTep>KHH llJapUHpHo 3aKpenJIen
B TOl/He C, K .n.pyroMY KOHLlY A npllhpen,'leH ImHeu BepcL \H,
54
I

nepeKllHyroH lIepe3 ABa MOKa H 3aKpenJIeHHOH APyrHM KOHllOM
Ha 6anKe (pHC. 89). Ha paCCTOflHHH 1 = 0,60 M OT roliKIl A Ha
CTep>KeHb J1ellCTBye-r CHJIa F = 75 H BepTHKanbHo BHH3, J1JISI
} paBHoBeUIHBaHltSI Koropoii nOJ1BerneH K nOJ1BIf>KHOMY 6JIOKY
rpY3 Maccoii m = 10,25 Kr. OnpeJ1eJ1HTb J1JIHHY pbllJara H cHny
AaB.I\eHHSI Ha rnapHHp C.
I I .13. lllar BHHTa J10MKpaTa h = 0,50 CM, J1nHH8 PYKOHTKlt
1 = 30 CM, CHna, J{eiiCTBYIOUlaH Ha PYKOSI'rKY, F = 120 H,
Knll J10MKpaTa 1] = 45%. KaKYIO CHJIY pa3BHBaeT J10MKpaT?
11.14. fpY3 MaccoH M = 2,1 T nOJ1HHMae-rCfI C nOMOUlblO
BopOTa. KaKafi CHJIa npltJIaraeTCfI K KOHllY PYKORTKH J1.'IHHOll
Pile 89
PIIC. 90
1 = 50 CM, eCJIH rpY3 nOJ1I1HMaeTcH lIa BblCOTY h = 15 CM 3a
BpeMfI, B TelleHHe KOTOpOro PYKoHTKa J1eJIaeT n = 10 060pOTOB?
TpellHe He YIIHTblBaTb.
II. I 5. KaKYJO CIfJIY IIY>KIIO npUJIO>KHTb K KOlIllY PYKOflTKl1
J1Hqxpepellllllanblloro BOpOTa, IIT06b1 YJ1ep>KaTb rpY3 MaccoH
M = 50 Kr? .lI.nHlla PYKOflTKH 1 = 98 eM, paJ{HYC 6oJIbUIoro
UHnHHJ1pa BopOTa '1 = 20 CM, paJ1HYc Manoro 's = 10 CM
(puc. 90)
11 .16. KaKoB AOJI>KeH 6b1Tb Ko34xPHUHeHT TpellHfI J{JIfi TOro,
'iTo6b1 KJlHII, 3aKonoliellHblH B 6peBllo, lie BblCKaKHBaJI H3
lIero? Yron npH BepUIHHe KJIHHa a = 30<'.
11 . I 7. .lI.nH TOro 1ITo6b1 TeJlO HaXOJ{HJIOCb B paBlloBecHH, He-
06XOJ{HMO H J1OCTarollllo BbmOJIllellHH J1BYX YCJIOBHH: cYMMa
CHJI, J1eHCTBYK>lUHX Ha TeJlO, paBHa HynlO H eYMMa MOMeHTOB
3THX eHn paBHa IIY.'IIO. B KaKHX CJIYllafix npH paceM9TpeHHH
paBHoBeCHH TeJIa J{OCTaTO'lHO HCnOJIb30BaTb OJ{1I0 H3 3JHX YCJIO-
BH3?
11.18. Ha nnocKoe TeJlO, H\felOlUee «PoPMY paBHocToPOHHC-
ro TpeyrOJIbHHKa, ..'I.eHcTBYIOT ABe paBHble CHJILI F 1 = F 2 =
= 10 H. CIfJIbI npH.']O>KeHbI K BeplllllllaM Tpeyro1bHlfKa II
55

.i1:eHCTBYIOT B;J.O.1Jb CTOpOH TpeyroJlbHHKa (pIlC. 91, a-z). Ka.
K)'IO CIIJlY F s IIY>KHO npIlJlO:>KIITb K TeJIY, 'lTOW 0110 lIaXOJlII-
.-WCb B paBHOBeCJJH? OnpeJle.1l1Tb reOMeTplllJecKoe MeCTO TOqel(
npIlJlO:>KeHHH CIIJlbI F s.
11.19. K BepTIIKaJlbHOH rJla)lKoii CTeHe Ha BepeBKe ,lI)IHHOti
I nO,'].BemeH map Maccoii m (puc, 92). KaKoBbI CHJla HaTH>KeHUH
BepeBKlI II CIIJla JlaBJIeHHH mapa lIa CTeHKY, eC"'1f ero paJlHyc
paBeH R. TpeHHeM 0 CTeHKY npeHe6peQb.
II} & 5J -r, B} ' & J 
-
-- F,
fj - - --
 "ili F,
PRe. 91
11.20. BpYCOK B E':f,'].C napaJIJleJIemme;J.a co cropoHaMH a 
= 42 CM H b = 24 CM (pIlC. 93) npllCTaBJleH K a6COJllOTHO
rJIaJlKOH CTeHe H nOJlBemeH Ha HHTII, npHKpenneHHoH OJlHHM
KOHUm.1 K 6PYCKY Jla paccToHlU1H 1=,12 CM OT CTCHbI, If JlPY-
ruM hOHUOM K CTeHe. Onpe.u.eJIJITb JlJIIIHY HIITII L, ecnH 6py-
COK npHiKaT K CTeHe BCe" nOBepxHocTblO.
11.21. lllap MaCCO" m = 4,9 Kr OmlpaeTCH Jla JlBe rna.llKHe
nJIOCKOCTH, 06pa3yroUlHe yroJI, npHlleM neBaSl. 06pa3yeT C
roplf30HTOM yroJl a = 35°, a npaBaH - yrOJl  = 20°. Onpe-
PIIC. 92
PHC. 93
JleJlHTb CHJlbI, C KOTOpblMlf map .llaBIIT Ha nnOCKOCTH. PemHTb
3aJlall YMH cnoc06ar.m: 1) pa3J10>KelUfeM CIIJI; 2) npaBHJlO!\I
OMCHTOB.
11.22. JIeCTHlfua Maccon Af H .llJIHHOn I npllCJIOHeHa K
rJl2;1.KOH BepTHKaJIbllOii c-reHe no.ll yrnoM a. lI.eHTp TIDKecTH
neCTHIfUbl HaX0.D.IfTCH Ha BhlCOTe h OT nona. 4eJIOBeK TSlliCT
56

_";THIIUY 3a cepeJl.IIHY B ropn30HTaJ1bHmi Hanp3BJleHllIt C
1.10ii F. Ka Koii Mil JIIfMa.1Jb HOM Be.'III'lllllbI J1.0!DKn3 6b1Tb 3T3
'la, 'lT06b1 qeJlOBCK C'for OTO.'lBIIHYTb BepxmIii KOHeu J1eCTHIlUbI
ur CTelll>l? TpeHlle 0 n0.1 HaCTOJlhKO BeJIlfKO, liTO HII>KHllil KOHel1
,l€CTlIIIUbI He CKO.'lh3I1T.
11.23. Do.!!, KaKIIM :.nU!lfM3.'lhHbIM yrJlOM K ropIf30HTY MO>KHO
npllCJIOHllth K BepTlfKanbHoii r.'laJ1.Koii CTeHe O.ll.HOpO.ll.HYJO J1eCT-
"IIUY? Ko34$IIUlleHT TpeHlHI MC>K.lI.Y JIeCTHHueu It nonOM J.1 =
= 0,40.
11.24. CTep>KeHb AB Maccoii m = 5,0 Kr npllKpenJIeH K
Heno;J.BIf>KIIOU onope rnapHHpoM A If MO>KeT Bpaur.aThcH B Bep-
TIfKaJlbHOH nJlOCKOeTH (pltc. 94). K KOHUY B
CTep>KHH nplfKpenJIeHa HIfTh, KOTopaH nepe-
KHHYT3 'lepe3 6.10K .c, H K - Heu nO.ll.BerneH
rpy3 MaceOH m 1 = 2,5 Kf. Celt 6.noK3 C II
mapllHpa..1 p3eno.'10>KCHbI Ha O;J,HOH BepTIt-
KaJlIf, npll'lCM AC = AB. DpH KaKOM yrJIe
a Me>K,!!.Y CTep>KHeM II BCpTltKaJlbJO ClfeTeM3
6y.ll.cr B paBHOBeCltH? K3KaH ClfJl3 ,!I.('uCTByeT
Ha CTep)f{CHh n T01lKe .4? KaK nanpaBJIeHa
3T3 CIf!la?
11.25. Ha 3efJle ne>KaT nnJIOTHYJO .lI.B3
O,!!.IfHaKODblX opeBHa UIfJIlfH.lI.plt'leCKOH 4x>P-
'.'!>l. CBepxy K.IJ3.l1.YT TaKoe >Ke 6peBHo. DpH
KaKO:\f Ko3$PIflJ.HeHTe TpeHIIH Me>K.lI.Y HJlMH OHH He paeKaTHTeH
(no 3eMJ'Ie 6peBHa He CKO!lh3f1T)?
11 .26. Koneco pa;J.lfycoM R If MaCCO" .m CTOHT nepc;J. CTY-
ne1lbKOU BhlCOTOU h. KaKYK> H3It'ofeHhIlJYK> ropU30HTaJIhH}1O
CIfJlY F Ha.ll.O nplfJlO>KlfTh K OCH KOJIeCa, WiT06b1 OHO Mor .'10 no.ll.-
I!<JThCSI Ha cTyneHbKY? TpeHlteM npeHe6pe'lh.
11.27. KaKYlo MltHIfMaJlhHYIO ropH30HTaJlhHYK> CMY HY>K-
HO nplfJIO>KltTh K BepxHeMY pe6PY Ky6a MaccoA M. H3XO.ll.HlIJ.erO-
CfI H3 ropn30HT3J1bHoA nJlOCKOCTH, tlT06b1 nepeKHHYTh ero
'lepe3 pe6po? nplt K3KO\f K034$Hl1HeHTe TpeHHSI MeJK)1Y K)'OOM
If nJlOCKOCTblO MO>KHO nepeKHHYTh Ky6?
11.28. K3K .'lerrle C.lI.SHHYTb C MeCTa >KeJIe3Ho.ll.OpO>KHhlH Ba-
rOH: npllJIarafi ClfJIY K Kopnycy BarOHa HJlH K BepxHeA WiaCTH
OOO,!l.3 Ko.IJCca?
11.29. npn pe3KO!\1 TOpMO>KeHHIf 3BTOMOOltJIfi ero nepe.ll.OK
onycKaeTcfI. Doqe:'IY?
11.30. TfI>Ke.'loe 6peBHo BTflfllBaJOT sBepx no naKJlOHHOH
n.l0CKOCTII C nm.IOlIJ.blO .lI.BYX napaJlJIC!lhHblX K3HaTOB, 3aKpen-
lIeHtlhIX, KaK YK33aHo n3 pllC. 95. Macca 6peBHa M = 400 Kr,
!!'rcoTa HaI<.10HII(..1 nJlOCKOCTH h = 1,0 \I. )I..'lIfH3 I = 2,0 M,
B
PHC. 94
57

KaKYIO cHny F HY}KHO npHnO}KHTb K KaiK.:I.OMY H3 KaHaTOB,
lIT06bI BTHHYTb 6peBHO? PelllHTb 3a.l1aIJY .l1B)'MH cnoc06aMH.
11,31, KaKoH .l1JIHHbI KOHeu. HMO oTpe3aTb OT O.l1HopO.l1HOrO
CTep:>KIIH, IJTOObi u.eHTp TH>KeCTH era nepeMecTuncH Ha 10 CM?
11.32. lI.ITaHra COCTOHT H3 CTep>KHH .l1JIJmoH 1 = 50 CM,
MaccoH M = 2,0 Kr H .l1Byx cKpenneHHbIx C HHM wapoB paJ{uy-
caMH Rl = 3,0 CM H Rz = 6,0 CM
II MaccaMH m 1 = 1,5 Kr H m 2 =
= 12 Kr HaHTH u.eHTp TH>KeCTH
WTaHrn. JO
10
20
40
0 /f0 "$0
2.0
10
PIIC. 95 PIIC. 96
11.33. llBa wapa, aJIIOMHHHeBblH H u.UHKOBblll, OJ{HHaKOBO-
ro 06'beMa CKpenJIeHbI B TOIJKe KacaHHH. HaHTH u.eHTp TIDKeCTH.
11,34. Ha BepeBOIJHOA neTJIe ypaBHoBeweH CTBOJI J{epeBa,
OJ{HH KOHeu. KOTOporo TOHbllle J{pyroro. ECJIH pa3pe3aTb J{epe-
BO no JIHHHH OXBaTa ero neTJIeH, TO KaKoii KOHeu. OK8>KeTCH
6oJIbwero Beca - TOnCTbIH HJIH TOHKHii?
11,35. JIHlleHKa J{JIHHOii 1 = 1,0 M BbI.l1BHHYTa 3a KpaH cTO.Tm
Ha IJCTBepTb J{JIHHbI H .l1aBHT TOJIbKO lIa KpaH CTOJIa, KorJ{a Ha
cBeWHBalOl1.lHikH KOHeu. ee nOJIO>KeH rpY3 m 1 = 250 r. "leAfY
paBHa Macca JIHHeHKH? Ha KaKYID lIaCTb
JJ)JHHbI MO>KHO BbIJ{BHHYTb JIUHeHKY 3a
KpaH CTOJIa, eCJIH Ha cneWHBalOl1.lHHCH KO-
Hell. nOJIO>KHTb rpY3 m z = 125 r?
11.36. HaATH u.eHTp TH>KeCTH O.l1HO-
pOJ{HOH nnaCTHHKH, pa3MepbI KOTOpOH YKa-
3aHbl Ha pHC. 96.
11.37. HaHTH u.eHTp TIDKecTH OJ{HO-
pOJ{HOH nJIaCTHHKH C Bblpe30M. pa3Mepbl
KOTOpOH YKa3aHbI Ha pHC. 97.
11.38. C nOMOl1.lblO JIHHeilKu H KapaHJ{allia Onpe.lleJIHTb
u.eHTp TH:>KeCTH O.llHOpO.llHOH nJ1aCTIIHKH (pHC, 98).
11.39.11oKa3aTb, 1J:TO u.eHTp T.H>KeCTH nJIOCKOrO OJ{HopO.llHorO
TpeyrOJIbHHKa lIaXO.l1HTCH B TOIlKe nepeCeIJeHHH MeJ{Hau.
11.40, C nOMOW,blO JIJfHeliKH H KapaII.llaWa lIaliTH u.emp
TH>KeCTIf O.llHOpOJ{HbIX nnOCKUX <l>Hryp (puc, 99): a) napaJI'Ie-
JIOrpaMMa; 6) Tpaneu.uH; B) IJeTbipexyrOJIbHHK3.
20 1 r-;o-l
lU
o JO
PIIC, 97
58

11.41. 113 o.n.nOpO;J.HOH KpyrnoH nnacTHHbJ pa.nHYCOM 9,0 CM
Bblpe3anH Kpyr B,Z!.Boe MeHbwero pa.n.Hyca, KacalOwerOCH KpaH
nJI8CTHHbl. HaHnl LleHTp Tfl>KeCTH nOJlY'leHHOH nJIaCTHHbI.
11.42. 113 O;I.HOpOJJ.HOH Kpyrnoii nnaCTHHbI pa.n.HYCOM R
Bbl'pe3aJIH KBa,Z!.paT, ,Z!.HaroHanb KOropOro COBna,Z!.aeT C pa,Z!.HYCOM
II paB Ha eMY, HaiITH LleHTp TSUKeCTII nOJIY'leHHOH nJIaCTHHbI
o
a]
/
51
/ Q
8}
(]
PHC. 98
PHe. 99
11.43. 113 nJIocKoii KBa.npaTHoii nJIaCTHHbI CO CTOpOHoii a
BbIpe3aH: a) KBa,Z!.paT CO CTOpOHOH a12; 6) Kpyr .n.Har.leTpoM a12.
HauTH LleHTp TSUKeCTH nOJIY'leHHblX qJHryp (pHC. 100).
11.44. .f,Z!.e HaXO,Z!.HTCS! LleHTp TS!>KeCTH Ky6a, H3 KOTOpOro
y,Z!.aJICH Ky6HK C peopoM, paBHblM a/2 (pHC. WI)?
11.45. Ha .non:e ,Z!.JIIlHoii 1 = 60 CM CTOHT cnnOlilHoii LlH-
.'Hm.n.p, y KOToporo BblCOTa B TPH pa3a 60JIbwe .n.HaMeTpa OCHO-
DaHMS!. Ha KaKYIO Hau60JIbwylO BblCOTY MO>KHO nO,Z!.HS!Tb O.n.HH
H3 KOIiLlOB .n.OCKH, 'lTOObl LlII.'IMH.n.p He ynan?
 o [T1 ld a
JL I
Z I
a
d-!!..
z
a}
61
PIIC. 100
PHC. 10 I
11.46. ll.u.'lUH.llP DblCOTOH h = 8,0 CM, ,Z!.uaMeTpOM D =
-" 6,0 CM JIe>KHT Ha 'z!'OUle'lKe, KOTOPYIO Me.n.JIeHHO nO;I.HUMalOT
3a O)].HU KoneLl. HaiiTH npe.1l.eJIbHblii yro.'I a HaK.TIOna 'z!'ome'lKH,
npu KOTOpOM LlHJIHH.n.p eme 6y.n.eT HaXO,Z!.HTbCH D paBHoBecUJI.
K034$HLlHeHT TpellUS! llHJIHII'z!'pa 0 ,Z!.Oll.leIJKY fL = 0,30.
11.47. KnpnHIJ, pa3MePbl KOToporo 28 X 14 X 7 CM, MO-
"heT 3aHHMaTb TPH pa3JIHIJHbiX nOJIO>KeHHS!. Onpe.n.eU1Tb pac-
CTmIHlle OT nJIow.a;I.1I onopbl ;"'J LleHTpa TS!>KeCTH, BO Bcex nOJIO-
)! emUlX. B haKOM nOJIO>KeHHH KllpmI'l Hau60nee YCroiiIJHB?
flo IeMY?
59

t 1.48. YceqeltHblH KOHYC C.iJ.eJIalt 113 HeO)J.HOp0.n.HOro Ma-
Tepnana TaK. qro lleHTp TfUKecTH CMew.eH (pHC. 102) B KaKOM
CJlyqae nOJlO}f{eHHe KOHyca oo,:Iee YCTOHqHI30: Kor.n.a OH CTOHT
Ha llJHpOKO1 OCHOBaHHH HJlH Ha Y3KOM?
11.49. Tenerpa4>HblH CTOJl6 MHHoA L = 7.0 M H Maccon
M = 140 Kr npH YCTaHoBKe nepeMew.aercH H3 ropH30HTaJlbHO-
ro nOJIO}f{eHHH B BepTHKaJlbHoe. KaKaH npH 3TOM cOBepruaeTcH
pa6oTa?
11.50. KaK)'IO pa60Ty Ha.n.o cOBepuIHTb. IfrOObl nepeBepH)'Tb
BOKpyr pe6pa 1\)'0 MaccoH m=200 Kr? Peopo Ky6a a=I,O M.
25a
u-?
PIIC. 102
PIIC. 103
11.51. KaKYIO HY>hHO cOBepwHTb paooTY, qT06b1 nepeBep-
HYTb BOKPyr pe6pa nOJlblH KYO, HanOJlOBIfHY HanOJlHeHHbll1
BO.n.OH? Macca Ky6a MaJla no cpaBHeHHIO C MaccoH HanomUIIO-
Il{eif ero BO)J.bI. Pe6po Ky6a a = 1,0 M.
11,52. KaKoA MHHHMaJlbHo([ CKOpOCTblO .n.oJlama 06J1a.n.aTb
nepe.n. y.n.apold 0 HeOOJlbWOH BblcT}"n Tpeyro,,1buaH npH3M3 co
CTOpOHOH a = 17 CM (puc, 103), "1lT06bl OHa MOrJla nepeBepHYTb-
CH Ha .n.pyrylO rpaHb?
 12. )l(IIAKOCTH H ra3b1
12.1. l1.H.'lHHAPHQeCKHH cocy.n. C }f{1I.n.KOCTblO nJlOlQ,a.n.blO
S = 200 CM 2 nnOTHO npHKpblT nopwHeP,f MaccoH m = 1,0 Kr.
Onpee.nHTb, KaKoe .n.aBJleHlle OKa3b1BaCT nopweHb Ha }f{H.n.KOCTb:
1) 6e3 rpY3a; 2) C rpY30M MaCCOH M = 5.0 Kr; 3) no)J. .n.eH-
CTBHeM CHJlbI F = 200 H, HanpaBJleHIIOH no.n. yrJloM a = 30°
K nopwHIO. KaKoe .n.aBJleHUe OKa3b1BaeT }f{H.n.KOCTb. Ha noprneHb B
Ka}f{,J.OM H3 CJlyqaeB? H3MeHHTcH J1H OTBeTbl, eCJIH BMeCTO
)hH.n.KOCTH 6y.n.eT ra3?
12.2. C KaKOH CHJlOH .n.aBHT nap Ha npe.n.oxpaHIfTeJlbHblH KJla-
naH .n.HaMerpoM 80 MM, eCJIIf .naBneHHe BHYTPH cocy.na 10 Mna?
12.3. HeBecoMaH }f{H.nKOCTb, HaXO;J.HUlaHCH B UHJlHH.n.PH-
lIeCKOM cocy.n.e nnOlll.a.n.blO S, nJlOTHO 3aKpblTa JlerKHN nopwHeM,
60

Ha KOTOpLlH no}]. yr.'10M a ::::: 60 0 K HOpMaJIH J1.eHcTsyeT CJ1.I13
F. nOCTpOHTb rpa<lmK 3aBHCIIMOCTH p'aBJIeHHSl BHYTPIf 1KH.n.- \
KOCTH OT paCCTOSlHH.H P.O noplllHSl, KaK H3MeHIITCSl rpacpHK, eCJIH
CIIJIa 6yp' p'eikTBOBaTb npneHp'IIKYJISIpHO nOBepXHOCTIJ noplll-
HSl?
12.4. Ha CTO.1C crOIlT 6aHKa C BOP.OH. nOCTpOHTb rpacpllK
3aBliClIMOCTIf p'aBJIeHHSl BOp'bI OT fJIy6HHbI. KaK H3MellHTCSl
rpacpII.{, eCJIH p'aBJIeHlle YBeJIH1JlITcSI? YMeHblllIlTcSI?
12.5. B KaKHX enY1JaHX CHJIa p'aB.'IeHHSl 1KHJ1.KOCTH Ha .nHO
cocy.n.a 60JIbllle CHJIbI TIDKeCTH 3TOH 1KHp'KOCTH? MeHbllle cliJIbJ
TH1KeCTH? paBHa CHJIe TH1KeCTH?
12.6. n01leMY He YCTpallBaIoT ra30HanopHble 6alllHU, no
aHaJIOrHH C Bo.n.oHanopllbIM?
12.7. B nOJIblH Ky6 C pe6poM a HaJIHTa .n.oBepxy :H<1I.n.KOCTb
nJIOTHOCTblO p. OnpelleJIHTb CHJIY .n.aBJIeHHH Ha rpaHH Ky6a.
12.8. B O.n.HOM 113 onblTOB naCKaJISI B KpbUllKe np01J-
HOH .n.epeB.HHHOH 60IJKH CJ1.eJIaHO Y3Koe OTBepCTHe H BCTaBJIeHa
TYJ1.a .n.JIHHHaH Tpy6Ka, 1Iepe3 KOTOpYIO HaJIHBaJIaCb Bo.na. KorJ1.a
601lKa H Tpy6Ka 3anOJIHUjJHCb. .n.aBJIeHHe BOJl,bl pa30pBaJIO 6011-
KY. Onpe.n.e.nHTb CHJIY. p'eikTBOBaBlllYIO Ha .n.HHll{e 601lKH nJIO-
.m.a.n.blO 0.20 M 2 . Kor.n.a ypoBeHb BO.lJ.bI no.n.HSlJICH Ha BblCOTY
4,0 M OT .n.HHll1.a.
12.9. npep.cTaBHM, 1JTO B onblTe naCKaJISI (CM. 3ap'a-
IJY 12.8) nOCTynH.JIH ene.n.YIOm.HM o6pa30M: Kor.n.a ypoBeHb BO.n.bI
no.n.HSl.IJCH Ha BblCOTY 2,0 M OT .n.HHm.a, BCTaBUJIH B TP} 6KY
nopllleHb, nJIOTHO npllJIeralOIl,uIii K ee CTeHKaM. C KaKoH CUJIOH
Ha.n.o Ha.n.aBHTb na nop'llleHb, 1IT06bJ CHJIa, .n.eHCTB}'IOm.aH Ha
.n.HHm.e, wJIa TaKoH 1Ke, KaK nOJIYlJlIJIaCb B 3a.u.alJe 12.8?
nJIOl.l.la.n.b Tpy6KII B 100 pa3 MeHbllle nJIom.a.n.H .n.HHl.I\a.
12.10. KaKaSi CHJIa .n.aBJIeHHSI M01K 6b1Tb nOJIY1JeHa C no-
MOl.l.lblO rH.n.paBJIIIlJeCKOrO npecca. eenH K MaJIOMY noplllHIO
npll.10}l{ena CHJIa f = 100 H, a nJIom.a)l.b noplllHeH npecca
COOTBCTBeHHO paBHa S} = 5,0 CM 2 H Sz = 500 CM 2 ? KO*l>H-
IlHeHT nOJIe3HOrO .n.eHcTBIIH npecca 1') = 0,80.
12.11. MaJlblH nopllleHb rH.npaBJIH1IeCKOrO npecca 3a O.n.UH
xo.n. onYCKaeTCH Ha paccToHHHe h = 0.20 M, a 6oJIblllOH nop-
IlIelib no.n.HHMacSl Ha H = 1,0 CM. C KaKOH CHJIOH F .n.eHCTBY
npecc Ha 3a}l{aToe B HeM TeJIO, eCJIH lia MaJIblH nopllleHb .n.eii-
CTBY CIIJIa f = 500 H? Kna npecca 1') = 0,95.
12.12. npn nO;J.'beMe rpY3a Maccoii m = .2,0 T C nOMom.blQ
THJ1.paBJIHlJeCKoro npecca 6b1.'1a 3aTpaIJeHa pa60Ta A = 4oo.lI.>K.
Dpu 3TOM MaJIblH nopllleHb CJ1eJIaJI n = 10 XO.n.OB, nepeMem.aSlcb
3a OAHH XO;J. lIa h = 10 CM. Bo CKOJIbKO pa3 nJIom.a.n.b 6oJIbIlIO-
61

ro nOpWIISI OOnbUJe nnOIl.la.zt.H Manoro ItOpWHSI? I(I1)J, npecca
1') = 0,90.
12.13. B .n.Be coo6ll.lalOll.lHecSi TPy6KH pa3Horo CeqeHHSI Ha-
JIHJIH CHaqaJIa PTYTb, a nOTOM B WHpOKYIO Tpy6KY CeqeHHeM
S = 8,0 CM 2 HaJIIIJIIi BO.n.y MaccoH m = 272 r. Ha CKOJIbKO BbI-
llJe pacnOJIO}l{eH ypoBeHb PTYTH B Y3KOM KOJIeHe, qeM B IlJHpO-
KOM?
12.14. B Coo61.l.lalOI.l.llleCSI cocy.n.bI HaJIHJIH pTYTb, a nOBepx
Hee B O.n.HII cocy.n. HaJIIiJIH CTOJI6 MaCJIa BbiCOTOH hI = 48 CM,
a B .n.pyroH - CTOJI6 KepocHHa BblCOTOH ha = 20 CM. Onpe.n.e-
JIHTb pa3HocTb YPoBHeH PTYTH B o60HX cocy.n.ax.
12.15. B cocy.n. C BO.n.OH BCTaBJIeHa Tpy6Ka CeqeHHeM S =
= 2,0 CM'3. B Tpy6KY HaJIHJIH MaCJIO MaccoH m = 72 r, Hais-
TH pa3HocTb YPoBHeH MaCJIa H BO.n.bI.
12.16. PryrHbIH 6apOMeTp MO}l{HO paccMaTpHBaTb KaK
co06111aIOI.l.lIiHCSI cocy.n., B O,!J.HOM KOJIeHe KOTOpOro HaXO.D.HTCSI
pT}'Tb, B .n.pyroM - B03.n.yx, ECJIH 6bI nJIOTHOCTb aTMoccpepHoro
B03.n.yxa He H3MeHHJIaCb C BbICOTOH, TO KaKOBa 6b1JIa 6b1 BblCO-
Ta an.mccpepbl npH HOpMaJIbHOM .D.aB leHHH?
12.17. OLleHHTb Maccy aTMoccpepbl, OKpY}l{alOllleH 3eMlloH
llJap,
12.18. ECJIH 6bI nOJIb30BaJIHCb BO,!J.SlHblM 6apOMerpOM, TO
KaKOH 6b1 BbiCOTbI CTOJI6 BO.n.bI COOOTBeTCTBOBaJI HOpMaJIbHoMY
aTMoccpepHOMY ftaBJIeHHIO?
12.19: MO}l{HO JIH HaCOCOM, HaXOJ\SlI.l.lHMCSI Ha KPYTOM 6y-
pery Ha BblCOTe 15 M OT nOBepxHocTH BOJlbI, KaqaTb BO.ny 113
peKH?
12,20, .lI.JIHHHYIO 6apOMeTpHqecKYlO Tpy6KY HaKJIOHHJIH no.n.
yrJIo\1 a = 30° K ropH30HTY H 3aTKHYJIH np06KoH. KaKaSi
CHJIa .n.aBJIeHHSl 6y.n.eT .n.eHcTBoBaTb H3 np06KY, eCJIH Tpy6KY
BblHYTb H3 PTYTH napaJIJIeJIbHO caMOH ce6e? ecJIH 3areM Tpy6-
KY nOCTaBHTb BepTHKaJIbHo? BHyrpeHHHH pa.n.HYc Tpy6KH paBeH
R = 6,0 MM.
12.21. B cocyn C BO.n.OH onYl.l.leH KYCOK .n.epeBa, 113MeHHTCfI
JIH OT 3TOro .n.aBJIeHHe H3 .n.HO H CTeHKH cocy.na, eCJIH Bo.n.a H3
cocY.;J.a He BbUlHBaeTCSl?
12.22. Cocy.n., HMelOlllHi'i 4>oPMY ycelJeHHoro Konyc3 C npH-
CT3BHbIM .n.HOM, onYllleH B BO.n.y. ECJIH B cocy.n. HaJIHTb 200 r
BOJlbI, TO .n.HO OTOpBeTCSl. OropBeTcSl JIH .n.HO, eCJIH Ha Hero no-
CTaBHTb rHplO MaCCOH 200 r? HaJIHTb 200 r M3CJI3? HaJIHTb 200 r
PTYTH?
12.23. nOpllJeHb, nJIOTHO npHJIeralOlllHH K BHyrpeHHHM
CTellKa:\1 Tpy6KH, MO}l{eT ncpeMelllaTbcSI B He" C nO!\fOlllblO .n.J1HH-
HOro WTOK3. Tpy6KY C nOpllJHeM, 3aHIIM310111HM KpaHllee HIDK-
62
.

I
Hee nOJIO}l{eHHe, BepTHKa.'lbHO onYCTHJI" B COCY.ll C PTYTblO.
3aTeM nopmeHb HallaJI" nO.llHHMaTb. KaKaSI 6bIJIa COBepmeHa
pa6OTa, KOr.lla nopmeHb riOAHSlJIH Ha BblCOTY h = 1,0 M? AT-
MOC<j)epHoe .llaBJIeHHe HOpMaJIbHOe, nJIOIl.la.llb nopmHSI S =
= 1,0 CM\!. TpeHHe He YIIHTbIBaTb.
12.24. nOtJeMY B03HHKaeT BbiTaJIKIIBalOIl.laSi CHJIa B }l{HA-
KOCTHX H ra3ax? BY.lleT JIH B031J11KaTb BblTaJIHBalOIl.laSl CHJIa B
lIeBeCOMOCTII ?
12.25. !lepeBHHHblH Ky6HK JIe}l{HT Ha AHe cocY.lla. BCnJIbiBeT
JIll OH, eCJIH B COCY.ll HaJIHTb BOJI:Y (BO.lla He npOHIIKaeT no.ll
Ky6HK)?
12.26. npSlMoyrOJIbHaH Kopo60IlKa H3 }l{eCTH MaccoH m =
= 76 r C nJIOIl.la.llblO .llHa S = 38 CM II H BbiCOTOH H = 6,0 CM
nJIaBaeT B BO.lle, OnpeJ1,eJIHTb BbiCOTY Ha.llBO.llHoH lIaCTH KG-
p060IlKH.
12.27. Kycol\ AepeBa nJIaBaeT B BO.lle, norpY}I{aHCb Ha 3/4
cBoero 06neMa. KaKoBa nJIOTHOCTb .llepeBa?
12.28. KYCOK Me.llHoro Kynopoca BeCHT B B03.llyxe PI =
= 100 MH, a B KepocHHe P" = 70 MH. Onpe.lleJIHTb nJIOT-
HOCTb Me.llHorO Kynopoca. .Me.llHbIH Kynopoc B KepOCHHe He
pacTBopSleTcSI.
12.29. .lI.JISI onpe.lleJIeHHSI nJIOTHOCTH aLleTOHa 3anaSlHHbIH
MeTaJIJIHlleCKHu LlHJIHH,np (BbICOTOH h = 10 CM H .llHaMeTpoM
D = 7,0 CM) 6blJI B3Bemen B BO.lle H aLleTOHe. Pa3HOCTb B Bece
nOJIYIIHJIaCb !!P = 0,75 H. KaKoBa nJIOTHOCTb aLleTOHa Ha
OCHOBaHHH .llaHHblX onblTa?
12.30. Onpe.lleJIHTb HaHMeHbmylO nJIJIl.la.ztb nJIOCKOH JIb.llH-
Hbi TOJIIl.lHHOH h = 40 CM, cnoc06Hoil Y.llep}l{aTb Ha BO.lle lIeJIO-
BeKa MaccoH m = 75 Kr.
12.31. nOJIbIH map, OTJIHTblH H3 CBHHLla, nJIaBaeT B BO.lle,
norpY3HBmHcb pOBHO HanOJIOBHHY. HauTH 06neM V BHYTpeH-
HeM nOJIOCTH mapa, eC.IJH Macca mapa m = 5,0 Kr
12.32. nOJIblH map (BHemHHH paAHYc Rb .BHyrpeHHHH R 2 ),
c..'J.eJIaHHblH H3 MaTepHaJIa C nJIOTHOCTblO PI' nJIaB3eT Ha no-
nepxnocTH }l{H.llKOCTIf C nJIOTHOCTblO P2' KaKoBa .llOJI}I{Ha 6b1Tb
nJIOTHOCTb p BelD,eCTBa, KOTOpblM CJ1e.llYeT 3anOJIHHTb BHYTpeH-
HIOIO nOJIOCTb mapa, IIT06b1 OH HaXO.llHJICH B 6e3pa3.'IHIIHO!of paB-
HOBeCH" BHYTPH }l{JI.llKOCTH?
12.33. O.llHH KOnel! HMTH 3aKpenJIeH Ha .llne, a BropOH npH-
KpenJIeH K np06KoBOMY nOnJI8BKY. npH 3TOM n = 0,75 Bcero
o6nel'tf3 nOnJIaBKa norpY}l{eHO B BO.llY. Onpe..'J.eJIHTb CHJIY naTH-
h-.eHHSI HHTH, eCJIH acca. nOnJIaBKa paBHa m = 2,0 Kr.
12.34. TOHK8H O.ll.II0pO.ll.HaSi naJIOIiKa mapllHpHo YKpenJIeHa
 a BepXI!Hii KOnel!. HJI}I{HH qaCTb naJIOqKH norp.Y}I{eHa B
53

BO.llY. npHlJeM paBHOBeCHe .llOCTliraerSI TOr.lla. !<or.lla nano'n<a
pacnOJIO}l{ena HaKJJOIIHO K nOBepXHOCTy. BO;1hI Ii B BO.lle HaXO!lIlT-
CSI nO.'IOBIiHa naJIo'nm. KaKOBa n.'10TIIOCTb MaTepHana, 113
KOToporo CJ1e.nana nanOIJKa?
12.35. .LlBe O.llliHaKOBble 060..10'lKIi mapa, O:J,Ha 113 3naCTH'l-
HOH pe3HHbl, a BTopaH "3 npope311HeHHoif TKaHH. nanonHeHbI
O,nHIIM H TeM }l{e KOnH'IeCTBOf Bo,!!.opo,!!.a H HaXO:J,SlCb Y 3eM'iIl,
3aIIIlMa.'1H paBIIblH OUbeM. KOTOpblH H3 WapOB nO.l1.lIHMeTCSI
Bblwe Ii nO'le:\fY, fnH BO.llOpO.ll 113
HHX BblXO,nHTb He MO}l{eT?
12.36. Ha'lawe BeCOB ypaBHoBe.
weH CTaKaH C BOJIOH. HapywHTcSI JIll
- paBHoBecHe, eCJIIf B BO.llY CTaKaHa
norpY3HTb rnplO, nO.llDeWeHHYIO 38
HIITb?
12.37. B cocY.lle H8XOJUITCSI Te.nO
Bp8111eHIISI (pa3Mepbl nOKa3aHbl H8
pHC. 104). B cocY.ll 3a.'IHB8IOT >KH.ll-
KOCTb T8K, 'lTO OHa He npOHIiKaeT
no,!!. HH}I{Hee OCHOBaHue. nOCTpOIlTb
rpaclJUK 38BIICIIMOCTH BblTanKHB81O-
llleH Cllnbl, .lleiiCTBYlOllleH Ha Teno, OT
ypOBHSI BO.llbI B cocY.lle.
12,38. Ha .llHe cocY.lla C Bo,!!.oil HaXO;J.IITCSI HaK.1l0HlfaH
nnOCKOCTh C yrnoM HaKJIOHa a = 30° npH OCHOBaHHH. Ha
HaKnolflfYIO n.'IOCKOCTb nOn01KH.'1H anlOMHHlleBYIO TpeyrOJIb-
H}IO npu3MY BblCOTOH h 1 = 3,4 CM, co CTOpOHOH a = 2,0 CM.
S
hi
h,
d l
PHC. 104
H
PHC. 105
- -
-----
PIIC. 106
P8CCTOSlHHe OT npH3MbI AO nOBep'{lIOCTH BOJlb[ H = 7,0 CM
(pHC. 105). Onpe,!!.eJIHTb, C KaKOH CII.'Ioii .llaBIIT npll3Ma H8
HaKJJOHHYIO nnOCKOCTb.
12.39. Ha .llHe BO.lloeMa YCTaHOBJIelfa KOIICTPYKl.lHSI rpll60-
BII;J.HOii 4x>PMbI. pa3Mepbl KOTOpoii YKa3aubl 1f8 pliC. 106. rJIY-
611Ha BO.1l.oeM8 H. C KaKoii CIIJIoii .llaBIiT KOHCTPYKilHSI Ha .llHO
BO.lloeMa? nJ:!OTHOCTb BO;!.bl Po, MaTeplla:la KOIICTPYKUIIU 2po'
64


'I
12.40. Ky6HK co CTOPOHOH a = 5,0 CM nnaBaeT MC>I<.lI.Y
KepOCHHOM H BO.n.OH, HaX0.ll.SlCb HH>I<e ypOBHSl KepOCUlia Ha hI =
= 2,5 CM. HH>KHSISI nOBepXHOCTb Ky6uKa -Ha h z = 1-,0 CM HH>I<e
nOBePXHOCTU pa3;J.eJIa. KaKOBa nJIOTHOCb Ky6HKa? OnpC;J.cnHTb
cHnbl AaSJIeHHSI Ha BepXHlO1O H IIIUKHIOIO rpaHH Ky6uKa. 1,'13-
MClIHTCSl JIll r.'Iy6HHa norpY>l<eHUSI hy(5I1Ka B BO.n.y npH .n.OJIU-
BaHUU KepocHHa?
12.41. BpYCOK .lI.epCBa nnaBaeT B BO.lI.C. KaK H3MeHHTCSl rny-
6nHa norpY>l<emul 6PycKa B BO.ll.e, eCJIIf nOBepx nOAbl HaJIUTL
Macno?
12.42. CTanbHoi{ Ky6uK nJIaBaeT B pTYTH. nOBepx PTYTII
HanUBaeTCSI Bo.na TaK, qTO olla nOKphlBaeT Ky6HK. KaKoDa BblCO.
Ta h CJJOH BOll,bl? D.nHHa pe6pa Ky6HKa a = 10 eM. Onpe.ne.'1UTb
.n.asneHlle Ha HIUKHIOIO rpaHb Ky6uKa. ,
12.43. J1bAHHa nJIOI.1.la)l.blO nonepeliHoro ee'lellHSl S =
= 0,50 M I H BblCOTOH H = 40 CM n.laBaeT B Bo.n.e. KaKYIO
pa60Ty Ha.n.o COBCpWllTb, IiT06b1 nOJlHOCTblO norpY311Tb JIb,lJ.H-
HY B BO,lJ.f?
12.44. TeJIo, mlelOI.1.lee Maccy m = 2,0 Kr II 06'beM V =
= I,D . 10- 3 M 3 , Haxo.n.HTCH B 03epe Ha rJIy611He h = 5,0 M.
KaKaH pa60Ta J10Jl>l<Ha 6blTb COBepweHa npH ero nO.ll.'ber-:e Ha
BbiCOTY H = 5,0 M Ha.n. noscpXIIOCTblO BO.!J.bI? PaBHa JIM :na pa.
60Ta 113MeHeliHIO nOTem.lIla.'IbHOH :;meprull TeJla? 06'bHCHHTe
pC3YJlbTaT.
3a.n.aQH K rJlaBe III
111.1. BHYTPH rJla.n.KOH nOJlyc<lJepbl Jle}l{HT rpY3 MaCCOH m lt
coe.ll.lllleHHblH nepe6powcHHoi{ liepe3 MOK HllTblO C rpY30\l Mac-
eOH m 2 (puc. 107). Onpe.ll.eJlUTb OTlloweHHe Macc rpY30B,
ecJIu yroJl a Me>K.lI.Y pa.n.HycoPor; -npoBc.n.eIlHblM K TeJJY, U ro.
pH30HTOM eOCTaBJlHeT 60°.
111,2. B C<lJePUIiCCKOH 'lawe .'IC}I{HT HesecoMblH Crep}l{eUb C
TOQe'lHblMU MaccaMH m l = 0,20 Kr U m 2 = 0,40 Kr Ha KOHLlax
(pHC. 108). D.JIIlHa CTep}l{HSI paBHa pa;I.HYCY c<lJePbl. TpeHHe
OTCYTCTBYCT. Onpe.n.eJJHTb. no.n. KaKHM yrJloM K ropH30HTY pac.
nOJlOiKeH CTep}l{eHb.
PHC. 1 O
3 .K. 1897
PRC. 108
65

...............
111.3, KaKoH HaH60JIl,llJeH J1.IIHHbI L MBICC .n.OCKa MO>KeT 6bITL
sa6I1Ta Me>KJI.Y .n.BY:\UI BepTHKaJIbHblMH CTeHKaMH, pacnoJIo .
1KeHHbl'dH Ha pacCToHHHH 1 = 2,0 M .n.pyr OT .n.pyra (pHC. 109),
eCJIH Ko3<M>IU.lHeUT TpeHHH Me>K.n.y .n.OCKOH H CTeHKaMH 11 = 0,40?
Macco" .n.OCKIf npeHe6pe%.
111.4. CTep>KeHb AB, mapHHpHo 3aKpenJIeHHblH B TOIJKe A,
OnllpaeTCH KOHl.lOM B Ha nJIaT<lx>PMY (pHC. 110). KaKYIO MHIIH.
MaJIbHYIO CHJIY F HY>KHO npHJIO>KHTb .n.JIH TOro, 1I1"06bl CAB!!.
HYTb nJIaT<lx>PMY C MeCTa? Macca CTep>KHH m, Ko3<M>Hl.lHeUT


PHC. 109
PHC.IIO
PHC. III
TpeHHH crep>KHH 0 nJIaT<lx>PMY 11, H yrOJI, 06pa3yeMblii CTep}!{'
HeM C BepTlIKaJIblO, paBeH a. TpeHileM KalJeHHH KOJIeC H TpeUH'
eM a OCHX npeHe6peQb.
111.5. TH>Ke.naH OAHopO.D.HaH .n.OCKa MaccoH M ynHpaeTcH
O.n.HHM KOHl.lOM a YI'OJl Me>KJJ.Y cTeHKoH H nOJIOM, K .npyroMY
KOHl.lY npHBH3aH KaHaT. Onpe.ne.nHTb CHJIY HaTH>KeHHH KanaTa,
eCJlH YI'OJI Me>KJJ.Y .n.OCKOH H KaHaTOM p = 90°. KaK MeHHeTCH
CIfJIa HaTH>KeHHH KaHaTa C YBeJJHQeHHeM yrJIa a Me1K.n.y .noc.
KOH H nOJIOM, eCJIH yroJI p OCTaeTCH nOCTOHHHbIM? KaK MeHHeT'
CH HanpaSJIeHHe CHJIbl, .n.eHcTBYlOllleH co CTOpOHbl CTeHKH II
nOJIa, Ha Crep}KeHb?
111.6. napa.nJIeJIbHO OCH l.lHJIIIH.u.pa pa.n.HYCOM R Ha pac'
CTOHHIIH Ri2 OT ero ueHTpa npOCBepJIHJIH KpyrJIoe OTBepCTlle.
Pa.n.HYC OTBepCTHSI paBeH R/2. lI.HJIHH.n.p JIe}KHT Ha .n.olllelJKe,
KOTOPYIO MeMeHHo no.n.HHMaIOT 3a O.n.HH KOHel.l (pHC, Ill).
HaihH npeAeJJbHhlH yroJI HaKJIOHa .n.olllellKH, npH KOTOpo:.l
l.lHJIIIHJl.p ellle 6y.n.eT HaXo.D.HTbcH B paBHoBeclIIl. Ko3<M>HUHeHT
TpenHSI l.lIlJIlfH.npa 0 .n.ollle'IKY 11 = 0,20.
111.7. Ha .ll.BYx HeBeCOMblX HHTHX aHCHT neoAHopo.!l.nall
naJIKa (pHC. 112). Onpe.n.CJIIITb nOJIO}KeHHe l.leHTpa Macc na.'IKH.
111.8. K nOTOJIKY Ha HCKOTOpOM paccToHHHH .n.pyr OT .n.pyra
nO.D.BellJeHbl Heaecor-me }JHTH. K HIIM npllKpenHJIH sa KOHUbl
CTep}KeJlb MaccoH m = ] ,0 Kl' TaK, 'Ira o.nHa 113 HlITeR oKa3a'
66

n3Cb nepneH.lllfKYJUlpHOii C-repJKHIO, H on COCTaBIIJI C ropIl30a:-
TOM yroJI a = 30°. HaMTII Cl-fnbl HaTSlJKeUIIH HlfTelf.
111.9. BO.!l.3 B LlII.luH.a.pllqeCKOM eocYll.e nnOlllaJJ..blO S =
::;:= 2,0 . 10- 2 l,I2 nJIOTHO npUJKaTa nOpll1HeM Maccoil m =
::=:: 1,0 Kr. Cnepxy Ha nOpll1eHb .llaBIIT CTep>KeUb pblqara. Ha
pblqar .lleHcTnyeT cuna F = 10 H (pHC. 113). Onpe.ll.eJI, IfTb
J{3Koe .llaBJIeHlle OKa3b1BaeT Bo,!{a Ha AHO eocY.lla. eCJJII 11 =
=10 CM, /2 = 20 eM. h = 10 CM.
I, 12
"
 .
...,
...
F
= -= - h
Pile. 112
J
PIIC. 113
II J. 1 O. Kpyr na II .llbIpKa n.l0111a.llblO S B .llHe cocY.lla 3a-
I\pLITa "P06KOM, c;J.eJIaUHOH B BII.lle KOH}Ca C nJIOlllaD.bJO acHO-
BaHIISl4S. npH KaKOM HaH60.'Ibll1eM 3HaqeHHH nJIOTHOCTU Ma-
TepHana npo6KH p MOJKHO .l106HTbCSI ee Bcn.'IbiTHSI, .llOnllBaSl JKII.ll-
KOCTb B COCYA? n.'10TUOCTb JKH.llKOCTM Po.
111.11. B eocY.lle. HanOJIHeHIIOM BO.llOH, naXO:\HTCSI Ha naK-
JIOHHOM .lI.He Ky6HK 113 aJIIOMIIHIISI C pe6pOM a.= 10 CM. Oope-
n.eJlHTb cIIny AaBJIemlSl Ky6HKa Ha AHO H cIIny TpClIlISI Me.>KJI.Y
-- -- -
-_I -ZR--=-
Zr --=-_
.
.
.
PIIC. 114
PIIC. II 5
KYOIIKOM I{ .llUOM. MeM;1YAIIOM H IIHJKHeH rpaHbIO Ky6ItKa BO;J.a
lie npOIUIKaeT. PaCCToslHHe h OT pe6pa Ky6HKa .11.0 nOBepXHOCTI{
BOAbi paBHO 50 CM. YrOJI Hah.1UlIa .llHa cacYAa a === 30° (pHC.
114).
111.12. 113 CacYA3, 3anO.'lHeHIIOro BO,!{OH, BblXO.il.HT Tpy6a
P<lAIlYCOM T. Tpy6a 3aKpblTa KpaeM KpyrnoM anlOMIIHHeBOH
3-
67

nnaCTHHKH pa.D.HYCOM R == 2, " TonlllHHOH h = 5,0 MM, KO.
TOpylO npmKHMaeT K TPy6e CHJIa .D.aBJIeHHH BO.D.bl (pHC. 115).
1-13 cocy.n.a llepe3 MaJIeHbKoe oTBepCTHe BblTel<aeT BO.D.a. Onpe.
,ne.1HTb, np" KaKOM ypoBHe BO.D.bl Ha.z\ nJIaCTHKoii OTKpoeTCII
Tpy6a.
f JI A B A IV. MEXAHH'IECI(HE I(OJlE6AHHSI
it BOJlHbJ
 13. KUHeMaTHKa rapMOHHqeCKOrO KoneC)aTe.ll..Horo
Jl.BH)KeHHA
13.1. CocTaBHTb ypaBHeHHe rapMOHHQeCKOr0 Kone6aHHH, ec-
JIH aMnnHTY.n.a Kone6aHUH A = 5,0 CM, a nepHo;J. nOJIHOrO KO-
ne63HHH T = 0,50 C.
13.2. CocTaBHTb ypaBHeHHe rapMOHHlJeCKOrO KOJIe6aHHH,
eenH aMnnHTy.n.a Kone6aHHH A = 4,0 CM, 8 IJaCTOT8 Koneoo.
HHH 'V = 50 fLt.
13.3. !J.Ba TeJla COBep1ll31OT KOJIe6aHHH C O.llHHaKOBoH IJav
TOTOH. nOCTpOHTb rpa<pMKH 3aBHcHMocreA Koop.D.HHaT TeJI 01
BpeMeHH .llJlH enYllaeB: a) Kone6aHIIH TeJI npOHcXo.llHT B <Pa3e;
6) C.llBHr <Pa3 Me1K.llY Kone6aHHHMH Ten COCTaBJIHeT n/4; B) KO-
ne6aHHH TeJI npOHCXO.D.srr B npOTHB<><Pa3e.
13.4. 3a KaKYIO IJaCTb nepHo.n.a T TeJlO, cOBeplllalOlD,ee rap'
MOHUqeCKHe KOJIe6aHHH, npoxoAHT Bec.. nyrb OT cpe.n.Hero no.
JIO)KeHHH .llO KpaHHero? nepBYIO nonoBHHY
nyrH? BTOPYIO ero nonoBHHY?
13.5. KaK)'IO 1I8CTb nepHo.ll8 T rpY3
MaHTHHK8 HaXO.llHTCH B npe.n.eJIax I,D CM
J( OT nonO)KeHMH p8BHoBecHH, ecnM aMnnll-
Ty:\a ero KOJIe6aHHH paBHa 2,0 CM?
13.6. TOIJKa paBHoMepHo ,lI,BH)KeTCSI no
PHC. J 16 OKPY)KHOCTH. npoeKLtHH TOIJKH Ha JIHHHIO,
J}£)KalllYIO B nnOCKOCTH ee ,lI,BH1KeHHH
(pHC. 116), H3MeHHeTCH co BpeMeHeM no rapMOHHIJeCKoMY 3aKO-
BY. 3anHcaTb, KaK MeHSllOTCH co BpeMeHeM Koop.llHHaTa x TOllKH,
npoeKLlHH CKOpOCTH 118 OCb x, npoeKLlHH YCKopeHHH Ha OCb x,
eenM B HaIJanbllblH MOMeHT x = o. nOCTpOHTb rpa<pHKH 38BJI-
CHMOCTeH X (t), V z (t), a z (t).
13.7. PClllHTb 3a.z\aIJY 13.6, eCJIH B BaIJaJIbHblH MOMeH
x = R. Onpe.lleJIHTb pa3HOCTb 4>33 MeJKJlY Koop.llHHaTOH If
CKOpOCTblO, KOOPJl.HH8TOH H YCKopeHHeM, CKOpOCTblO H YCKo-
peHHeM.
68

13.8. TOIiKn cOBepwalOT KOJIeUaHHH B.o.OJIb OCH x no 3aKoHY
x = A cos (wt - n/4). DOCTpOUTb rpaqJHKH 3aBIlCHMOCTeH:
CMem,CHIiH x, CKOpOCTH J" 'H YCKopeHHHQ" OT BpeMeHH.
13.9. fpY3lfK Ha npY>lulHe KO.1C6JICTCSI B,!{Ollb O.o.HOH npH-
PolO" C aMnJIHTYAoH A = 2,0 CM. DepuoJ\ KOJIe6aJIHH T = 2,0 c.
B nalia.'IbHblH MOMeHT BpeMeHH rpY311K npoxoJ\H., nonmKCHHe
paBlioBecHH. OnpeAeJlUTb CKOpOCTb H YCKopeHlfe rpY3HKa liepe3
BpeMSI t = 0,25 c.
13.10. no YCJlOBHIO 3aAal.IH 13.9 onpe.o.eJIHTb cpe,aHIOIO
CKOpOCTb ABHmeHHSI rpY3HKa OT nonomeHHH paBHoneCHSI .0.0
MaKCIfMa.'IbIlOrO OTK..10IleHHSI OT nOJIOmellllSi paBHonecHH
13.11. TOIJKa cOBepWaeT rapMoHHliecKHe KOJIe6aHlISI B.!I.OJIb
HeKoTopoH. npSlMOH. c nepHoAoM T = 0,60 C H amJIHTy.o.oR
A = 10 CM. HathH Cpe.o.H101O CKOpOCTb TOIiKH 3a BpeMSI, B
TelJeHlle KOToporo OHa npOXO.o.HT nYTb A12: 1) 113 KpaHHero no-
JIO>KeHHSI; 2) H3 nO,,10>KelmH paBlioBecHH.
13.12. lJaCTHLla cOBepwaeT rapMoHHliecKHe KOJIe6aHliH B.o.OJIb
OCH x OKOJIO nOJIO>KeHHSI paBHOBCCHH x = O. t{aCTOTa KO.'le6a-
Hllii w = 4,9 pa.n.le. OiJpe.ll.eJIUTb, B KaKOH MOMeHT BpeMeHH
noc.'Ie npOXO>K.ll.eHHH nOJIO>KeHHH paBHOBeCIiH liaCTHLla 6YAeT
HMeTb KoopAHHaTY x = 25 CI H CKOpOCTb V x = 100 cMle.
 14. J].HHaMHKa rapMOHHlJeCKOrO Kone6aTenbHoro
ABH)KeHHA
14,1. Ha HHTH .llJlIIHOH I nO.llBeCHJIH MaJIellbKIIH rpY3HK
MaccoH m. fpY3HK OTKJIOHHIOT OT nOJIO}KeHIIH paBHoBecHSI H
om YCKalOT , 11306pa311Tb CIiJIbI, AeitcTBYIOm,He Ha rpY3HK.
06'bJICHIITb, nOlJeMY nepuo.o. KOJIe6aHHH rpY3HKa, nO.o.BeWeH-
HOro Ha HIITH, lie 3aBHCHT OT ero MaCCbl. Onpe.lleJIHTb I1epuoA
MaJIbI KOJIe6aHHH 3Toro rpY3HKa (MaTeMaTHliecKoro MaSiTHH-
Ka).
14.2. Ha rJIa.llKOM CTOJIe HaX0.llHTCSI rpY3HK MaccoR m, npH-
KpenneHHblH K BblcTyny npY}KIIHOH )KeCTKOCTblO k. fpY3HK
OTKJIOHSIIOT OT nOJIO>KeHHH paBHoBecHSI. HapUCOBaTb CUJIbI,
.lleHcTBYIOm,He Ha rpY3HK. Onpe.1l.eJIHTb nepuo.ll KOJIe6aHHA
rpY3HKa Ha npY)KMHe (npY}KHHHOrO MaHTHHKa),
14.3. nOKa3aTb, 'ITO nepHo.ll KOJIe6aHHH npY}KHHHOrO
MaSlTHHKa (Of. 3a.zla1iY 14.2) He H3MeHHTCSI, ecJIH npY)KHHY C
rpY3HKOM nOeCHTb BepTHKaJIbHo.
14.4. fuMeHHTCSI JIM nepHOA KOJIe6aHHH }faHTHHKa OT Toro,
liTO MbI era nOMecTHM B BOJ\Y? MaHTHHKY npHAaHa H)1eaJIbHO
06reKaeMaSi ct>opMa H KO)KHO npHHBTb, _ qTO TpeHHe 0 BOA)'
Ci9

paDUO liYJIIO (paCCMOTpeTb MaTeMaTHtzeC){HH H npY>KJllIHbIH
MaSITHHKH).
14.5. JlJIHlIa MaSlTHHKa, YCTaHOBJIeHHOrO B McaaKueBcKoM
co60pe B JIelUlllrpa.n.e, paDHa 98 M. 3a KaKoe BpeMSI MaSlTHHK
COBepllJaCT nOJIlIOe Ko.'Ie6aHHe?
14.6. JJ.nSl onpe.n.eJIeHHSI YCKopeHHH cBo60.n.Horo na,neHHH
(jbIJI B3HT MaHTHHK, COCTOHIlJ.Ui't H3 npOBOJIOKH .n.JIUHOH 1 =
=90,7 CM H MeTaJI,'IIfI-IeChOrO llJapHKa ,nHaMeTpoM d=40,O MM.
npOAOJI>KHTeJIbHOCTb n = 100 nOJIlIbIX KO.'le6aHHH MaSlTHHK3
OKa3a.'IaCb paBHoH t = 193 C. BbItJHCJlHTI: no 5THM Jl.allllbIM
YCKopeHHc cBo60.n.Horo na.n.eHHSI.
14.7. Ha KaKYIO tJaCTb .n.JIHHbI HaAO YMeHbllJHTb ,nJIHHY Ma-
TeMaTHliecKoro MaHTHHKa, IiT06bI nepHoJi. KOJIe6aHHH MaSiTHUKa
. Ha BblCOTe h = 10 KM 6bIJI paBeH nepHoAY ero KOJIe6aHHH Ha
nODepXHOCTH 3eM.1H?
\ 14.8. OnpeAe.1HTb, KaK 6y,ayr OTJIHqaTbCSI nOKa3aHHH Pyq-
HblX qaCOD H liatoB-xo.n.HKOB liepe3 CYTKH nOCJIC Toro, KaK
IIX no.n.HSlJIH Ha BblCOTY h = 5,0 KM Ha.n. nOBepxHocTblO 3eMJIU.
14.9. B HenO)I.BH>KHOM JIH4n"e BUCHT MaSlTHHK, nepHo,n KOJIe-
(jaIlHH KOToporo Tl = 1,0 c. C KaKHM YCKopeHHeM ,nBH>KeTCH
J1H4n", CJIIf nepHo,n KOJIe6aHUH SToro MaHTHHKa CTaJI paBHbIM
T 2 = 1,1 c? B KaKOM HanpaBJIeHIIH )l,BH>KeTCH JIHclJT?
14.10. HauTH nepno.n. KOJIe6aHHH MaTeMaTHliecKoro MaHT-
HIIKa ,nJIHIIOH I, nOABellJeHHOrO B BaroHe, Jl.I3U>Kym.eMCSI C YCKO-
peHHeM a.
14.11. He60JIbllJoe TeJIO CKOJIb3HT no BnyrpeHHcH nOBepxHo-
cm CcpepbI pa.n.HYCOM R. OnpCAeJIHTb nepHo.n. MaJIblX KOJIe6a-
HHH TeJl3. TpeHHe OTCYTcTByeT.
14.12. rpY3HK, no.n.BellJHHbIH Ha HHTH ,nJIHHOU I = 1,0 M,
OTKJIOHHJIH lIa He60JIbllJoH yro:I OT nOJIO)!{eHHH paBHoBecHH H
. omYCTHJIH. Onpe.n.eJIHTb, Iicpe3 KaKoe Bper.m rpY3HK BepHeTCSI
B lICXO.n.HYIO TOIiKY, eCJIH npH .D.BH>KeHIIH IIHTb 6b1JIa 3a,nep>KaHa
lL'TlIqrroM, nOCTaBJIeHHblM Ha O,nHOH BepTHKaJIH C TOIiKOH nOA-
Deca, nocepe,nHlle JIHHbI IIIITH.
14.13. HaHnf nepHo.n. Ma.'lblX BepTHKaJIbHblX KOJIe6aHHu
TeJIa MaCCOH m B CHCTeMe, H300p>KeHHoH. Ha pHC. 117, a, H Ma-
JIblX ropH30HTaJIbHbIX B CHCTeMe, H306pa>KeIiHOH Ha pHC. 117,6.
)KecTKOCTH npY>KHH paBlIbI k 1 H k 2 . TpeHHeM npeHe6peqb.
14.14. BblliHCJlHTb nepHo,!{ MaJIblX KOJIe6aHHH apeoMeTpa,
norpY1KeHHOrO B DO.n.y, KOTOpO\fY COO61lJ.HJIU He60JIbllJoH TOJIIiOK
B BepTHKaJIbHOM HanpaBJIeHliH. .Macca apeOMeTpa m = 50 r,
paAHYc ero TPYOKH r = 5,0 M\!. ConpOTUDJIeHUeM BO)IbI npe-
He6pclib,
7{)

14.15. MaS1THHK COCTOHT H3 TS1:H<e..10ro mapHKa, Macca KO-
Toporo m, nO.1BemeHHoro Ha HIITH .lJ..'IJIHOH 1. Onpe.lJ.e.liHTb 3Hep-
rlflO, KOTOpOH o6.na.lJ.aeT MaHTHHK, ec.'IH lIaH60.nbmHii yro.1J ero
OTK.IJOHeHHfI OT BepTHKaJIbHOrO nOnO>KeHHSl paBeH a.
14.16. Onpe;J.e.IJHTb 3Heprmo, KOTODoii o6na.lJ.aeT MaTeMaTH-
qecKIfH MaSITHHK Maccoii m If .n.mfHoH t, ecnH aMn.llHTY.!la
Kone6aHHii paBHa A.
14.17. MaHTHHK Ko.'1e6.1eTcfI OKOJIO nOnO:H<eHHS1 paBHoBecHSI.
TpeHHc oTcyrcTByeT. KaK MeHHeTCSI B 3aBHCHMOCTH OT Dpe-
MeHH nOTeHlfa.llbHaS1 3HeprHH? KHHeTHQeCKaSI 3HeprlfH? non-
HaSI 3HeprllH? nOCTpOHTb rpa4>HKH 3TlfX 3aBHcHMocreii.
m
rrJ
, , ,'
51 h

",,///
fiv.
Puc. II 7 Puc. 118
14.18. nplfKpcnneHHblii K BepTHKanbHoii npY1KlfHe rPY3
MCJI.JleHHO onycKalOT .lJ.O nOJI01KeHlfSI paBHoBecHSI, npHqeM
npY:H<HHa paCTflrlmaeTCSI Ha .n.nHHY xO' Ha CKOJIbKO paCTSIHeTCJl
npY:>KllHa, eCJIH TOMY :H<e rpY3Y npe.n.ocTaBHTb B03MO:H<HOCT
na.n.aTb cBo60.n.HO C TaKoro nOJIO:H<eHHSI, npH KOTOpOM npY1KIiHa
He paCTSIHYTa? KaKoii MaKcHManbHoii CKOpOCTH .n.OCTHrHcr
nplf 3TOM rPY3? KaKoB xapaKTep .n.BH:H<eHlfSI rpY3a? MaccoA
npY:H<HHbl npeHelSpellb.
14.19. TeJIO Maccoii m ynano C BbICOTbl h Ha lJaIllY npYnHlH-
IIblX BecOB (pHC. lIB). Macca lJamH H npY)KlfHbl npeHe6pe)f{Jf-
MO MaolIa, :H<eCTKOCTb npY1KHHbl k. npHnHnHYB K lJallle, TeJIO
HaqHHaeT COBepmaTb I'apr.IOHHqeCKHe KOJIelSaHHSI B BepTHKanb-
HM HanpaBJIeHHH. HaiiTH aMnnHTY.lJ.Y KOJIe6anHii H HX 3Hep-
i"UIO.
14.20. Ha ropH30HTanbHoii npY:H<HHe YKpenneno Te.JIO
Maccoii At = 10 Kr, ne)Kamee Ha a6cOJIIOTHO I'na.n.KOM CTOJIe.
B 3TO TeJIO nona.n.aeT H 3aCTpeBaeT B HeM nynSI Maccoii m =
= 10 I', neTsnnaSI co CKOpOCTblO v = 500 WC, HanpaBJIeHHOA
B.n.OJ1b OCH npY:H<HHbl. TeJIO Bl>Iecre C 3acrpSIBIlleii B HeM nyneii
OTKJIOHSIeTCSI ()1' nOJIO)KeHliJi paBHOBeCHSI H HaqHHaeT KOJIe.
11

6aTbCSJ OTHOCHTeJlbHO Hero C 8MnJUIT)'.n.oH A = 10 CM. HaHTH
nepHO.n. KOJIe6aUHH Tena.
14.21. Ha HeKOTOpblx yqaCTKaX cTapblx, OO'be3}f(eHHblX
rpYHToBblX .n.opor aBTO'dOOHJIb lIa t lJlHaeT CHJIbHO paCKaqH-
BaTbCSJ. 06'bSlcHHTe 3TO SlBJIeHHe.
14.22. B03MO>KHO JIH pacKallaTb TH>Ke'IIJle KallenH, nplf-
JIaraSi K HHM O'leHb MaJToe YCHJIHe, H nOJIY'UlTb 6oJIblll}'lO aM-
nJIHTY.n.y KOJIe6aHHH, HecMoTpSJ Ha MaJIOe 311aqeHHe 3aTpallH-
BaeMoH MOll{HOCTH?
14.23. npH KaKOU CKOpOCTH noe3.n.a MaflTHHK JJ.JIHHOH I -=
= II CM, no.n.BerueHHbIH B BaroHe, OC06eHHO CHJIbHO paCKa-
'lHBaeTCSJ, ec.'1H paCCTOSlHHe Me>K.n.y CTblKaMH peJIbCOB L =
- 12,5M?
 15. BOJlHbI. 3SYK
15.1. 3BYK nYlllellHoro BblCTpeJIa .n.omen .n.o lIa6.mo.n.aTe.lJfI
'Iepe3 BpeMSJ "t = 30 C nOCJ!e TOro, KaK 6b1JIa 3aMelleHa Bcnbllll-
Ka. PaccToSlHHe Me>K.n.y nYIllKoH H Ha6,lIIo.n.ateneM 1= 10 KM.
()npe.n.eJIHTb CKOpOCTb pacnpOCTpaHeHHSJ 3BYKa B B03.n.yxe.
15.2. nepBblH pacKaT rpoMa .n.omeJI .n.o Ha6.mo.n.aTeJIfi lIe-
pe3 BpeMSJ "t = 12 C nOCJJe Toro, KaK 6blJIa 3aMelleHa BcnbllllKa
MOJIHHH. Ha KaKOM paccToSJHHH OT Ha6.lIIo.n.aTeJUI B03HHKJIa
MOJIHHSJ?
15.3. CKOpOCTb pacnpOCTpaHenHSI 3BYKa B Bo.n.e 6b1JIa onpe-
.n.eJIeHa CJIe.n.YIOIlJ.IIM o6pa30M: Ha nOBepxHocTH 6oJIbworo 03cpa
Haxo.n.HJIHCb .n.Ba Kopa6.nSJ Ha paccTOSJHHH 1 = 14 KM .n.pyr OT
.n.pyra; Ha O.n.HOr., H3 HHX 6blJlO YCTaHOBJIeHO npHcnoco6.'1eHHe,
C03.n.aBaBwee o.n.HoBpeMeHHo 3BYKOBOit CHrHaJI B Bo.n.e H CBeTa-
BOH B B03.n.yxe, a Ha .n.pyroM Haxo.n.HJICSJ Ha6.nIO.n.aTenb. OT\le-
IJaBUIHli no 'laCaM BpeMfi npHcMa TOro H .npyroro CHrHaJIa.
()Ka3aJIOCb, 'lTO 3BYKOBOH ClirRaJI 6WJI 3aMeIJeH cnycTSJ "t =
= 10 C nOCJJe cBeTOBoro. KaKoBa CKOpOCTb pacnpOCTpaHeHIfS1
3BYKa D Bo.n.e?
15.4. HaH60JIee HH3KHH 3BYK, ell{e BocnpHHHMaer.fblH 'lenD-
BeKON C HOpMaJIbHblM CJIYXOM. HMeeTlJaCToTY v= 16 fit. KaKo-
Ba ,nJIHHa BOJIHbl (B B03,nyxe), COOTBeTCTBYIOll{aSJ 3TOH lJa-
CTore?
15.5. ()npe,nenHTb .n.JIHHY 3BYKQBOii BOJIHbl B BO.n.e, BW3blBae-
MO" HeTOIIHHKOM Kone6aHHH e qaCTOTOH v = 200 rLl, eCJIH
CKOpOCTb 3BYKa B Bo.n.e paBHa v = 1450 we.
15.6. Bo eKOJIbKO pa3 H3MeHHTCS1 JJ.JIHHa 3BYKOBOH BOJIHbI npH
nepexo 3BYKa H3 B03,nyxa B BO.n.y? CKopOCTb 3BYKa B Bo.n.e
Vi = 1450 Mle, B B03.n.yxe v:: = 340 M/e.
72

15.7. 3BYKoBble Ko.'1e6aHml 1IaCTOToA 'V HMelOT B nepBOii
cpe.n.e .n.JlHHY BOJlHbI '''1. a BO BTOppii cpe.ne A 2 . KaK H3MeHHTCH
CKOpOCTb pacnpOCTpaneHJIH 3THX J\OJle6aHHit npll nepexo;J.e H3
nepBoii cpe.n.bI BO BTOpylO, eCJ1H AI = 2'-2?
15.8. KaKHe BOJ1HbI, npo.n.OJIblibie IIJ1H nonepellHble, pacnpo-
cTpaHHIOTCH: 1) B ra3e; 2) B :H<1I.n.KOCTH; 3) B TB<?p.n.OM TeJIe?
15.9. npO.n.OJIbHbIMH HJlII nOnepeI.JllbIr-m HBJlHIOTCH BOJ1Hbl.
B036Y>K.n.aeMble CMbIqKOM B CTpYHe,- CTPYHOH B B03.i1.yxe?
15.10. CocTaBHTb ypaBHeHH nJIoeKoA BOJIHbl. paenpocTpa-
HHIOI..U.eHeH B B03.n.yxe. 'tIaCTHl.{bI KOTOpOH KOJIe6.nIOTcH C 'lac-
TOTOii 'V = 2 Kfl.{ H aMnJlHTy.n.oA A = 1,7 MKM. CKOpOCTb
pacnpocrpalleHHH 3BYKa B B03.J1yxe v = 340 M/c.
15.11. CocTaBHTb ypaBHeHlle n.lJocKoA BOJIHbI, pacnpocTpa-
HHIOI..U.eikH B cpe.n.e, TOllKH KOTOpOH KOJle6JIIOTCH C'tIaCTOTOH 'V =
= 1,5 Kfl.{. D.JlHHa BOJIHbJ, cOOTBeTCmYJOI..U.aH .n.aHHoii qaCTQTe
paBHa A = 15 CM. MaKCII'daJ1bHble CMeI..U.eHHH TOlleK cpeJl,bl OT
nOJlO>KeHHH paBIiOBeCHH B n = 200 pa3 MeHbwe 11.'1HHbI BOJlHbl.
15.12. B O.D.HOpO.n.HOH ynpyroii cpe.n.e paenpOCTpaHflercH
nJIOCKaH BOJIHa BH.n.a y = A cos ( wt - kx), J1306pa311Tb .n.JlH
MOMeHTa t = 0 rpa«t>HKH 3aBHcHMoCTeii OT x BeJlH'tIHH y H v Y '
15.13. YpaBHeHHe 6eryw.eH nJlOCKOH 3BYKOBOA BOJ1Hbl
H\feeT BH.n. y = 60 cos (1800t ,- 5,3x). r11e y - CMeI..U.eHHe.
MKM; t - BpeMH. c; x. - paecToflHHe. M. HaitTH OTHoweHHe
aMnJ1HTY11b1 CMeI..U.eHHH lIaCTHI.{ cpeJ1bl K Jt.1IIIHe BO.'1Hbl.
15.14. CKOpOCTb 3BYKa B BO.D.e v = 1450 M/e, Ha KaKOM
paccToHHHH HaX011HTCH 6.nH>Kaitume TOIIKH. cOBepWalOI..U.He
KOJle6aHHH B npoTHBOnOJlO>KHbIX «t>a3ax. ecJlH qaCTOTa KOJIe6a-
HHH 'V = 725 fl.{?
15.15. BOJIHa pacnpocTpaHflercH co CKOpOCTblO v =360 M/e
npH qaCTOTe 'V = 450 fl.{. 4eMY paBHa pa3HoeTb «t>a3 11BYX
TOlleK BOJIHbI, OTCTOHI..U.HX .n.pyr OT .D.pyra Iia paCCTOHHHlI
x = 20 CM?
15.16. KaKoii KaMepToH 3BYIIHT .n.OJlbwe: 3aKpenJIeHlfbIii
B_ THCKax HJIH CTOmu.Hii Ha pe30HaTOpHoM mI1.IIKe?
15.17. B KOMHaTe OObf1lHOrO pa3Mepa 9XO BOBee He Hat5.'1I0-
.B.aerCH. XOTH B Heii HMeeTCH WecTb OTpa>KalOUJ.HX nOBepXIIOCTeii.
tIeM o6'bHcHHereH TaKoe Ka>KYI..U.eecH OTeYTeTBlfe OTpa>KeHHH
3BYKOB?
15.18. fpOMKOCTb BocnpHHHMaer-mro 3Byt<a y6bIBaer oopaTHo
npOnOpl.{HOHaJIbHO KBa.n.pary paeCTOHHHH OT HCTOIIHHKa. YIJe-
ItHK, CHAmu.uii B nJlTOM PHAY. Haxo.n.HTeB npll6.nH3HTeJIbHO
BTpoe .naJIbme OT }'IIHTeJlH. lIeM CH.n.HInHii B nepBOM PH.n.y.
OltHaKo yc.nOBijH CJIbllI.IHMOeTH B oOOmc CJ\f'laHX MaJIO OTJIH-
qalOTCH .npyr OT .npyra, nOqeMy:t
73

3a.na'lH K rnaoe IV
IV. I. TOIln:a, COBeplllalOaH rapMOHH'leCKHe KOJIeOaHHH, B
HeKOTopblil MOMenT Bpelenu IIMeeT CMeeHue x =4,0.10- 2 M,
CKOpOCTb V = 0,050 M/c II YCKopenue a = 0,80 "flc". OnpeJl.e-
JIHTb: 1) aMn.'IHTY;J.Y H nepuoD; KOJIeOanHil TOIlKU; 2) $13Y KO-
JIeoaHuH B paccMaTpuBaeH MoeHT BpeMeHH.
IV.2. TeJIo r.I3CCOH m CKpenJIeHO npY:>KIIHOH :H<eCTKOCTblO k
C TeJIOM Maccoii At (pHC. 1 19). npY:>KHHY C:H<HMaT H omycKa-
lOT. OnpCJl.eJIHTb nepHOJl.bl KOJIeOaHHH TeJI. TpeHHe OTCYTcTByeT.
u


Pue. 119
PHC. 120
IV.3. O.n.HOpO.n.HYIO .n.OCKY nOJIO:H<HJIH Ha .n.Ba ObICTpO spa-
llI.aJOI1I.IIXCH pOJIHKa, KaK nOKa3aHO Ha pHC. 120. PacCToHHHe
Me:H<.lJ.Y OCHMH pOJIHKOB I = 20 CM, K03<MJHUUeHT TpeHHH Me>KJI.Y
.n.OCKOU H pOJIUKaMH J.L = 0,18. nOKa3aTb, 1frO D;OCKa 6Y.lJ.eT
cOBepmaTb rapMoHHllecKHe KOJIe6aHHH. HauTH ux nepuo.n..
IV.4. npe.lJ.CTaBUM maxTY, npoHu3bIBalOllI.YIO 3eMJIIO no
ee OCH BpaHHH. CIlHTaH 3eMJIIO 3a o.n.HOpOJl.llbIii map H
npeHeoperaS1 conpOTUBJIeHHeM B03.n.yxa, HaUTH:
 I) 3aKOH .n.BU:H<HHH TeJla, ynaBmero B maxTY;
2) CKOJIbKO BpeMeHH nOHa.n.o6HTCH 3TOMY TeJlY,
Qro6b1 .n.ocTHrHYTb npOTHBOnOJIO:H<Horo KOHU(i
maXTbI; 3) CKOpOCTb Te.i1a B ueH-rpe 3eMJIH.
IV.5. fpY3HK ua HHTH YKpenJIeU Ha TeJIe:H<Ke.
B HeKOTopblH MOMeHT BpeMeHH TeJIe:H<K3 HaIlH-
HaeT .wmraTbCH C YCKopeHHeM a. On pe.n.eJIHTb ,
Ha KaKoH MaKCHMaJIbHblH yroJI OT BepTHKaJIH
PHe. 121 OTKJIOHHTCH rpY3HK.
IV.G. fpY3 D no.n.BemeH K npY:H<HHe BC c
nOMOlll.bIO HHTH DB (pHC. 121). KaKoB3 .n.OJI:H<Ha 6bITb ar.WJIH'
Ty.n.a KOJIe6aHHH rpY3a, IlTOObI 3TH KOJIe6aHH 6b1JIH rapMO'
IIIllleCKHMH? Macca rpY3a m = 0,10 Kr, :H<eCTKOCTb npY:H<Hlfbl
k = 1600 HIM.
IV.7. npY:H<UHHbIH MaHTHHK BblBeJIH 113 nOJIO:H<eHHH paB-
HOBeCHH H omYCTHJIH. tJepe3 KaKoe BpeMH (B .n.OJIHX nepHOJl.a)
KHHeTUllecKaH 3HeprHH KOJIe6.nlOllI.erOCH TeJIa 6y.n.eT paBHa no-
TeIlUHaJIblJOH :meprUH npY:H<HHbl?
74

IV.S. nJIOCKaR 6eI'yul3R BOJJHa npe.nC1'aBJJeHa ypaBHeHUe\f
y = 0,05 sin (1980 t - 6x), I'.ZI.e y - CMelll.eHHe qaCTlll.(br,
C>d; t - BpeMR, c; x - paccTORHHe, M, no OCH, B.ZI.OJIb KOTOpoii
pacnpOCTpaUReTCSI BOJIHa. Onpe.Zl.enllTb pa3HOCTb $13 M.ZI.Y
Kone6.nlOllI.IIMIICfI TOqKaMH, HaXO.Zl.RllI.HMHCSI Ha paCCTORHHH
x = 35 CM .ZI.pyr OT .ZI.pyra.
IV.9. KaK H3MeHHTCR 3BYQaHHe HOTbI «.ZI.O» BTpen.eH OK-
TaBe (qaCTOTa Kone6aHUli "1 = 261 fit), 3anHcaHHOH Ha nJIac-
THHKe npH qaCTOTe Bpa1ll.eHHR .ZI.IICKa n1 = 33 OO/MIIH, eCJIII npo-
HrpblBaTenb nOCTaBJIeH B nOJIO>KeHlle n 2 = 45 OO/MHH?

11 ACT b B TOP A St. l\lOJ1EKYJUIPHAji H3HKA
f nAB A V. Mon EKY n SI PHO-KII H ETHIJ ECKASI
TEOPHSI CTPOEHHSI BEI.l.lECTBA
 16. Macea H pa3Mepbl Mo.rreKY.'1
16,1. Bo CKO.rrbKO pa3 HOJIOKO MaeeoH m = 200 r TH*e.rree
aTOla BOJI.OpOJI.a?
16.2. Bbl1mc.IJIITb Macey MOJIeKYJIbI BO.IJ.bI.
16.3. rJI.e 60JIbllJe aTOMOB: B CTaKaHe BOJI.bl HJlH CTaKaHe
PTYTH?
16.4. B o3epo I'JIYOHHOH h = 20 M H nJlOlII,aJI.blO S =
= 10 K{2 6pOCHJlH KpHeTa.IJJlIfK nOBapeHHoH COJIH Maecoi{ m=
= 0,010 1'. Cf<OJIbKO MOJIeKYJI 3TOH COJIIf OKa3a.'IOCb Obi B IIa-
nepCTKe BOJI.bl OO"beMOM V = 2,0 eM 3 , 3a'lepnHYToM H3 3Toro
o3epa, ecJIH ClJ:HT3Tb, 'ITO eO.IIb, pacrBopHBlIIHeb, paBHoMepHo
pacnpe;J.cmlJlaCb B 03epe?
16.5. OLlellHTb JI.JIH me.rre3a: 1) IJ:HC.IJO aTOMOB B
OO'beMe V = 1,0 eM 3 ; 2) paeCTOsIHHe Me)l{.1I.Y LleHTpaMH coeeJI.-
HHX aTOMOB.
16.6. OLleHUTb JI.JIH ra3a npH HOpMaJIbHbIX YCJIOBHnx: 1)
IlIICJIO MOJIeKYJI B 1,0 CM 3 ; 2) epeJI.Hee paecTOHHlfe Me)l{.1I.Y co-
CeJI.HHMH MOJleKYJlaMIf.
16.7. BbIIJ:IICJIHTb KOHLleHTpaLlHIO r.IOJleKYJI ra3a nplf HOp-
M8JIbHblX yeJIOBunx.
16.8. Onpe.::.e.'IHTb n.'IOTHOCTb yrJIeKHCJIoro ra3a npH HOp'
MaJIbHblX YCJIOBHHX.
16.9. CKOJIbKO MOJIeH C0JI.ep*HTCH B 1,0 Kr BOJI.bI?
16.10. KaKoH oODeM HMeJOT N = 1,0.10 22 aTOMOB aJIMa3a?
16.11. H3BecTHO, lITO He.rrb3H 3acramlTb Kane.rrbKY Heq,TH
06'beMOM 1,0 MM 3 paCnJlblTbCH no nOBepXHOCTH BOJI.bl TaK, 1fr06bl
OHa 3aHHJIa DJlO1II.aJI.b 6o.IIblIIe 3,0 M 2 . Ou.eHHTe no 3THM JI.aHHbl\f
MHHHMaJIbHble pa3Mepbl qaCTHLlbl HeqrrH.
16.12. PaeeToHHHe MeJK,Zty LleHTpaMH eOCeJI.HHX aTOMOS 30-
JIOTa paBHo 2,9.10- 10 M. CKOJIbKO aTOMOS YJlQ)KHTCH no TOJIntlf-
He JlHCTOIlKa 30JlOTa TOJI1II.HHOH 0,10 MKM?
76

16.13. CIJHTaSl. qro o6beM MOJIeKYJIh[ BO.,nhl palleH V = 1.1 X
X 10-S3 eMs. Haih6i. KaKOH npOu.eHT OT Bcero npOCTpaHCTBa,
saHHTOro BO.D.oA. np8XO.D.HTCH Ha .D.OJIIO C3MHX MOJIeKYJI.
16.14. OLHTaH. IJTO .D.H3MeTp MOJIeKYJlbI KHCJIOpO,l{a paBeH
d = 3.0.10- 8 CM, Ou.eOHTb, KaKOH JVlHHbJ nOJlYIJHJIaCb 6b1 HHTb,
ecJIH 6b1 Bce MOJIeKYJllil. eO,l{ep1K3lIJ.HeCH B m = 1,0 Mr KHCJlO-
pO,l{a. 6h1JIH paCnOJImKeHhl B O)l.HH P$!,l{. BnJIOTHYJO ,l{Pyr K ,l{PY-
ry. Bo CKOJIbKO pa3 .D.JIHHa 3ToA HHTH OKa3aJIaCJ 6b1 OOJIbWe
epe.D.Hero paCCTOHHHH OT 3eMJIH JJ.O JIYHbl?
 17. .D.BH1KeHHe MoneKyn, 83aHMOAeHCTBHe
MoneKyn
17.1. CKOpOCTb ABH1KeHHS1 ra30BbiX MOJIeKyn npH 06blIJHbIX
YC.IJOBHHX H3MepHeTCH COTHHMH MeTpos B eeKYH.D.Y. nOlJeMY A\:e
npoLlecc JJ.UqxpY3HH ra30B npoHcXO,l{HT cpaBHIfTe.JIbHO MeAJIeH-
HO? -
17.2. XOpOIllO OTKalJaHHaH .naMna HaKaJIHBaHHH 06'be:\lOM
V = 10 CM 3 HMeeT Tpe1ll.HHY, B KOTOPYIO eceKYH.nHo npoHH-
KaeT Z = l()'llJaCTHu. ra3a. CKOJIbKO BpeMeHH nOHa.D.o6HTCH .D.JIH
HanOJIHeHHH JIaMnbl AO HOpMaJIbHOrO .D.aSJIeHHH, eCJIH CKOpOCTb
npoHHKHoneHHH ra3a OCTaeTCH nocTOHHHOii? Te!>meparypa t =
= O°C.
17.3. nOlJeMY 6pOYHOBcKoe ABII>KeHlle oc06eHHO 3aMCTHO Y
HaHOOJIee Me.JIKHX B3BemeHHbIX qaCTHu., a Y ooJIee KpynHblx
OHO npOHCXO.D.HT MeHee HHTeHCHBHO?
17.4. 1..Jer.1 06'bHCHHTb B03pacTaHue CKOpOCTII ,l{HqxpY3HH C
nOBbIllleHHeN TeMnepaTyphl?
17.5. 3a speMH t = 10 CYT nOJIIIOCTblO UCnapHJIOCb H3 cra-
KaHa m = 100 r BO)J.bI. CKOJIbKO B cpeAHeM BblJIeTaJIO MOJIeKyJI
C nOBepXHOCTU BO)J.bI 3a 1,0 c? -
17.6. KaKoB XapaKTep TenJIOBOrO .u.BH1KeHHH B aToMapHbIx
ra3ax? KaK .D.BH>KYTCH aTOMbI B KpHCTaJIJIe?
17.7. 1..Jro o61l1.ero H B lJeM pa3JIHQHe Y JIb.n.a, BO.ll.hl U BO.D.HHO-
ro napa c TOIJKH 3peHHH MOJIeKYJIHpHo-KHueTH'lecKoif TeO-
pHH?
17.8. nO'leMY 83 OCKOJIKOB pa36uToro CTaKaHa HeB03MO>KHO
Co 6 paTb u.eJIbIH cTaKaH?
17.9. 1..JTO o6JIa.n.aeT oo.'1bllleii BHYTpeHHeH meprHeii: Bo.u.a
npH 100 0 C HJIU TaKaH 1Ke Macca Bo.n.HHoro napa npH TOB 1Ke TeM-
nepaType?
17.10. KaK H3MeHHJIOCb 6h1.n.aBJIeHHe B cocYJJ.e c ra30M. eCJlH
6h1 BHe3anHO HC'le3JIH CHJIhI npHTHJKeHUH Me)f{,ll.Y MOJIeKYJIaMH?
77

......
 18, TeltnOBOC paCWHpeHHe TBep.l1b1X
H )KH.II.KHX Ten
18.1. nOqeMY C 113MeHeHHeM Te!omeparypbl Tena H3MeHH1OT
tOOH pa3Mcpbl? 3aBHCHT Jill Ko3<M>HLlHeHTbl JIHHeHHoro H OO"beM-
Horo pacllmpeHIfH OT TeMnepaTYPbl?
18.2. )KeJIe3H}1O JIHHeuKY )J.JIHHOH 1= 30 CM npH 0° e
HarpeBalOT Ha 6 T = 100e. )KeJIC3HblH Crep:H<eHb JVIHHOH I =
= 30 CM nplf lOC HarpeBalOT Ha liT = HrC. Ha CKOJIbKO
Y13eJIlf ' lHBalOTcH )J..'IHHbl JIIfHeHKH II CTep:H<HH npH 9TOM?
18.3. KaK .lI.OJI>KHbl OTHOCHTbCH JVIHHbl 1 1 H I" )J.BYX CTep>K-
Hen, C)J.eJIaHHblX 1f3 pa3HbIX MaTepHanOB, C Ko3<M>mtHeHTaMH
JIlflleHHoro paClllHpeHHH a1 H ah
@  IITo6bl npH JII060H TeMnepaType pa3-
0 , ". - - HOCTb )J.JIHH CTep>KHen OCTaBaJIaCb
nOCToHHIIOH?
18,4. nOlleMY JVIH CHHTHH BHYT-
peHIIHx HanpH>KeHHH B MaTepHaJIaX
PHe. 122 HX nOCJIe HarpeBa oxna>KAalOT OqCUb
Me)J.JIeIlHo?
18.5. MeTa.'IJIJf1JeCKOe KOJIbLlO H .lI.HCK C Bblpe3allHblM ceK-
TOpOM C yrJIOM paCTBopa q> (pHC. 122) HarpeBaJOT. I13MeHHTcH
JIH DHYTpeHHlIH )J.HaMeTp KOJIbLla? 113MeHHTcH JIH yrOJI paCTDO-
pa q>?
18,6. 06"bSICHUTb, noqer.ry CTeKJIHHHaH 6allKa, ec.IJH ee no-
CTaBUTb lIa oro lib, pa3JIeTHTCH Ha KYCOIlKIf, a MeTaJIJIUllecKaH
KaCTplOJlH paCnJIaBIITCH? nOlleMY XHMUqeCKYIO nocyll.Y )J.eJIalOT
H3 J<capLla?
18.7. KaJ<ue HanpH>KellHH B0311HKalOT B TpzMBai'IHblx peJIb-
cax npu TeMnepaT)'pe -10°C, eCJlu IIX YKJla.ll.bfBaJIH npH TCM-
nepaType 100C?
18.8, CTa.'1bHaH cTpYHa )J.JlHHOH 1= 3,0 M, nJIolltaJJ.blO no-
nepe1Jlloro celleHIfH S = 1,0 MM" flaTHHYTa Me:H<)J.Y .D.BYMH cre-
HaMU. Ha CKO..lbKO lf3MeflHTCH CHna HaTH:>KeHHH CTPYHbl npH
OXJIa>K)J.eHHH ee Ha 6 T = 30 K? KaK H3",eHHTCH nOTeHLlH3JIb-
JlaH 3HepmH CTPYJlbI? TOqKIf 3aKpenneflHH CIlHTaTb HenO.D.BU>K-
HhIMH.
18.9. nOl{a3aTb, IlTO Ko3<M>HIJ.HeHT 06"beMHoro paCIlJlfpeHHH
p B TPH pa33 60JIblUe Ko34xt>HIJ.UeHT3 JIHHeHHoro paclllHpeHHH
a C .D.OCT3TOIlHO 6onbllJoii TOIlHOCTblO. .
18.10. Me.D.HhfH JIHCT n.'10lltaJJ.blO So = 0,30 M 2 npH 20° C
HarpeJIlf .lI.O 600° C. RaK H3MeHHJIaCb ero nJIOllta)J.b?
18.It. npH Telomeparype t = O°C JVIHHa a.'1IOMH}fHeBOro
creP)KHH I = 50 CM, a >KeJIe3HOrO D3 lil = 0,50 MM OOonbIDe.
78

Ce'leHIHI CTep:H<HCil O.l1.HHaKOBbI, DpH KaKOii TeMnep8Type t,
6y.nYT O.nHHaKOBbI .nJIHHbI CTep>KHeH H npH KaKOA TeMnepa-
Type t 2 6y.nYT o.n!IHaKOBbi !IX 06"beMbI?
18.12. B >Ke.1e3HbIH ()H.nOH eMKOCTblO V o = 10 JI HaJll1T .no
caMoro Bepxa KepOCIIH npll Tel.mepaType 5°C. KaKoH o()"beM
KepocHHa BbiTe'leT, eCJ1H nOMeCTHTb 6H.nOH B KOMHaTe, r.ne
Ter.mepaTypa 20°C? PacwHpeHHe ()H.noua He Y'lHTbIBaTb.
18.13. KaK}'1O nonpaBK)' HaJ{O BueCTH B peweuHe npeJ{bl-
J1ymeH 3aJ{aQH, eCJ1H YQHTblBaTb pacwHpeHHe ()HJ1oHa?
18.14 HaHTH nJ10THOCTb pryTH np" TeMnepaType 100°C.
18.15. Bec 6eH3HHa npH O°C PI=88 H. DpH 6O°C Bec
6eH3HHa, 3aHHMalOmero TOT >Ke O()"beM, P 2 =83 H, OnpcJ{e-
JIHTb K034><lmIJ.HeHT O()"beMHOrO pacwHpeHHH ()eH3HHa.
18.16. Pa3HocTb TeMnepaTYP B KOJIeHaX co06malOmero-
CH cocYJ{a paBHa !!.T. DpH 9TON B OJ1HOM KOJIeHe BbICOTa
>KHJ{KOCTH hI. B .nPyroM h 2 , OnpeJ{eJ1HTb K034>4>uIJ.HeHT O()"b-
eMHoro pacllIHpeHHH >KHJ{KOCTII. GeM YJ{06eH 9TOT MeTOJ].
onpeJ{eJIeHHH K034>4>HIJ.HeHTOB 06"beMHOrO pacwHpeHHH
>KH.nKocTei\ ?
18.11. CMe-WaJ1H J{Be paBHwe MaCCbl BOJ{bI C TeMnepary-
paMH t l = 1° C, t 2 =7° C. M3MeHHTcH J1H o()mHA" o()"beM BO-
J{bI, Kor!1a TeMneparypa YCTaHoBHTcH?
18.18. nOQeMY }l.a>Ke B O'IeHb CHJIbHble MOp03b1 03epa He
npOMep3alOT J{O J{Ha? .
18.19. TOJ1mHHa ()HMeTaJlJIH'lCCKOH nJ1aCTHHKH, COCTaB-
J1eHHOH 113 O;J.IIHaKOBbIX nOJIOCOK CTaJ1H H IJ.HHK3, paBHa
d=O,10 MM, OnpeJ{eJlHTb paJ{HYC KPUBU3Hbl nJIaCTHHKII npll
nOBblweHHH TeMnepaTYPl>l Ha !!.T';; 10 K OT TeMnepaTypbl,
npll KOTOpOH nJ1aCTHHKa ()blJIa pOBHOH.
J8.20. AJIIOMHHHeBblH wapHK MaccoH m=50 r onymell
Ha IUlTH B KepocHH. Ha CKOJIbKO H3MeHHTCH CH.1Ia HaTH>Ke-
HIIH HIITII, eC.'1H BCIO cilcTeMY HarpeTb Ha !!.T=50 K?
r JI A 8 A VI. CBOnCJ'BA rA30B
 19. MOneK}'JIHpHO-KHHeTH'leCKaH TeopHH ra30B
19.1. KaKHc MOJIeK)'JIbl B aTMoc4>epe J{BII>KYTCH ()blCT-
pc: MOJleKym.>l KHCJIOpoJ{a HJ1H a30Ta?
"\ 19,2. BblIJHCJ1HTb cpe.nlllOlO KBa.npaTHIJHylO CKOpOCTb aTO-
MOB rem!H npH TeMnepaType 21" C.
19.3. Dpll nOBblweHHH TeMnepaTypbl HJ{eaJIbHOrO ra3a lIa
6T I = 150 K cpe.nHHH KBa.npaTHIJUaH CKOpOCTb ero MOJIeK}'JI
YBC.IIIfqfIJlaCl> s... vI=400 M/C AO v2=500 M/C, Ha CKOJIbKO
79
(
0-

HY:H<HO Harperb 3TOT ra3, IJT06b1 YBeJIHIJHTb Cpe.nHlOIO KBa.npa.
THIJH}'IO CKOpOCTb era MOJIeKYJI C U 1 = 500 M/C .no Us =
= 600 M/C?
19.4. Onpe.neJIHTb KOHu.eHTpau.HIO MOJIeKYJI H.neaJIbHOro
ra3a nplf HOpMaJIbHOM .naBJIeHHH H T.eMnepaType t = 23° C.
CKOJIbKO TaKHX MOJIeKYJI 6y.neT co.nep>KaTbCSI B KOJI6e eMKo.
CTblO V = 200 MJI?
19.5. D.Ba o.nHHaKOBblX cocy.na, co.nep>Kau.r.Hx o.nIlHaKO-
Boe IJHC.'10 MOJIeKYJI a3OTa, coe.nHHeHbI KpaHoM. B nepBoM co-
cY1J.e Cpe.J1HSISI K Ba 1J.paTHIJHaSl CKOpOCTb MOJIeKYJI paBHa v 1 =
= 400 M/C, a BO BTOpOM v 2 = 500 M/C. KaKaSl YCTaHoBHTcH
CKOpOCTb, eCJIIi OTKpbITb KpaH, Coe1J.HIUIIOu.r.HH cocYJJ.bI?
19.6. B 3aKpblTOM cocy.ne Haxo.nHTCSI lf1J.eaJIbHbIH ra3. KaK
H3MeHHTCSI era .naBJIelllfe, eCJIIf Cpe1J.HSISI KBa.npaTHIJHaSl CKO-
pOCTb era MOJIeKYJI YBeJIlflJHTCSI Ha 20%?
19.7. KaKoBo .naBJIeHHe o.nlloaTOMHora ra3a, 3aHJfMalO-
u.r.era 06"beM V = 2,0 JI, eCJIJf era BHYTpellHSISI ::;meprHSI U =
= 300 D.>K?
19.8, KaKaS1 TemepaTypa COOTBeTCTByeT cpe.nHeil KBa.npa-
THIJIIOH CKOpOCTH Mo.lJeKYJI yrJIeKHCJIOra ra3a v = 720 KM/IJ?
19.9. nOIJC\1Y B aTMoc<l>epe 3eMJIH HeT MOJIeKYJI BO.nopo.na?
nOlleMY Y JIYHbI HeT anloc<l>ePbl?
19.10. CKOJIbKO MO.leKYJI KHCJIOpo.na Haxo.nHTCSI B cOCYJl.e
06'beMOM V = 1,0 JI, eCJIH Tel\mepaTypa KHCJIOpo.na t = 150° C,
a 1J.aBJIeHHe paBHo p = 0,132 Hna?
19.11. CKOJIbKO CTOJlKHOBeHHH B ceKYII.ny HcnblTblBalOT
MOJIeKYJIbI KJlCJIOpo.na, ec.nH Cpe1J.HSISI .nJIHHa cBo60.nHora npo-
6era npH HOpMaJIbHbIX YCJIOBHSlX paBHa 'J.. = 65 11M?
19.12. Cocy.n, co.nep>Kau.r.HH HeKOTopoe KOJIlflJeCTBO O.nHO-
aTOMHoro ra3a, 1J.BH>KeTCSI co CKOpOCTblO t., 3aTeM BHe3amiO
OCTaHaBJIIfBaeTCSI. Ha CKOJlbKO YBeJIHIIHTCSI npH 3TOM KBa.npaT
cpe.nHeil KBa.npaTHIJHOH CKOpOCTH MOJIeKYJI?
19.13. Ha CKO.'lbKO H3MeHHJIaCb BHYTpeHHSlSI ::;meprlfH 10 MO-
JIeH 01J.HoaToMHoro ra3a npH era HarpeBaHHH Ha tJ.T = 100 K?
 20. ra30Bble 3aKOHbI. YpaBHeHHe COCTOJlHHR
H.II.eaJlbHOrO ra3a
20.1. KaKoB OO'beM 0,25 MOJISI H.ne3JIbHOra ra3a npH .naBJIe-
HHH 83 KIla H TeMnepaType 127" C?
20.2. KHCJIOpO.n npH TeMnepaType 77° C H J(aBJIeHHH
0.20 Mna 3aHHMaeT 06"beM 10 JI. KaKoBa ero Macca?
20.3. B cocy.ne OO""eMOM 12 JI HaXO!l.HTCSI 25 r raJa npH
TeMnepaType 27° C H .naB,IIeHHH 1,85 KDa. l\aKoii  ra3?
80

20.4. KOr..'l.a H3 COCY;1a BhmYCTUJlU HeKoTopoe KOJlHlJeCTBO
ra3a, l1aBJleHHe B HeM ynaJlo Ha 40%, a a6cOniOTHaH Tep>mepaTY-
pa - Ha 10%. KaKYIO lJaCTb ra3a BbmyeTJIJ1H?
20.5. HaIJepTJITb rpaIIK H3MeHeHIIH nnOTHOCTH H.n.eaJlb-
HOro ra3a B 3aBHeHMOCTH OT Te\mepaTypbl npH H30TepMHlJe-
CKOM, H306apHoM H H30XOpHOM npoll.eecax.
p  V
V T
PHC. 12 PRe. 124
20.6. Ha pile. 123 11306pa>KeHbI .n.Be H30TepMbl l1J1H o.n.Holi
H TOM >Ke MaeCbl ra3a. 4eM OTJllIlJalOTCH eOCTOHHHH ra30B, eCnH
ra3b1 O.ll.HUaKOBbl? 4eM OTJlHlJalOTeH ra3b1, eeJlH HX Te},mepaTY-
pbl o.n.IIHaKoBbI?
20.7. 4eM OTJllIlJalOTCH .n.pyr OT .n.pyra rpa4JIIKH 33BHCHMO-
eTH l1aBJleHHH ra3a OT a6conIOTHoH TeMnepaTypbll1J1H: 1) .lI.BYX
o.n.HHaKOBblX Macc l1aHJloro ra3a, HarpeBaeMbiX H30XOpHO B co-
ey.n.ax pa3Horo 06'beMa; IJ
2) .n.BYX pa3HblX Mace, DJ
HarpeBaeMblX H30XOpHO B P LL P l==-
O.ll.HHaKOBblX no 06'beMY I IZ
eocy.n.a x ?
20.8. Ha pllC. 124 z
npe.n.CTaBJleHbI .n.Be "306a-
pbl l1J1H O.ll.HOH H Toli >Ke l' T
MacCbI HeKoToporo ra3a. PHC. 125
KaK OTHOCHTCH .n.aBneHHH
ra3a, ecnH yrJlbl HaKJlOHa H306apbl H OCH a6cll.HCC paBHbI «1
II «2?
20.9. no rpaHKY, npHBeAeHHOMY Ha pHC, 125, onpe.n. e -
JlHTb KaK H3MeHHTCH 06'LeM H.n.eanbHoro ra3a "PH nepeXO.ll.e 113
COCTOHHHH 1 B COCTOHHHe 2.
20.10. npH paclliHpeHHH ra3a "PH nOCTOHHlIOH TeMnep8TY-
pe 6b1J1a nonYlJeHa 3aBHCHMOCTL p OT V, npHBeAeHHaH Ha
pHC. 126. 1.Jro npoHexo.n.HJlO C ra30M?
20.11. no rpa4>HKY, npHBeJteHHOMY Ha pHC. 127, onpe.n.e-
JIHTh, KaK H3MeHHnOCb .n.aB.lleHHe H.lI.eanbHoro ra33 npH nepexo-
11,e H3 COCTOHHtfH I P COCTOHliHe 2.
81

20.12. npn H306apHoM narpeBalIHH 6blJIa nOJIyqeHa 3a-
BHCHMOCTb V OT T, H306pa}KeHHaH Ha pHC, 128. tho npOHCXO-
AUJIO C ra30M?
20.13. Ha pHC. 129 ,n,aHbI napaMeTpbl Jl.BYx COCTOHHHH ra3a.
Tpe6yeTcH COBepllIHTb nepexo.l1. H3 COCTOHHHH 1 B COCTOHHHe 2
C nOMOlll.bIO: 1) H306apbl H H30TepMhl; 2) H30TepMbI H H30XO-
pbl; 3) H306apbl H H30XOpbl. HalIepTHTb B KOOp.l.(HHaTaX p, T
Ka>K)l.blH 113 YKa3aHHblX nepeXO,IJ.OB,
p
v
/
2
,.
1 = _
T
v
r
PHe. 126
PRe. 127
PRC. 128
20.14. Ha pHC. 130 npe,IJ.CTaBJIeH 3aMKHYTblA lI.HKJI. BbI-
qepTHTb :.TY AHarpaMMY B Koop.l1.HHaTaX p, T H V, T.
20.15. Ha pHC. 131 Hso6pa}KeH 33MKH)'TblH lI.HKJI, COCTOH-
llI.HH H3 H30XOPbl, H306apbl H H3orepMbI. npe.l1.CTaBHTb 3TOT
lI.HKJI KOOp,IJ.HHaTaMH p, T H V, T. -
20.16. 11306pa3HTb B KOOp,IJ.HHaTaX V, T H p, V lI.H KJI ,
H306pa}KeHHblH Ha pHC, 132.
20.17. Ha imc. 133 npe,IJ.CTaBJIeH 32MKHYTblH lI.HKJI. BbI-
qepTHTb 3TY ,lJ.HarpaM\fY B KOOp.l1.HHaTaX p, T H p, v.
 t -------iZ
p/ --.,1 :
I I
I I
I I
1j JZ T
p
:0:
v
Pile. 129
PIIC. 130
20.18. no rpa4>HKaM, npHBe.l1.CHHblM Ha pllC. 134, onpe.l1. e -
JIHTb, KaK H3MeHHJIaCb TeMnepaTypa H,lJ.eaJIbHoro ra3a
20.19. B Tpy6Ke, 3aKpblToH C O,IJ.HOro KOHlI.a, CTOJI6HK B03-
.l1.yxa 3anepT CTOJI6HKOM PTYTH MHHOii H = 20 CM. KOr,IJ.3
Tpy6Ka pacnOJIO}KeH3 OTKpbITbIM KOHlI.OM BHH3, ,lJ.JIHHa CTO.'l-
6HKa B03.'1.yxa paBH;:t h = 10 CM. ECJIH }Ke Tpy6KY llaKJIOHHTIt
82

no,IJ. yrnoM a = 30 0 K ropH30HTY oTBepcTlfeM BHlI3, JI.JU1II3 B03
.lJ.)'llJHOrO CTOJIOHKa CT31IOBHTCSI paBuoll h 2 = 8,46 CM. Onpe-
,lJ.e.'IHTb aTMOC<PePHoe ,lJ.aBJIeHHe,
20.20. CTeKJUIHH}'1O Tpy6KY ,lJ.JlHHOll L = 10 CM Ha 1/3 no-
rpY}f<aIOT B PTYTb, 3aTeM ee 3aKpbIBalOT nanbu,CM H BblIIHMaIOT.
KaKoll ,lJ.JlIfHbI CTOJl(}HK PTYTH OCTaneTCH B Tpy6Ke? CTon611K
PTYTH B PTYTHOM 6apoMeTpe H3XO.ll.HTCH n3 BbiCOTe H = 75 CM.
p
2
p
,,
1
, ,/'
'"
t'
v
T
Pile 131
PHe 132
20.21. Bap0!\1eTpH'lCCK3H Tpy6Ka onYI1.\,CH3 B DepTIlKanb-
Hblll 6oJlbwOH cocy.l1. C PTYTbIO. Cro.'16 PTYTH B Tpy6Ke HMeeT
BblCOTY hI = 40 MM, a cron6 B03.l1.yxa Ha,IJ. PTYTblO h 2 = 19 CM.
Ha CKonbKO Ha,IJ.O onYCTHTb Tpy6KY, 'lro6b1 CTon6HKH PTYTH
OKa3anlfCb Ha O,IJ.HOM ypOBHe? PTYTb B PTYTHOM 6apOMeTpe
H3XO;J.HTCH H3 BbiCOTe H = 76 CM.
v V P
2  P
, / :J4 II ./'
'/.
r , 2
/ ,
/ ,
/
T T V
PHe. 133 Pile. 134
20.22. 3.r.eKTpH'leCKaH .r.ar.mmIK3 eMKOCTblO V = 0,50 JI
HanonHeH3 a30TOM npH ,lJ.3BJIeHHH p = 76 Kn3, K3Koe KO-
JlH'lecTBO BO,'l,bl BOH,lJ.eT B n3Mny, ecJIH y Hee OTnOMI:Tb KOllqHK
no.l1. BO,IJ.OH lIa rny6HHe h = 1,4 M? AnlOc<PePHoe ]J.aBJ1eHlle HOp-
r.t3J1bHoe.
20.23. KOl1mpeccop 3aC3CblBaeT H3 an1oc<PePbl KaJK.llYIO ce-
KYHJI.Y 4,011 B03.l1.yxa, KOTopble no;talOTCH B 6annOH eMKOCTblO
120 n, 4epe3 CKOJ1bKO BpeMeHH )l.aBneHlfe D 6aJ1J10He 6Y.l1.eT npe-
83

BblllIaTb aTMO*pHoe B 9,0 pa3? HaqaJlbHoe A8BJIeHHe B &.n-
nOHe paBHO aTMoapepHOMY.
20.24. CKOJlbKO Ha.IJ.O C.lJ.e.naTb XO.ll.OB nopillHSI, qro6bl Haeo-
COM eMKOCTblO VI = 0,50 JI OTKa'laTb B03.l1.YX B KOJl6e Om.eMOM
VI = 5,OnOT HOpMaJlbHOrO.l1.aBJIeHHSI.lI.O.IJ.aBJleHHSlp = 50na?
20.25. B03.l1.YX B OTKpbITOM coeY.lI.e Me.l1.JleHHO HarpeJJ.H .lI.O
TI = 400 K, 3aTeM, repMeTHqecKH! 3aJ<"pblR, rocy.l1. oxna.IJ.HJlH
.lI.O T I = 280 K. Ha CK(lnbKO r.PH 3TOM H3MCIIII.1OCb AaBJIeHHe
ra3a B cocY.lJ.e?
20.26. MaHoMeTp Ha 6aJlJlOHe C ra30M B nOMew.eHHH e TeM-
nep3TYPoH TI = 17' C nOKa3blBae-r A8BJIeHHe PI = 350 JUla.
Ha ynHlI.e NaHOMeTp nOKa3blBae-r P.. = 300 Kna. KaKoBa TeM-
nepaTypa HapYiKHore B03.IJ.yxa, eeJiH aTMoe4>epHoe .lJ.aBJIeHHe
HOpMaJlbHoe?
20.27. JJ.aBJIeHUe B03.l1.yxa B llIuHe aBTOM06HJlSI paBHO PI =
= 5,0 aTM npH TeMnepaType II = 17' C. Bo CKOJlbKO pa3
YMeHbillHTcSI nJlOll1.a.Il.b conpHKocHoBeHHSI KOJIeca e .noporoii,
eCJIU BO BpeMH e3J1.bl TeMnepaTypa B illHHe nOBblCHJlaCb .lJ.O I.. =
= 57' C? ATMoeq>epHoe .lJ.aBJIeHUe HOpMaJlbHoe. H3MeHeHHeM
06'beMa llJJlHbl npeHe6pe'lb.
20.28. Bo CKOJlbKO pa3 YBe.nH'lHTCSI 06'beM B03.IJ.YillHoro llIa-
pa, ecJJH ere BHecTU C YJlHlI.bl B TenJloe nOMell1.eHHe. TeMnepa-
Typa Ha ynulI.e - 3° C, B nOMell1.eHHH + 27' c.
20.29. 06'beM'" HeKOTOpoii MaCCbl ra3a npH HarpenaHuH Ha
llT = 10 K npH nOCTOSlHHOM .nanJleHHH YBeJm'lHJlCH Ha n =
= 0,030 cBoero nepnOHa'laJlbHOrO oG'beMa. Onpe,!J.eJlHTb HaqaJlb-
HYIO TeMnepaTYPY ra3a?
20.30. 11.0 KaKoA TeMnepaTypbl npH 1I0pMaJlbHOM aTMOC-
.pepHOM .n.aBJleHHH Ha.IJ.O HarpeTb KUCJIOPO.IJ., IJT06bl ero nJIOT-
HOCTI> CTana paBHa n.'JOTHOCTH a30Ta npH HopManbHblx YCJIO-
BHSlX?
20.31. KaKaSi Macca B03.IJ.yxa BblH.lJ.eT H3 KOMHaTbl, ecJJH
TeMnepaTypa B03.l1.yxa B03pOCJIa C 11 = 10° C .no I.. = 20° C?
06'beM KOMHaTbl V = 60 M'. 11.aBneHHe HopManbHoe.
20.32. BnYTpH 3aKpbITOrO C OOOHX KOHlI.OB repH30HTanb-
Horo llHJlHH.ZIpa HMeeTeSi TOHKHH nOpllJeHb, KOTOpblH MO>KeT
CKOJlb3HTb B lI.HJlHH.lI.pe 6e3 TpeHIlH, C O.IJ.HOH eropoHbl nopillllH
HaX0.l1.HTCSI BO.IJ.OpO.l1. MaCeO" m l = 3,0 r, C .D.Pyro" - a30T Mac-
co" m 2 = 23 r. KaKYIO lJaCTb Om.eM3 lI.HnHII.ZIpa 3aHHMaeT BO-
AOpO.IJ.?
20.33. E eTaJlbHOH 6anJlOH eMKoeTblO V = 10 n HarHeTa-
eTCH BO.n.OpO.l1. npH TeMnepaTYpe T = 290 K. CKOJIbKO -BO.IJ.OpO-
.n.a MO>KHO nOMecTHTb B 6anJloH, eCJIH .lJ.OnYCTHMoe A8BneHHe Ha
CTeHKH 6aJlJIOHa P = 50 MIla?
B4

20.34. BannoH, cOJ1ep)!{a1l1H ma = 1,0 Kr a30Ta, npH HcnLl-
TaHHH B30pBanCH npH TeMnepaType TI = 630 K. KaKoe KOJlH-
qecTBO B0J10pO;J.a MO)!{HO xpaHHTb B TaKOf }Ke 6anJIOHe npH TeM-
nepaType T I = 270 K, HMeH .lJ.eCHTHKpaTJII>iH 3amrc npOqHOCTU?
20.35. B Tpy6Ke, nOKa3aHHoH Ha pUC. 135, BblCOTa cToJI6a
B03;:tyxa 1 = 30 CM, a BblCOTa cToJI6a PTYTH h = 14 CM.
TemepaTypa B03.IJ.yxa t l = 27° C:;, a .lJ.3BJIeHHe 3TMOC4>epbl co-
OTBeTCTByeT ypOB1l1O PTYTH B 6apOl\feTpe H = 76 CM. KaK H3Me-
HHTCH ypOBeHb PTYTH, ecnH .lJ.aBJIeHHC
aTMoc4>epbl OCTaHeTCH npe}KHUM, a Ter-we-
paTypa nOHH3HTCH .lJ.O t 2 = 12° C?
20.36. .D.Ba o;:tHHaKOBblX cocY.lJ.a, co-
.lJ.ep}Ka1l1He ra3 npH T = 290 K, Coe.IJ.H-
HeHbl ropH30HTa.1bHoH Tpy6KOH .lJ.HaMeT-
pOM d = 4,0 MM, nocepe;:tHHe KOTOpOH na-
XO.IJ.HTCH KaneJIbKa PTYTH. 06'beM coCy;:tOB
BMeCTe C Tpy6KOH paBeH V = 0,40 n. Ha
Kah.oe pacCTosIHue nepeMecTIfTcH KanenbKa
PTYTH, ecJIU TeMnepaTYPY O.IJ.HOro cocY.lJ.a nOBblCHTb Ha
11 T = 1,0 K, a ;:tPyroro Ha CTOJIbKO }Ke nOHH3HTb? PacwH-
peHHef CTeHOK cocY.lJ.OB npeHc6peQb.
20.37.. ABa cocY;:ta, co;:tep}Ka1l1Ifx O.IJ.HHaKOByro Maccy Oil-
noro H Toro >Ke ra3a coe.IJ.HHeHbl Tpy6KOii C KpaHoM. B nepBoM
cocy;:te ;:taBJIeHUe PI = 1,0.10 5 na, a BO BTOpOM P2 = 3,0 x
X l()!i na. Te!>mepaTypa O;J.llllaKOBa. aKoe YCTanOBlfTCH .lJ.aBJIe-
HHe nOCJIe OTKpblTlfH Kpana?
20.38. B cocY.J. 06'beMOM V = 1,0 n nO\fe1l1alOT KHcnopo,!t
MaccoH mJ( = 2,0 r H 330T MaCCO" ma = 4,0 r, KaKoBo .lJ.aB-
JIeHlfe CMeCH npH TeMnep3Type T = 273 K?
20.39. B cocYlle 06'beMOM V = 1,5 JI 113XO;:tHTCH CMeCb KIiC-
JIopOJ1a II -yrJIeKHCnOro ra3a. Macca CMeCIf m = 40 r, Tel1me-
paTypa T = 300 K, ;:taBJIe:lHe p = 2,0 Mna. HaHTH Maccy
Ka>KJ{OrO H3 ra30B.
20.40. B 3aKpblTOM cocY.l1.e naXO;J.HTCH B03.l1.YX H KanJIH BO-
.D.bI MaccoH m = 1,0 r. 06'beM cocY;J.a V = 75 JI, .lJ.aBJICHHe B
HeM Po = 12 K11a H TeMnepaTypa T = 290 K. KaKHM 6Y.lJ.eT
;:taBJIeHHe B cocY.l1.e, Kor;:ta KannH HcnapHTcH?
20.41. B aTMoc4>epHOM B03;:tyxe Ha .lJ.OJIIO a30Ta npHXO.IJ.HT-
CSI na = 0,76 MacChI, a Ha ;:tOJIIO KHCJIOpo;:ta "J( = 0,24 (eCJIH
npeHe6peQb npHMecHMH ;:tpyrnx ra30B). BWlHCJIHTb cpe;J.HIOIO
MOJIHpHyro Maccy B03J1.yxa.
I
PRC. 135
85

S 21. CBOHCTB3 napOB. Bn3mHocTL
21.1. nap. HaXO.IJ.SJllHiicSI B llHJlHH..lpe no.IJ. nopumeM. Me,!},-
JleHHO C>KHMalOT npH nOCTOSlIIHOH Ter.mepaType .lJ.O nOJlHOro
OKH>KeHHSI. HaqepTIfTb rpa<l>IfK 3aBIfCIfMOCTIf .n.aBJleHHSI OT
06'beMa.
21.2. CpaBHHTb nOBe.IJ.eHHe MOJleKYJl B Jf.IJ.ea.1LHOM ra3e If B
HaCbll1{enHOM nape npH C>KaTHH.
21.3. B llIfJlIfll.IJ.pe no.IJ. nopwHeM HaX0.IJ.HTCSI 3.0 r BO.IJ.SlHO-
ro napa npH TeMnepaType 30° C. fa3 H30TepMIfqeCKH OKHMalOT,
npH KaKOM 06'beMe Bbma.IJ.eT poca?
21.4. B 6aJlJ!one eMKOCTblO 50 JI HaXO.IJ.HTCSI 0.30 r BO.IJ.SlHO-
ro napa npIf TeMnepaType 17' C. KaK C.lJ.eJlaTb nap HaCblIl{alO-
W.IfM?
21.5. Tpy6Ka, O.IJ.UH KOHell KOTOpOH 3anaslH. HanOJlHeHa
BO.IJ.OH n OTKpl>lTbIM KOHllOM onyw.ena B CTaKaH C BO.l1.0H. BO.l1.a
H B CTaKaHe H B Tpy6Ke nOCTeneHHO HarpeBaeTCSI .lJ.O 100°C.
tho npH 9TOM .lJ.OJ1>KHO npOHCXO.l1.HTb B Tpy6Ke?
21.6. KaKoBa nJlOTHOCTb HaCblllleHllOro napa BOJ1.bl npH TeM-
npaType 100° C?
21. 7. Bo CKOJIbKO pa3 nJlOTIIOCTb BO)1.bl npH 20" C 60JlbWe
n.1OTIlOCTH lIaCbIl1{enHoro napa?
21.8. B llIfJlIfH.l1.pe no.IJ. nopwHeM naXO.IJ.SlTCSI BO.IJ.a Maccoii
m l = 35 Mr H nap MaCCOH m" = 25 Mr npu TeMnepaType
t = 27° C. fa3 H30TepMHQecKIf pacwIfpSleTcSI, npH KaKOM
06'beMe BO.lJ.a B llIfJlHH.l1.pe nOJlHOCTblO JICnapHTcSI?
21.9. B llHJlHH.lJ.pe no;:t nopwHeM Haxo;:tHTCSI BO;:tSlHOH nap
np" TeMnepaType t = 100° C H ;:taBJleHHH PI = 40 Kna. Ka-
KOBO 6Y.lJ.eT .lJ.aBJleHHe napa B llIlJUlH;:tpe. eCJIH 06'beM ero 1130-
TepMHQeCKH YMeHbWHTb B nSlTb pa3?
21.10. B cOBepweHHo nycToH cocY.l1. eMKOCTblO 0,50 JI BBO-
.lJ.HTCSI nOCTeneIlHO BO.IJ.SlHOii nap npH KOMHaTHoH TeMnepaType
(20 0 C). CKOJlbKO Ha.IJ.O BBeCTH BO.IJ.SlHOrO napa. QT06bI ;:taBJleHlIe
ero Ha CTeHKIf cocY.IJ.a CTaJlO paBHbIM 100 illa?
21.11. B 6apOMeTpnQeCK}1O Tpy6KY HaJlHBalOT no KaneJlb-
I<e BO;:ty ;:to Tex nop. nOl<a npOHCXO.!l.HT ee Jlcnapenue. Ha CKOJlb-
1\0 CIII13HTCSI npH .3TOM ypoBeHb PTYTJI B Tpy6Ke, eCJ1If TCMncpa-
Typa B03;:tyxa 21° C?
21.12. B 3anaSlHHbJH U-06pa3HoH Tpy61<e HaXO.IJ.IfTCSI Bo;:ta.
Kal< Y3HaTb, B03.IJ.YX HJlH TOJIbKO H8cblllleHHbIH nap HaXO.l1.IfTCSI
HaJJ. BO.IJ.OO B Tpy6l<e?
21.13. B cocy;:te eMKOCTblO V = 10 JI HaXO.IJ.HTCH cyxoil
B03.l1.YX npH TemepaType t l = 0 0 C H .l1.aBJleHHIf PI = 0.10 J\U1a.
KaKuM 6Y.IJ.eT .lJ.aB.'1eHIfe B 3TOM cocY.IJ.e, eCJlH TY.l1.a HaJlHTb BO;:ty
eG

aCCOH m = 2,0 r H HarpeTb cocy.11. ;0.0 Te1.mepafYPbl 1 1 =
= 100° C? .
21.14. CocY.11. 06'beMOM V = 10.1 3anOJIIleH CYXHM B03.11.YXOM
nplt .11.aBJIeHHH PI = 0,10 U1a H TemepaType 11 = 10°C.
KaKOBO 6Y.IJ.eT .11.8BJ1eHHe BJIa}KHOrO B03.11.yxa, eenH B COCY.IJ. Ha-
nlin BO.11.Y Maccon m = 10 M H HarpeTb ero .11.0 TeMnep3Typbl
i l = 100° C?
21.15. B 3aKpblToM C o60Hx KOHUOB UHJIJlH.l1.pe 06'beMOM
V = 2,0 .'1 CBOOO.IJ.HO XO.11.HT HeBecoMblH TOHKH" nopweHb. B
npocTpaHCTBo no.11. nOpWHeM HaJIIIBalOT BO.11.Y MaCCO" m B =
= 0,090 r, HaJJ. nopWHeM - m K = 0,16 r KHcnOpO.IJ.a. Onpe.11.e-
JIItTb nO.'JO}KeHHe nopwHH B lllfJIHH.lJ.pe npH TeMnepaType I =
= 100° C.
21.16. B03.11.YX HMeeT TemepaTYPY i 1 = 38° C H a6COJIIOT-
HYIO BJIa}KHOCTb PI = 25 r/rr. KaKoH 6Y.IJ.eT a6cOJIIOTHaH BJIa>K-
HOCTb 3TOro B03;t.yxa, eCJIH Te!1mepaTypa nOHH3HTCH .11.0 i l =
= 10° C?
21.17. 1.JeMY paBHa OTHOCHTeJIbHaH BJIa}KHOCTb B03.11.yxa,
3anOJIHHlOlUero 6aJIJIOH CMKOCTblO V = 700 JI npH TeMnepa-
Type i = 24° C, ecJIH .11.0 nOJIHOrO HaCbllUeUHH napa nOHa.11.06H-
:lOCb HcnapHTb B 3TOT 06'beM BO.11.Y MaCCOH m = 6,2 r?
21.18. B cocY.11.e eMKOCTblO V = 100 JI npH TeMnepaType
I = 29° C HaX0.IJ.HTCH B03.ZIYX C OTHOCHTeJIbHOH BJIa}KIIOCTblO
fl = 8,3%. KaKoBa 6Y.11.eT OTHOCHTeJIbnaH BJIa}KIIOCTb, ecnH B
cocy.11. BBeCTH BO.ZIY MaCCOH m = 15 Mr?
21.19. npH KaKJlX ycnOBJHIX MO}KeT YMeHbllIHTbCH OTHOCH-
Te.1lbHaH BJIa}KHOCTb, HecMOTpH .Ha YBCJIHIJeHHe a6COJIlOTHOH
BJIan<HocTH?
21.20. Ha YJIHUe Ue.nblH .11.eHb MOpOCHT XOJIO.IJ.IIbIH oceHHHH
)J.O)lQb. B KOMHaTe pa3BeweHo BblCTJlpaHHOe 6eJIhe. BblCOXHeT
JIH 6e.nbe 6b1CTpee, ecnH OTKpbITb q,opTOIJKY?
21. 21. B KOMHaTe npJl TeMnepaType i 1 = 25° C OTHOCH-
Te.nbHaH BJIa}KHOCTb fl = 12%. KaK H3MeHHTCH OTHOCHTeJIb-
HaH BJIa>KHOCTb, ecJIH TeMnepaTypa B KOMHaTe nOCTcneHHO no-
HH3HTCR .lJ.O i l = 14° C? .
21.22. OrHOCJlTe.nhH3H BJIa}KHOCTb B03.IJ.yxa Be'IepOM npH
TeMnepaType 11 = 14° C fl = 8%, HO'lb1O TeMnepaTypa B03-
ltyxa nOHH3HJIaCb .lJ.O 1 2 = 6° C JI BblnaJIa poca. CKOJIbKO BO.IJ.HHO-
Horo napa CKOH.11.eHCJlpOBaJIOCb H3 B03.11.yxa Om.eMOM V = I,O?
21.23. KaKoBa 6Y.IJ.eT OTHOCHTeJlbHaH B.1a}KHOCTb B03J1yxa
B KBapTJlpe, eCJIJI OTKpbITb .lJ.Bepb Mf)K.lJ.Y CMe>KHblMH KOMHaTaMH
nJIOlll.a..'J.blO SI = 15 M I H Sf. = 10 },fl, OTHOCHTeJlbHble B.'I3}K-
HOCTH B KOTOp.blX COOTBeTCTBeHHO f1 = 60% H fl = 5O%? TeM-
nep3Typa O)J.JlHaKOBa.
trl

3aJlaqH K rJl3Be VI
VU. B TOHKOii .llJIHHHOA Tpy6Ke Jl.1lHHOii 114 o.f, 33n3S1H.
HOH C o.n,Horo KOHUi:1, 3 C .llpyroro KOHU3 nnOTHO 33KpblTOH np06.
Koii, H3X0J1HTCSI 330T npH J13B.'IeHHH, COCT3BnSllOll.teM 2/3 OT
3TMoc4>ePHoro. Tpy6KY 33KPblThlM KOHUOM BepnfK3nbHo no-
rpY3HnH B COCY.ll C pT)'TblO 113 rny6HHY 38 CM. Onpe.lleJ1UTb P33-
HOCTb ypOBHeH PTYTH B Tpy6Ke H cocY.lle, nocne TOro K3K Bbl-
lIynH npo6KY. D.3BneJme 3TMOC4>ePbI HOpM3JIbHoe.
V1.2. D.B3 COCYJ13 O.llH H3 KOBOro 06'beM3 coe.ll.HHeHbI Jl.1lUHHOii
TOIlKOH Tpy6KOii. Onpe.llenUTb, K3K3S1 Q3CTb r333 nepeii.n.eT H3
p p
1/ 7 ' 2po I
h2
Po
I 1-
;,;,-' I 1
V D 2 V D V
V
Pile. 136 PHC. I;i;
O.ll.HOrO COCYJ13 B J1py.roH, eCJIIi TeMnep3TYPY O.llUoro no;J..'tep}J{U-
B3Tb nOCTOSlHHOH, 3 Tellmep3TYPy BTOpOro YBenUqUTb B 1,5
p333. Bo CKonbKO p33 H3MPHUTCSI .lI.aBJIeHUC B COCY.ll.3X?
VI.3. H3 puc. 136 H306pa>KCH 3aMJ{HyrLIH UUKJI. Hapuco-
BaTb 3TOT UUKJI B KOOp.ll.HHaT3X V, T U p, T.
VIA. O.ll.UIf MOJIb HJ1e3JIbHoro r33a nepeDO.llSiT U3 COCTOHHHSI
1 B COCTOSlHue 2 (puc. 137). Onpe.lleJIUTb MaKcHM3nbll}'1O TeM-
nep3TYPY, KOTOPYIO HMen r33, eCJJH Po = 747,9 rOa, V o =
= 20 n.
V1.5. Tpy6KY .llJIUHOH 1 = 60 CM, 3anaSlHHYlO C O.ll.HOro
KOHua. OTKpblTblM KOHUOM BepTHKa.lbHo norpY>KaIOT B PTYTb,
Opu KaKoH rny6uHe norpY>KeHUSI B Tpy6Ke Bbm3.l1.eT pOC3?
TeMnepaTYP3 B Tpy6Ke He MeIlHeTCSI. Anmc4>epuoe .lI.3BneHue
HopM3nbuoe. Bna}J{HocTb B03.ZIYX3 f = 80%.
f nAB A VII, TEnnOTA If PA60TA
 22. H3MeHeHHe BHYTpcHHeii 3HeprMH nYTeM
TenJloo6MeHa
22.1. Y H3Koro li3 Ten TennoeMKocTb (5oJIbwe: y KYCK3
c,BIIHU3" MaccoH 1,0 Kr HJIH Y KYCK3 >KeJIe33 M3CCOH 500 r?
8B

22.2. KYCKH )KeJIe3a, CBHHua H amoMHHHH HMelOT o.nHHa-
OBblH OODeM. KOTOpblH H3 HHX HMeer HaHOOnbwylO TenJIoeM-
J{ocTb. KOTOpblii - HaHMeHbwYJO?
22.3. Ha rpact>HKe (pHC. 138) nOKa3aHbl 3aBHCHMOCTH TeM-
nepaTYPbl .nBYX Ten OT KOJIHtleCTBa renJIOTbl. coot5U.J;eHHoii HM.
y KaKOTO H3 TeJI renJIoeMKocTb 6oJIbwe?
22.4. no rpact>HKaM 3aBHCHMOCTH TeMnep3Typbl Ten OT
c006ll1.eHHOH JiM TenJIOTbI (pHC. 138) onpe.neJIHTb: 1) Y KaKO-
t:c
50
-o
'0
20
10
'(
t.e
PHC. 138
Pue. 139
ro H3 TeJI YJ1.CJIbmlH TenJlOeMKOCTb 6oJIbwe, eeJIH MaCCbl TeJI
paBHbl; 2) Y KaKoro H3 TeJI C)OJIbWe Macca, eCJiH y.neJIbHble ren-
noeMKOCTH Ten paBHbI?
22.5. rOpHtiaH BOJ1.a Ha.'1HTa B aJIIOMHHHeB)'IO KPY:>HKY, Mac-
ca KOTOpOH o.nHHaKOBa C Maccoii HaJUIToH BO)I.bl, Ha o,!J.HHaKo-
B If! JIll tlHCJIO rpa.nycoB OXJIaJ1.HJIaCb BOJ1.a H HarpeJIaCb KpY:>HKa?
Ha TO >l\e JIH IIHCJIO rpaJ1.YCOB OXnaJ1.HTCH Bo.na, eeJIH ee BbI'HTb
B )KeJIe3HYIO KPY:>HKY TaKOH :>He MaCChI? nOTepSlMH TenJIOTbl B
npY:>HalOll1.ee npocrpaHcTBO npeHe6pelIb.
22.6, Harperoe MeraJl.'1HlIecKoe TeJIO onycTHJIH B coey.n C
I{HJ1.KOCTblO. rpact>HK 3aBHCHMOCTH reMnepaTypbl TeJIa H cocy.na
C )KHJ1.KOCTblO OT BpeMeHH nOKa3aH Ha pUC. 139. OnpeJ1.eJIHTb.
110 CKOJIbKO pa3 OTJIlltialOTCH renJIOeMKOCTH MeTa.'1JIUtieCKOrO
TeJIa H cocy.na C :>Hll.nKOCThlO.
22.7. t..1T06bl OXJIaJ1HTb 2,0 JI BOJ1.bl. B3S1TOH npH 80° C, .no
60° C, B lIee .n06aBJJHIOT XOJIOJ1.HYIO BO.ny npH 10".c. KaKoe KO-
JlHtleCTBO XOJIO.nHOH BO)I.bl Tpe6yercH J1.06aBHTb?
22,8. 11ml npHTOTOBJIellHSI BaHllbI Heot5xOJ1.HMO CMewaTb
10JIO.!l.IIYlO BOJ1Y npH 11 = 11 ° C c ropHtleii npH tf. = 66° C. Ka-
Itoe KOJIHlIeCTBO Ton H J1.pyroH BO)I.bl lleOOXOJ1.HMO B3HTb .nJlH no-
.lYtleHHH V = 110 JI BO]1.li npH t a = 36" C?
22.9. B CTeKJlHHHbIH CTaKaH MaccoH ml = 0,12 KT npH TeN-
IepaType t 1 = 15° C HaJIHJIH m" = 0,20 KT BO)J.bl npH t 2 =
.. 100" C. KaKaH TeMnepaTypa BO)I.bl YCTaHOBIf,1J8Cb B CTaKaHe?
59

22.10. B CTeKJIHHHblH CTaKaH MaccoH mt = 100 r Ha.1l JiT o
m 2 = 200 r B01J.bl. TemepaTypa BO.l(bl H CTaK311a t l = 75C.
Ha CKO.1lbKO nOHH3HTCH TemepaTypa BO.l(bl npll onycKal1l1Jj
B Hee cepeGpslHoH .1I0>KKII Maccoo m 3 = SO r npH t 2 = 15° C?
22.11. B KaKOM OTHoweHIIH J{OJDKHbl 6bITb B3HTbl Macc",
m l H m" Anyx >KHAKocrei( C YACJlbHblMH Ten.1loeMKocTSIMIf c 1
H c 2 , lIaQa.1lbHblMH TeMnepaTypaMH TI H Ts (T I .> T 2 ), qT06",
o6all TeMnepaTypa noc.1le HX CMeu{eHHH nO.1lYQHJlaCb paEHOH
To? TenJloeMKocTb cocy.n.a. B KOTOpOM HaXOJ{HTCH >KHAKOCTII,
He YQHTblBaTb.
22.12. B Ka.'IOpHMeTp Maccoii m R = 75 r npH TeMnepaTY-
pe T K = 278 K HaJlHJlH >KHAKOCTb MaCCOH mm = 32 r. JlMelO.
l1{eii TeMnepaTYPY T m = 293 K. KorAa B KaJlOpHMeTpe YCTa.
HOBHJlaCb TemepaTypa TI=288 K, B Hero onYCTH.1IJI MeAHYIO
rHplO Maccoo mil! = 400 r, HMelOl1{eii TCMnepaTYPY T II! = 281 K..
nocJle 9Toro TeMneparypa B KaJlOpllMeTpe CTaJia T z = 285 K..
OnpeAe.1UITb YAe.nbHble TenJlOeMKOCTH MaTepJlaJl3 Ka.'10pHMeTpa
H >KH.n.KOCTH. TenJloo6MeHoM C oKPY>KalOl1{eH cpe.n.oif npelle.
6peQb. .
22.13. 1 Kr JlbA3, B3HTO:\IY npH TemepaType - 50° C, co-
06m.HJlII 520 K.lbK TenJlOTbl. nOCTpOliTb rpa4>HK 3aBHCHMOCTII
Tet.mepaTypbl OT BpeMeHH nocTynJleHHH TenJlOTbl. CKOpOCTb no.
cTynJleHHH TenJlOTbl nOCTOHHH3H.
22.14. B COCYA C BOAOii C o611{eH Ten.'10eMOCTblO C =
= 1,5 K.lI.>K!K npH TeMnepaType t l = 20° C n€MeCTHJlH m l =
= 56 r JlbJ{a npH TeMnepaType t 2 = - 8° C. KaKaH ycraHO.
BliTCH TeMnep3Typa?
22.15. B cocy.n C BO.n.OH C o6m.eii TenJloeMKocTblO C =
= 1,7 K.lI.>K/K npH t l = 200 C nO'deCTHJlII m = 100 r Jlb.n3 npl(
t 2 = - 8° C, KakaH TeMnepaTypa YCTaHoBHTcH B cocy.ne?
22.16. B Me.n.HblH KaJlOpHMeTp MaccoH  = 100 r, Co.n.ep-
>Kam.HH BO.ny MaccoH m 2 = 50 r npH TeMnepa-rype t l = 5° C,
onYCTHJlH JleA npH TeMnepaType is = - 30° C. Macc3 Jlb.n3
m 3 = 300 r, KaKaH TeMnepaTypa YCTaHoBHTcH B KaJlOpHMeTpe?
22.17. CMecb, COCTOHI1{}TIO H3 m l = 5,0 Kf Jlb.n8 H m 2 =
= 15 Kr BO,lJ,bI npH ot5w.eii TeMnepaType t = 0° C, HY>KHO lIa-
rpeTb.no t l = 80° C C nOMOl1{blO BOAHHoro napa npH t 2 = 100° C.
Onpe.n.e.nHTb neoGxo.n.HMoe KOJIIIQeCTBO napa.
22.18. DblCTpO OTK3'lHBaH B03.nyX H3 cocy.n.a, B KOTOpOM
lIaXO,lJ,HTCH lIeOOJlbwoe KOJIHQeCTBO BO.l(bl npH 0° C. MO>KHO
npeBpaTHTb BOJ{Y B JleA. KaKaSl QaCTb nepBOHaQaJlbHOro KOJlJl-
tIeCTBa BO.l(bl MO>KeT t5bITb 06paw.eHa B Jle.n npH 0° C? npHHSlTb
y,lJ,e.nbHYIOTenJlOTY napoo6pa30BaHHH npH 0° Cr =2.3ML1.>K1Kr.
90

22.19. Ha cnlfpToBKe HarpeBaJiIf BO,ny MaccoA m 1 = 100 r
T t 1 = 16° C 11..0 t 2 = 71°C. npH 3TOM 6b1n CO>l<>I<eH cnHpT
)l8ccoil m 2 = 10 r. HaHTH Ko34xPHu.HeHT nOne3HOrO 11..eHCTBHH
)cranoBKlf,
22.20. JInH narpeBaHHH BO,!l.bl 06"be!1lo1 V = 2.0 n. naX011..H-
meikH B anlOMHHHeBOH KaCTplOJle MaccoH m 1 = 400 r, OT t 1 =
= 15° C. 11..0 t 2 = 75° C 6b1.'1 H3pacKo)J.oBaH ra3 MaccoH m z =
= 30 r. Onpe11..enHTb Ko3<}xpHllHeHT none3Horo 11..eiiCTBHH ra30-
Boil nnUTbI, CIJHTaH TennOTY, H3paCK011..0BaHH)'IO Ha HarpeBaHHe
COCY11..a, none3Hoii. KaK H3MeHHTCH pe3ynbTaT, ecnH none3Hoil
CQIlTaTb TonbKO TennOTY, H3paC v O,i.1.0BaHHYIO Ha HarpeBaHHe
BO.lI.bI ?
22.21. B 1JaiiHHK co CBHCTKOM HanHnH BO.n.y MaccoH m 1 =
= 1,0 Kr H nOCTaBII.'1H Ha 3.'1eKTpHlJecKYIO mIHTKY MOlltHOCTblO
/I = 900 BT. LIepe3 't 1 = 7,0 MHH pa311..anCSI CBHCTOK. CKonbKo
BO)J.hI OCTaHeTCH B 1JaiiHIIKe nocne KHneHHH B01J.bI B TelJeHHe
"2 = 2,0 MHH? KaKoB KnJI nnHTKH? Ha1JanbHaH TeMnepaTYPP
B011..bl t = 20° C.
22.22. KaKoe KO.'1HtJeCTBO Ten.'10ThI Ha11..0 COOOlltHTb )Kene3-
HOH 6anKe nnOllta,!l.blO CelJeHHH S = 20 CM 2 . 1JTOObl OHa Y11..nHHH-
naCb Ha I1l = 6,0 MM?
22.23. KaKoe KonHtJeCTBO TennOTbl OOOOlltHnH Me11..HoMY wa-
PY. ecnH o6beM ero YBeJIH1JHJICH Ha 11 V = 10 CMS?
22.24. JIBe Me11..Hble nnaCTlIIIKH 011..HHaKOBoii nnOllta11..H, TOJI-
II{HHOH h 1 = 4,0 MM H h z = 6,0 M\, HMeIOlltHe TeMnepaTypbl
II = 20° C II t 2 = 200° C, CJI0>l<HnH BMfCTe TaK, 1Jro oopa30-
1!a.laCb 011..Ha nnaCTIIHKa. Onpe11..enHTb TOJIlltHHY nnaCTHHKIJ,
eC.'1II TenJI006MCHa C OI{PY>I<aJOllteii cpe11..0ii He npoHcX011..HT.
 23. IbMeHeHlle BHYTpeHHeii SHeprHH
B npou.ecce cOBepmeHHB pa60Tbl
23.1. ABToMoollnb MaccoH m = 1,0 T, .lI.BHraDWIIHcH co
CKOpOCTblO v = 36 KM/1J, pe3Ko 3aTopM03Hn nepe11.. CBeT<><tJoPOl\I.
l(aKoe KonHtJeCTBO TennOThI Bbl]J.eJIHnOCb npn TOpMO>l<ellHIf
aBTOMoonnH?
23.2. KaKYIO Ha11..0 cOBepwHTb paooTY, 1Jroobl pacnnaBIITb
TpeHHeM 11..Pyr 0 .nPyra 11..Ba KycKa nb11..a Maccoii 5,0 r? TeMne-
paTypa nbD.a 0° C.
23.3. C 011..HHaKoBoii BbICOTbl Ha KacpenbHblii non na11..alOT
pll wapHKa pm3HOH MaCCbl: O,!l.HH wapHK - Me11..HblH.11..Pyroit -
anbHoH, TpeTHii - >l<ene3HhIii, 1) KaKoii H3 HHX narpeeT-
cx 11..0 oonee BblCOKOH TeMnepaTYPbl? 2) KaKoii H3 .lI.BYX wapH-
1<OB, )Kene3HblH HJIlI CTa.iIbHOH, HarpeeTcH 6blcTpee?
91

23.4. CBHltQonaSi nymr, neTeBlllafl co CKOpOCTblO VI:::o
= 500 wc, np0611na CTeIlKY. Onpe)J.e.'lIlTb, Ha CKonbKO rpa:ty.
COB HarpeJlaCb nY.'lH, eCJIH nOCJle creHKH CKOpOCTb ee CHH31!,
naCb )J.O V 2 = 400 WC. CIJIITaTb, 1Jro Ha HarpeeaUHe nynll no-
lllno n = 50% BbI)J.eJIHBUleHC1I rennOThI.
23.5. Ha CKonbKO rpa)J.ycoB HarpeBaeTcH BO)J.a y OCUOBa_
HHH BO)J.ona)J.a BblCOTOH h = 10 M? C1JHTaTb, IJTO lIa HarpeBaHlle
BO)J.bl H)J.eT n = 50% MeXaUHQecKoH 3HCprHH.
23.6. )Ke.'le3HOD.0p0>KHblH COCTaB, H)J.YIl1.Hii cd CKOpOCTLIO
v = 36 KM/IJ, pe3KO 3aTopM03Hn. Onpe)J.eJIHTb, ua CKo.,il>KO
nO)J.IIHnaCb TeMnepaTypa nepeB03HMblX >KH)J.Koc.TeH D llHcTep-
Hax: KepOCHHa, BO)J.bl, cnHpTa, cepHoH KHcnOTbl.
23.7. npH cBepneHHH nYUle1JHoro CTBona, KOTOpoe npOll3.
BO)J.IIJlH c nOMOll1.blO JlOrna)J.eH, PYM4x>P)J. ycneJI BCKHnHTHTb B
KOTJle, nOCTaBJIeHHOM Ha CTeOJl, BO)J.y 06'beMO\1 V = 10 ,II.
MHHHManbHaH reMnepaTypa BO)J.bl 6.blJla t = 20° C, 3a "t =
= 6,0 MHH BO)J.a MaCCOH m = 200 r 06paTllnaCb B nap. Ka:-<aH
pa3BHnacb MOIl1.HOCTb npll cBepneHlfH, eCJIH n = 80% I!CCH
BbI)J.eneHHoH npH 3TOM TenJlOTW nOlllJlO Ha HarpeBaHHc BOa
H 06pall1.eHHe ee B nap?
23.8. C KaKoH CKOpOCTblO )J.OJl>KHa JlCTCTb CBHHllOBaH nYJlH,
IJT06h1 npH y)J.ape 0 npemlTCTBHe OHa paCnJlaBHnaCb? nepBOHa-
lIanbHaH TeMnepaTypa ee paBHa 27° C._CIIIITaTb, liTO BCH Bbl)J.e-
nHBUlaHCH rennOTa COO61I.laeTCH nYJle.
23.9. C KaKoH BhlCOThI )J.on>KeH ¥nacTb MonOT MaccoH M =
= 1000 Kr Ha Me)J.HYIO OOnBalll<y MaccoH m = 25 r, 1JT06bl OHa
nOJIHOCTblO pacnnaBllnaCb? CIJHTaTb, liTO 60nBaHKe nepe)J.aeTCH
n = 50% BbJ)J.eJIHBllleHCH TenJlOTbl. HaIJaJlbHaH TCMnepaTypa
Me.n.1I t = 23° C.
23.10. nYJlH np06HBaCT HIl1.HK, CTOHIl1.IIH Ha rna)J.KoH roo
pH30HTanbHoH nJlOCKOCTH. .Macca nYJlH m = 10 r, Macca SlIl1.U-
Ka M = 500 r, nynH nO)J.JleTaCT K HIl1.HK}': co CKOpOCTblO VI 
= 1000 WC, a. BbineTaCT H3 Hero co CI<OpOCTblO V 2 = v l /4.
CKOJlbKO TennOTbi Bbl)J.eJlHJlOCb npH )J.B1I>KeHIIH nYJlH B flll1.lIKe?
HallanbHYIO H KOllelJHYIO CKOpOCTIl nynH CIIHTaTb ropH30HTanb-
HblMH.
23.11. CBHHlloBaH ny nH Maccon m = 10 r, neTHll1.aH roo
pH30HTanbllo co CKOpOC'!'blO v = 100 M/c, nona)J.aeT B )J.epeBHn-
HblH 6pyceK MaccoH M = 1,0 Kr, no;t.BellleuHblH lIa p,.,'HHHOii
HHTH. Ha CKonbKO rpa.n.ycoB HarpeJIaCb nynH, eCJIH n = 70o
BbI)J.eJIeIlHOH npH Y)J.ape renJlOTbi nOUlJlo Ha ee HarpeBallue.
23.12. KaKaH Macca nopoxa cropaeT npll BblCTpene H3 Ka-
pa6HHa? Macca nynH m = 10 r, CKOpOCTb npH BblneTe 113 )J.y.'1a
V = 700 Klc, KI1ll Kapa6HHa  = 30%.
92

23.13. HaATH pacxo,lt 6eH3UH3 aBTOM06HJUI «3anopo)Kenl
ua s = 1,0 KM nYTH UpH CKOpOCTH V = 60 KM/q. MOIl\.HOCTb MO-
TOpa N = 17 KBT, 1\:0$PHD.HeRT nOJle3Horo .n.eHCTBHH '1 =30%.
23.14. ABTOM06IIJib cMOCKBH1D pacxo.n.YeT 6eR3HH MaccoA
m = 5,67 Kr Ha s = 50 KM n}TTH. Onpe.n.eJlHTb MOlItHOCTb N,
pa3BHBaeMYIO .n.BHraTe.lIeM, ec.nH CKOpOCTb .n.SH>KeHHSr v =
= 90 KMfq H KfUI. .lI.BHraTe.lIH 'I = 22%,
23.15. Onpe.n.eJlHTb, Ha CKOJIbKO YBeJlHqHTCH pacxo.n. 6eH-
SIma Ha s = 1,0 KM nYTH npH .lI.BH>KeHHH aBTOM06HJlH Maceoii
M = 1,0 T no .n.o'pore C no.n.DeMOM h = 3 M Ha 1= 100 M n}TTH
no cpaBHeHHIO C pacxo.n.oM 6eH3HHa Ha ropH30HTaJlbHOil .n.opo-
re, KfUI. .lI.BHraTeJlH 'I = 30%. CKOpOCTb Ha Bcex yqaCTKaX
.n.oporH UOCTOHHHa.
23.16. ABTOM06HJJb pa3BHBaeT CKOpOCTb VI = 72 KM!q,
pacxo.n.yH npH 3TOM 6eR3HH Maccoii m l = 80 r Ha s = 1,0 HM.
KaKoe KOJlHqeCTBO 6eH3HHa 6y.n.eT pacxo.n.oBaTb aBTOM06HJlb
npH CKOpOCTH [12 = 90 KM/q? KaKyro MOlItHOCTb OH npH 3TOM
pa30BbeT? CHJIa cOnpOTHBJleHHH nponOpllHOllaJIbHa CKOpOCTH,
KOJI. .lI.BHraTeJlH !) = 28 % .
 24. npHMeHeHHe nepBoro HaqaJIa TepMo.n.HHaMIIKH
K ra3aM
24.1. .MO>KeT JlH ra3 06MeHHBaTbCH 3HeprHeH C oKpY>Ka-
lIteii cpe.n.oii, He H3MeHHH CBOero 06oeMa?
24.2. KaKoe KOJIHqeCTBO TenJlOTbl HeoOXO.n.HMO COO61l1.HTb
.llJIH HarpeBaHHH Ha !J.T = 20 K reJIHH MaccoA m = 40 r,
co.n.ep>KalIterocH B 6aJlJlOHe? 'lJeMY paBHa y.n.eJlbHaH TenJloeM-
KOCTb reJlHH?
24.3. HeoH. Haxo.n.HBlllHHCH npll HOpMaJlbHblX YCJIOBHHX B
3aKpbITOM cocy.n.e eMKOCTblO V = 20 n. OXJla.n.HJlH Ha !J.T =
= 91 K. HaiiTH H3MeReHHe BH}TTpeHHeii 3HeprHH ra3a H KOJIH-
qeCTBO OT.n.aHHoH HM TenJlOTbl.
24.4. B cocy.n.e eMKOCTblO V = 2.0 n l:IaX0lJ.llTCH KpHmoH
'o.n. .n.aBJIeHHeM PI = 1,0 .MIla. CTeHKH cocy.n.a Mor}TT BbI.lI.ep-
>KaTb .n.aBJIeHHe .n.o PI = 2.0 MIla. KaKoe MaKCHManbHoe Ko-
nHlJeCTBO TennOTbl MO>KHO Coo6Il\.HTb ra3Y?
24.5. BanJloH eMKOCTblO V = 50 n co.n.ep1KHT aproH npH
TeMnepaTYpe TI = 290 K 00)( .n.aBJIeHBeM PI = 500 KI1a. Ka-
KOBbi 6y.n.}TT TeMDepaTypa H .n.aBJIeHHe ra3a, eCJIH eM)' Coo6w.HTb
Q = 5,0 KlI.>K TennO'l1i?
24.6. O.n.HH MOJIb O.n.HoaTOMHOro ra3a RarpeBaeTCH npH no-
CTOHHHOM 060eMe .n.O TeMnepaTypbl T "= 280 K. KaKoe KOJIH-
93

qeCTBO TenJIOTbl Heo6xo.nnMO COOt5W.IITb ra3Y, QTo6u era .l1aoJIe-
IlHe YBeJIHqU.l0Cb B n = 3 pa3a?
24,7. MOnulO Jill nepe.n.aTb HeKoTopoe KOJIHqeCTBO TenJlOTbl
ra3Y, lie Bbl3blBaSi 3THU nOBblweHHSI TeMnepaTypbl?
p P
I 2 2 
Po - 7 )I , Pz ==n
I I
I I .'
J I 11
I I
 'l V z V
PIIC. 140 PHC. 1.11
24.8. npH 1130TepMnqeCKO\f pacwllpellHH I{HCJlOpO,!J.o 6u-
Jla cOBeplUeHa pa60Ta A. KaKoe KOJIHlleCTBO TenJlOTbi nOJlyqUJI
r23 npH 3TOM?
24.9. B 1l1l"'HUI;I.pe no.n. nopwlleM lIaxo.nHTCSI ra3, COCTOSlJIII
KOToporo MeHHeTCSI, KaK nOKa3aHO Ha pHC. 140, I(aK H3MeHH-
JlaCb TemepaTypa ra3a? KaKYIO pa60TY cOBepWHJI ra3?
24.10. HaHTH pa6OTy, KCTOPYIO cOBepwaeT ra3, nepeXo;r.H
113 COCTOSl.HIISI. 1 B COCTOSl.HHe 3 (pIlC. 141).
24.11. KaKYIO pa60Ty cOBeplUaeT ra3 npH nepexo.ne 113
COCTOHIlHSI 1 B COCTOSlHIIC 4 (pHC. 142, a, 6).?
24.12. reJIilii HarpeBa.lJc.SI npll nOCTOSlJIlIOM .naBJIeIlIIH. npR
3TOM eMY 6b1.'10 coo6w.eHo 20 KlJ.n< TenJlOTbl. Onpe.n.CJIIlTb 113Me-
HeHlle DHYTpeHHeii 3Hep-
rHII ra3a II COBepweHHYIO
11M pa60TY.
24.13. KpHnTOH Mac-
COH m = 1,0 r 6bIn Ha-
rpCT Ha T = 100 K npll
nOCTOSiHIlOM .naBJIeHlfif.
KaKoe KOJIllqeCTBO Ten.'I0-
Tbl nOJIyqHJI ra3?
24.14. B BepTHKa.'1bHO
pacnOJIon<eIlHoM llIlJIHHJI.-
pc no;I. nopwlleM Haxo.nHTCSI ra3 06"bCMOM V = 2,0 11 npH TeM-
nepaType Tl = 299 K. HaiiTII pa60Ty pacwHpeHIISI ra3a npH
narpcBaHIIII ero lIa  T = 100 K. Macca nOpWHSI. m = 10 Kr,
ero nJIow.a.nb S = 50 CM 2 , aTMoccpepHoe .naBJIelllle 1I0pMaJIbHoe.
24.15. KaKaSi pa60Ta coaeplUaeTCSI npll npCBpall.\,CHHII m =
= 1,0 Kr BOAbl B nap npH TeMnepaType T = 373 K? KaKoe
oj
fJ
5}
P EtL
Po _ T 2
P: -H3
v, Il V
7 2
 +=p-'4
I I I
v,
\ol  v
PUC. 142
94

KOJlHqeCTBO 3HeprHH H)J.er Ha pa3pblB CBSl3eH Me)KJI.}' MOJIeKY-
Jlam ?
24.16. B l.UfJIHH)J.pe no,;!. nopllIHeM nJlOlll.a)J.blO S = I,O]JJd2
Haxo.nHTCSI I MOlIb B03)J.yxa, K nopllIHIO qepe3 MOK
npHBelUeH rpY3 MaccoH M = 55 Kr. I..J.HJIHH)J.P OXlIIDK)J.alOT Ha
/),.T = 100 K. Ha KaKYIO BblCOTY nOHHMercSI rPY3? .Macca
nopllIHH m = 5,0 Kr. Anmcct>epHoe )J.aBJIeHHe HOpMaJlb-
Hoe.
, 2
p 2 t]
 J
, .
Tz If
I 5
, V V
PRe. 143 PHe. 144
24.17. KHCJIOpO)J. MaCCOH m = 0,30 Kr npH TeMnepaType
T = 320 K OXlIa)J.HJlH H30XOpHO, BCJIe)J.CTBHe qero ero )J.aBJle-
HHe YMeHblllHlIOCb B n = 3,0 pa3a. 3aTeM ra3 H306apHo pac-
lllHpHJIJI TaK, qTO TeMnepaTypa ero cra1I8 paBHoH nepBOHaqaJlb-
HOH. KaKYIO pa60Ty cOBeplllHlI ra3? KaK H3MeHHJlaCb ero BHY-
TpeuHSlH 3HeprHH?
24.18. PaccMOTperb 3Heproo6MeH ra3a co cpe)J.oH B HKlIH-
qeCKOM npoecce, COCTOHrneM H3 H30XOPbl, H30repMbI H H30-
6apbl (pHC, 143). .
24.19. PaccMOTperb 3Hepro06MeH ra3a co cpe)J.oH B HKlIHtJe-
CKOM npoecce, COCTomn.eM H3 )J.BYX H30TepM H JI.BYx a)J.Ha6aT
(HKJI KapHo) (pHC. 144).
24.20. B pe3YlIbTaTe LlHKJlHtJeCKoro npoLlecca ra3 cOBeplllHlI
pa60Ty A = 100 D.>K H nepe.naJi XOJlO)J.UJlbHHKY Q = 400 D.>K
TenJlOTbI, Onpe)J.eJlHTb K034$Hl.lIleHT nOJle3Horo )J.eMcTBHH
LlHKJla.
24.21. O)J.HH MOJIb O)J.HoaToMHoro raaa cOBeplllaer HKlI,
COCTOHUJ.HH H3 JI.BYx H30XOP H JI.BYx H306ap. npll 3TOM MaKCH-
MalIbHoe )J.aBJleHlle B n 1 = 2,0 pa3a 00lIblUe MHHHMaJlbHOrO,
a MaKCHMaJlbHblH o6'beM B n z = 3,0 pa3a OOJIbllle MHHHMalIb-
HOro. Onpe)J.e,1IIITJ> J<o3<}xpHHeHT nOlIe3HOrO )J.eHcTBHH
l\HKJia.
:}

24.22. Onpe)l.eJIHTb Ko$Pm.t.HeHT nOJIe3HOrO .neikTBHSlllHK.
na, COCTOHwero H3 .nBYX 8J1.Ha6aT H .nBYx H30XOP (pHe. 145),
cOBeprnaep-mro H.neaJIbHblM r830M, eCJIH H3BeCTHO, qTO B npOllee-
ce a.nHa6aTHoro pacrnHpeHHSI a6cOJIIOTHaSi TeMnepaTypa ra3a
T 2 = O,75Tlt a B npolleece 8)1.Ha6aTHoro C}KaTHSI T4 =
= O,75T J'
24.23. fa3 cOBeprnaeT llHKJI KapHo. A6conIOTHaSi TeMne-
paTya HarpeB8TeJlSI B TPH pa3a Bblrne a6cOJlIOTHOH TeMnepaty-
p pbl xono.nHJlbHHKa. Onpe.nenHTb Jl.OJIIO
TenJlOTIX, oT.n8DaeMoH XOJlO.nHJlb-
HHKY.
24.24. fa3, cOBeprnalOI1lHH llHK.,
KapHo, n = 70% TenJlOTbI, nOJlyqeHHoit
OT HarpeBaTeJlSI, OT.naeT XOJlO.nUJlbHIIKY.
,b Te,mepaTypa uarpeBaTeJ18 T.  430 K.
Onpe.neJIHTb TeMnepaTYPY XOJlO.nHJlb-
HHKa.
24.25. fa3 eOBeprnaeT llHKJI KapHo.
TeMnepaTypa XOJlo.nHnbHHKa Tl =
= 280 K, HarpeBaTeJISI T 2 = 380 K' Bo CKOJlbKO pa3 YBe-
nHIJ:HTCSI K03<M>HllHeIlT nOJle:moro .neHcTBHSI llHKJIa, ecnH TeM-
nepaTYPY HarpeBaTeJlSl nOBblCHTb Ha f!T = 200 K?
24.26. B" napoBoH Typ6HHe pacxo.nyeTcSI m = 0,45 Kr .nH-
3eJ1bHOrO TOnJlHBa, npH cropaHHH KOTOporo BbI.nenSleTCSI Ten-
JlOTa Ha cOBeprneHHe pa60TbI A = 1,4 KBT.q. TeMnepary-
pa nocTynalOU.t,ero B Typ6HHY napa T B= 520 K' TeMnepaTypa
XOJIO.nHJlbHHKa T:II: = 300 K. CpaBIIHTb «IJaKTHqecKHH Knn.
Typ6HHbI H Knn: H.neaJlbHOH TennOBOH MallIHHbI, pa60TalOU.t,eii
npH Tex }Ke TeMneparypHblx pe}KHMax.
24.27. KaKYJO MaKcHManbH)'IO none3HYIO MOU.t,1I0CTb MO}KCT
pa3BHBaTb .nBHr8TeJlb aBTOMarnHHbI, eCJIH OH pacxo.nyeT B Te-
lJeHHe 't = 1,0 q m = 5,0 Kr 6eH3HHa? TeMnepaT)'pa ra30B B
llHnHH.npe .nBHraTeJlH .nOCTHraeT Tl = 1200 K' Orpa6OTaHHble
ra3bI HMelOT Ter.mepaTpy T 2 = 370 K.
v
PHC. 145
3a.ll.aIJH K rJIaBe VII
VII. I. nepeOXJla>KJleHHaSi Bo.na, HMeBmaSi TeMnepaTYPY
- 5 D C, nepernJla B COCTOSlHHe TepMo.nHHaMHqeCKoro paBHOBe-
eHSI npn OD C. Onpe.nenHTb, KaKaSi 1JaCTb MaCCbI BO,U.bl npeBpa-
THn8Cb npH 9TOM B neJl.. CqHTaTb, 1JTO y.nenbHaH Tenn0e!4KOCTb
BOJlbl He 3aBHCHT OT TeMneparypbl.
VII.2. CBHH110BaSi nYJISI M8CCOH m = 10 r, neTeBrn8S1 ro-
pH30HTaJIbHO co CKOpOCTblO V = 100 we. nona)l.aer B CBHH.
9G

LlOBYIO rHplO MaCCOH M = 0,20 Kr, nOKomuYIOCH Ha rnaJJ.Kofi
rOpU30HTanbHOH nnocKocTH.()npeenHTb TeMnepaTYPY CHCTe-
MbI nynH-rHpR, ecJIH nepeD. y.napoM Ter.mepaTypa nY.1H paBlla
/1 = 230° C, a TeMnepaTypa rHpH Iz = 20° C.
VII.3. B xonoJJ.lfnbHHK, nOTpe6JUJIOll.\.HH MOll.\.HOCTb P =
= 200 BT, nm.leCTH.rIH BO.ny Macco m = 2 Kr npH Te\mepaTY-
pe t = 20° C. 1.:Iepe3 't = 30 MHIl BCH BO- P
.na npeBpa'i'Hnaeb B neD.. KaKoe hMIlIJe-
CTBO TenJlOTbI BbI.lI.enIlJlOCb npH 3TOM B 2p,
hOMHaTe?
VII.4. OJl,HH MOJIb HJI,ea.'IbHOrO ra3a
nepeBoJl,HT H3 COCTOHHIfH 1 B COCTOHHHe 2 Po
(pHC. 146). OnpeJl,MHTb, KaKoe KO.'IHqe-
CToo TennOTbI nOJIyqaeT ra3 npH Harpe-
BaHHH H KaKoe - npH OXJIa>K.il.eIlHH,
eCJlH Po = 160 rna, V o = 20 n.
VII.5. ()npeJl,eJIHTb KfIlJ. LlHKJIa (pHc.147), pa60IJHMTenoM
KOTOpOro HBnHeTCH lI.I1.eaJIbHblfi ra3, ecnH pz = 2Plt VI! =4V I .
VII.6. TennoBaH MaUIIIHa, pa60IJH1 TeJIOM KOTOpOH HBnH-
eTCH H;J.eanbHbJH ra3, COBepmaeT LlIIKJI, H306pa>KCHHbIH Ha
pllC. 148. HauTH Kru:r.3TOHMamHHbl,ecnH pz=2Plt V Z =4V 1 .
VII.7. B TennOH30JlHpOBaHHOM cocYJI,e noJl, nopmHeM Ha-
XOJl,HTCH Bo.na 061.eMOM V = 1,0 n II HaCbIIllellHbIH nap MaeCOH
m = 3,0 r npH TeMnepaType t = 100° C. BJl,BHraH nopilieub,
p P
=2
J I
"Yo 2"11 v
PHC. 146
I} = 1/1 Pz .1
P, p,
I I
I I I I
 V V, V z v
PHe. 147 PRe. 148
YMCUblUalOT o61.eM napa Jl,0 HYJIH. ()npe;J.enHTb, KaKaH 6blna 3a-
TpaIJeHa pa60Ta npH B.lI.BHraIlHH nopmHH. Ha CKOJIbKO rpay-
OB Harpe.nacb BOJl,a?
VII,S. B TennOH30JIllpOBaHHoM cocYll.e o(h,er.fOM V = 10 n
JaXOD.IITCH nepeOXna>KJ1eHUblH BO.'l.HHOU nap MaceoH m = 5,85 r
npH Ter.mepaType t = 89° C. T aK KaK TaKoe eOCTOHHae neye-
TOHIJHBOe, TO nap nalJHUaeT KOHll.eHClipOBaTbeH H npH paBHO-
BeCHH B cocYll.e yeTaHaB.'1HBaeTCH HopMa.'Ibnoe .naB.'JeHlfe. ()npe-
.!1.e.rIHTb yp,MbHYIO TenJloeMKocTb napa. Yll.enbHYIO TennOTY
napoo6pa30BaHHH BO,nbl CqHTaTb paBHOH r = 22,6.1()i /J.>K!Kr.
4 3&LIS91 97

II ACT b T PET b SI. 3nEKTPI111ECTBO
r JJ A B A VIII. 3J1EKTPOCTATHKA
 25. 3J1eKTpHlJeCKHe 3apR.II.bI. 3aKoH KYJlOHa
25.1. lllspHKH KPYTHJlbHbIX BeCOB KYJlOHa (pHC. 149) 38-
pSUKeHbI; BCJle)J.CTBHe 3TOro CTpe.nKa OTKJIOHHJlSCb OT nOJloll<e-
HHS! paBIIOBeCHH Ha yrOJI a 1 = 10°. Ha KaKOH yroJl CJle)J.yer
nOBepHYTb BepXHHH MHKpOMerp KpYlJeHHSJ,
IJT06b1 OTKJlOHeHlle YMeHblllHJlOCb )J.O
a z = 7'?
25.2. Haihll 3apSl.!l, Bcex 3J1eKTpOHoB B
KycKe Me)J.H MaccoA m = I,D Kr?
25.3. 1130JIHpoBaHHoMY npoBo)J.SlW.ellfY
lllapy C006I1leH nOJImKHTeJlbHbIH 3ap$l"l.
113MeHHTcSI JIll npH 3TOM ero Macca?
25.4. CpaBHHTe CHJlbI 9J1eKTpOCTSTHl,\e-
CKoro B rpaBIITaLl.HOHHoro B3aIfMo)J.eiiCTBHii
JI.BYx 3J1eKTpoHoB.
25.5. KaKou BeJlHIJHlIbI paBHbIe nOJlo-
}f{lITe.'1bHble 3apSl)J.bl )J.OJl:mHbI 6b1Tb nOMe-
w.eHbI Ha JIYHe H Ha 3er.l.'le )J.JI$I TOro, IlTO-
6bJ 3JIeKTpHIJeCKHe CHJIbI B3sHMo)J.eucTBHSI
3apS!.!l,OB ypaBHOBeCIIJlII )J.eiicTBHe CHJI rpa-
BIiTaLl.HOHHoro npIlTS!:meHIISI?
PIIC. 149 25.6. Ha JI.BYx O)J.HHaKOBbiX KSneJIb-
Kax BO,1,bl: lIaXO)J.HTCSI no O)J.HOMY JIHlllHeMY
3.lJeKTpoHY, npHlleM cuna 3neKTpocTaTllllecKoro OTIaJIKIIBaHHSI
Kane.neK ypaBHoBelllllBaeT CHJIY ilK B3aHMHoro TSiroreHIISI. Ka-
KoBW pa)J.HYCbI K8neJIeK?
25.7. Ka:m;t.bIH H3 )J.BYX :'>taneHbKIlX lllapliKoB nOJIo:mHTeJlb-
HO 3apSl:meH TaK, liTO IIX 06W.HU 3apS!)J. q = 5.l0- 1i Kn. KaK
pacnpe)J.e.'Ien 3TOT 3apSl.n Me:m)J.Y HHMH, eCJllf OHH, HaXO)J.S!Cb HB
paCCTOSlIIHH r = 2,0 M J1Pyr OT .npyra, OTfaJIKHB81OTCSI C cllnoi!
F = 1.0 H?
98

25,8. llBa 3apH)J.a ql = J,7 HKJI If qz = - 2,5 HKJI Ha-
XO)J.HTCH H3 paccToHHHH , = 3,2 CPof )J.pyr OT )J.pyra. r)J.e HymHo
nOMeCTIITb 3apM q:s = 3,4 HK.n ,IJT06b1 3apH)J. qz He lICnblTbiBaJI
;1eilcTBJHI CHJIbI?
25.9. I1MelOTCH )J.B3 cBo60;J.HbIx OTpHu.aTeJIbHbIX 3apH)J.a
4q II q, Haxo,!tHIl.\.IIXCSI Ha pacCToHHHIl a .npyr OT )J.pyra.KaKoH
3apH)J. H r)J.e HY)KHO nOMecTHTb, 'lT06b1 BCH CHCTeMa H8XO;l.IIJIaCb
B paBHoneclllf?
25.10. Tpll O.i{HHaKOBbiX 38pH,il.a no q = 1,7 HKJI nOMeIl.\.e-
HbI B BepIllHlfbl paBHocTopoHHero TpeyrOJIbHHKa co CTOpOHOH
a = 3,0 CM. KaKaH CHRa )J.eiicTByeT Ha Ka)K)J.blH H3 3THX 3apSl-
;l.on?
25.11. Tpll O)J.HHaKOBbIX 3apH;J.8 no 10 MKKJI pacno.'lO)KeHbl
n BepIllIlIJaX paBHocTopoHnero TpeyrOJIbHHKa. r)J.e H KaKoH 3a-
pH)J. IIY)KHO nOMeCTHTb, QT06bl nCH CllCTeMa naXO)J.HJlaCb B paB-
HOBeclUl?
25.12. t..IeTI>lpe O)J.HlIaKOBLIX 3apH,1J.a q pa3MeIl.\.eHbI B yr.lax
KBa)J.paTa. KaKoH a-apH)J. npoTHBOnOJIO>KHoro 3HaKa Ha)J.O no-
MeCTHTb B U.eHTp KBa)J.paTa, QTo6b1 BCH CHCTCMa 3apH,'\oB naxoJ1.lI-
. aCb B paBHoml?
25.13. HaAW'rH no,!tBeweH wapHK MaccoH m = 9,8 r, KO-
TOPOMY C006Il.\.HJIH 3apH)J. q = 1,0 MKK.'I. Kor)J.a K HeMY nO)J.Hec-
, H CHII3Y 3apSlmeHHbIH TaKIIM JKe 3apH)J.oM wapllK, CH.'la naTH-
}!{eHIHI HHTH YMeHbWllJI8Cb D qeTblpC pa38. Onpe)J.e.'mTb pac:
CTOHl11le Me)K.J.y u.eHTpaMII wapHKoB.
25.14. Ha3JIeKTpH30BaHHhIH Ma.leHbKlIH wapHK 6bJJI nplfBe-
eH B conpHKocHoDeHHH C paDIIblM eMY neHa3JIeKTpH30BaIlHblM.
nOMeIl.\.eHHLle 3aTeM Ha paccToHHIIH , = 9,0 C\! wapllKlf OTTaJI-
Z\.IIB8IOTCSI C CII.'lOH F = 0,25 MH. KaKoB 6blJI nepnoHa'laJIbHblii
3apSIl\, wapllKa?
25.15, .l1.na MaJIeHbKIIX npoBo)J.HIl.\.HX wapHKa nO)J.BeIliCHbi
H3 )J.JIIIIIIIblX HenpoBo)J.HIl.\.HX HHTHX K O)J.IIOMY KPlOqKY. llIapllKII
3apH)KelIbI O)J.HHaKOBbIMH 3ap}1J1.aMIi H HaXO)J.HTCH Ha paccToHIIHII
r =_5,0 CM .npyr OT )J.pyra. t..ITO npOl130H.!I.eT J10CJIe Toro, KaK O.'l.HH
113 wapHKOB pa3pMHTb?
25.16. .l1.Ba 3apH.'I.a B BaKYYMe B3aHMo;J.eHCTBYIOT C T31<OH
)f{e cllnoii Ha paCCTOHHIIH '1 = 27 CM, KaK B BO)J.e Ha paccTOH-
HHH , z = 3,0 CM. Onpe)J.eJIHTb )J.H3JIeKTpHlJeCK}"1O npOHHu. ae -
MOCTb BO)J.bI.
25.17. .l1.Ba 3apHmelIHblx lllapHKa, nO)J.BellIeHHbiX 113 HH-
tax O)J.HHaKOBOH )J.JIHHbl, onYCKalOTCSI B KepOCHH. KaKOBa )J.OJIm-
Ha 6bJTb nJIOTHOCTb MaTepHaJIa wapHKOB, <rro6b1 yroJi paCXO>K-
lleHHH HHTeH B B03)J.yxe H B KepOCHHe 6bIJI O)J.HH II TOT >Ke?
4.
99

25.18. lIIapHK Maccon m C 3apMoM q, nO)J.BeUJHH},IH Jfa
HHTH )J.JIHIIOH J, Bpan.taeTcst BOKpyr HenO)J.BH}KHOrO 3apMa,
TaKoro )Ke, KaK H 3apM rnapHKa. Yron Me}K)J.y HanpaBJIeHHeM
HIITH H BepTHKaJIblO paBell a. HaliTH yrnoDyro CKOpOCTb paBHo-
MepHoro Bpan.tenHSI rnapllK3 11 cHny HaTSUKeHHSI HUTH.
 26. 3JIeKTpH'IeCKoe none. HanpsuKeHHocTb.
Pa60Ta CHn 3JIeKTpHIJeCKOrO nonSi.
nOTeHqHan
26.1. 06'bstCHHTb. nOlleMY CHnOBbie JIHHlIH 3neKTpoCTa-
THllecKoro nOJIst He nepeceKalOTcst.
26.2. HapHcoBaTb KapTHHY CHJIOBblX JIHHHH nonSi Me}K..'J,Y
AB}'MSI 3apSl.ll.aMH B CJlyqaSlx: a} q H - q; 6} q H q; B} q H - 2q,
26.3. nOCTpOIlTb rpa<t>IIK 3aBHCHMOCTH HanpH}KeHUOCTH
3l'.KTpOCTaTHllecKoro nonSi. o6pa30BaHHoro 3apH)J.oM q =
= 1 HKJI, OT paccToSlHHSI )J.O 3apSl.ll.a. .
26.4. llBa O)J.1I0HMeHllbIX 3apH)J.a ql = 0.27 MKKJI II 'Jz =
= 0,17 MKKn Haxo)J.SlTCSI Ha pacCToSlHHH 1= 20 CM )J.)'\f OT
)J.pyra. Onpe)J.eJIHTb. B KaKoH TOqKe Ha npHMoH Me}K)J.y 3apSl)J.a-
MH HanpSl)KeHHOCTb nonSi paBHa HYJIlO.
26.5. B TOqKe A HanpSl)KeHHOCTb nOJIst TOllelJHoro 3apSl)J.a
E A = 36 B/M. a B TOIlKe C HanpSl}KeHHOCTb Ec = 9,0 B/M
(pHC. ISO). HaHTH HanpSl)KeHHOCTb
. B ToqKe 0, JIeJKa1l.\.eH nOCepe.ll.HHe Me)K-
, )J.y TOIlKaMH A H C.
26.6. D.Ba 3apMa paCnOJIon<eHbI Ha
OCH x. O)J.HII3apst)J., paBHblH 1,25 HKn,
paCnOno>KeH B TOIJKe Xl = 3,0 CM,
a )J.pyroH, paBiThlii - 1,25 IlKn, - B TOIlKe X z = - 3,0 CM.
BblqHCJlHTb Mo.nynb H HanpaBJIeHlle HanpSl}KenHOCTH nOJISI B
TOIlKax (0; 0), (0; 3,0); (0; - 3,O) Ha OCH y.
26.7. none C03)J.a1l0 )J.BYMSl3apH)J.aMH, pacnOnO}KeHHbIMH H3
OCH X. O)J.HtI 3apSIJI., paBHblH + e, pacnOJIO)KeH B TOIlKC
x = 1,0 CM, )J.p)'roii, paBHblii - 4e, - B TOIJKe X = - 2,0 CM.
HauTH KOop;I.HHaTbI TOlleK C HYJICBOH HanpSl}KeHHOCTblO. CKOJIb-
KO HMeeTCSJ T3KHX TOlleK?
26.8. llBa O)J.HHaKOBblX 3apSJ)J.a no 1,5 HKn Ka}KJ(bIH pacno-
JlO}KeHLI B nnOCKOCTH xy. O)J.IIH 3apSJ.lI. paCnQJIO}KeH B TOIJKe
X ;:z: 3,0 CM, Y = 0, .lI.PyroH - B TOIJKe x = 0, y = 2,0 CM.
BbI'IHCJlHTb MO.ll.YJlb II nanpaBneHHe HanpSl}KeHHOCTH B TOIJKe
(3,0; 2,0).
26.9. 4eTbipe O..'J,HHaKOBbIX 3apSJ.lI.a q = 40 MKKn pacnono-
}KeHbI B BeplllHllax KB8.npaTa co CTOpOHOH tl = 2,0 M. KaKoB3
.
q.
.
"
.
o
PHC. 150
100

6YJl.eT HanpH>KeIlJIOCTb nOJISI Ha paCCTOSlIIIUl 2a OT 1I.eHtpa KBaJ1-
paTa H3 npOJl.OJl>heHHII JI.lfaroHa.1u?
26.10. OnpeAe.'1I1Tb HanpH)f{eIlHOCTb nOw'1H, C03AaBae:\lOro
rollellUbIM ,nllno.1C:\f C ::meKTplfllecKHJ\I MOMeHTOM p = 2,0 X
X 10- 12 K.'1'M, Ha paCCTosUllf1f d = 10 CM OT lleliTpa J1.1lnOJlSl B
HanpaBJlellllH, ncpnell,nHKYJlHpHO:\1 OCII J1.lIn0,,1H.
26.11. PaccToHlllle Men<.ay 3apnP.aMII JI.lfnOJlH 1= 1,0 MKM.
HailTII DeJlH'mHY 3apJJAOB .11.11 nOJJn , eCJIIi Hanpn)f{eHHOCTb B
TOIlKC, YJl.aJlcHHoil OT o60Hx 3apHJl.OB lIa
d = 2,0 CM, paBlia Eo = 1,8 B/M.
26.12. DOJlc C03.:l3no TOllelIHbIJII 3apH-
,nOM, DOTeIIUHa.'1bl TOIlCK A H C paBHbl Z
CPA = 15 B II «Pc = 5,0 B (pIlC. 150).
HaHTlI nOTCHllllaJl TOIlKH 0, .'1C)f{am.eH no-
cepe,nIfHe Me)f{J1.Y TOIl!{aMH A II C.
26.13. llBa OJl.HOHMeJIHblX 3apHJJ.a no
1,0 IIKJI Ka)f{JI.blil lIaXOjJ.HTCH lIa HeKOTO-
pOM paCCTOSlHl1II J1.pyr OT J1.Pyra. OnpeJl.e-
JlUTb nOTeHuua.'1 TOil KII , Jle)f{am.eH lIa paCCTOHHIIH 9,0 CM OT
Ka)f{J1.oro H3 3apHJl.OB. KaK 113MellHTCH .:HOT nOTeIIU1l3.'1, eCJIII Bce
npOCTpaHCTBO, B KOTOpOM lIaX0Jl.HTCH 3apH,nbl, 3anOJlHHTb Ke-
POCUHOM? .
26.14. Ha nOBepxllocTH wapa paAHyca ro = 9,0 CM paB-
1I0MepHO pacnpeJl.eJIeH nOJlO)f{I:1TeJlbHhlH 3apHJI. q = 0,10 HK.'1.
HaHTH lIanpR)¥.ellHocTb II nOTeHUHaJl B lleHTpe mapa II lIa pac-
CTOHHHII r = 90 CM OT uellTpa.
26.15. Gpepa paAllyca R paBHoMepHo 3apR)f{eHa 3J1eKTpH-
IlCCTBOM C nOBcpxHOCTHOH nJlOTUOCTblO (], HaHTII MOP.YJlb Ha-
npH)f{eUHOCTII II' nOTeHUHaJl KaK cpYHKllHIO paccToRHHH OT lleHT-
pa C<!>cPbl. DocTpoHTb rpa<l>HKH <PYIIKllIIH E (r) H cP (r).
26.16. llBa wapa - 6oJlbwoii H MaJleHbKUH - paBHoMep-
HO 3apH)f{ellbl 3.'1eKTpllllecTBoM C nOBepxllocTHOH nJlOTIIOCTbJO
(], ByJl.YT JIll OJl.IIHaKODbI nOTeHllHa.'1bl wapoB?
26.17. MeTaJlJlHlleCKa H ccpepa, Jl.HaMeTp KOTOpOH d = 18 CM.
3apSl)f{aeTCH ,no nOTeHlllfaJla «p = 300 a. OnpeJl.eJlHTb, C KahoA
nJlOTHOCTblO pacnpeJl.e.'1eH 3apHJI. no nOBepxHocTH C<!>cPbl.
26.18. DO.'1b1H wap paBllo:\lepllo 3apR)f{eH 3J1eKTpHllecT-
BOL B lleHTpe wapa nOTeHUHaJl paBeH CPI = 120 a, a B TOIlKe
113 paCCTOHIIHH r = 36 CM OT ueHTpa nOTeHllHaJl paBeH CP, =
= 20 B. KaKoB paJl.IfYc wapa?
26.19. DOJle C03,nano Jl.BYMH paBlioMepllo 3apH>KeHHblMH
KOHueHTpHllecKHMH ccpepa:\1H (pIlC. 151). HaMTH lIanpIDKell-
1I0CTb B TOIlKax 0, A, C, 3HaJl, qTO 3apH,/I.bI C.pep paBHbI ql =
c
.
PHe. 151
101

=0.10 MKKn H Qz=-0,60 MKK.'I, a paCCTOSlHHe OT u,eHTpa .11.0
T01JKII A paBHo r 1 = 20 CM, .11.0 TO'lKH C paBHo r 2 = 50 CM.
26.20. Do.'Ie C03.!1,aHO JJ.BYMH paBHoMepHo 3apSl1KeHHbIMIf
KOHu,eHTpH'IeCKIiMIi cll>epat.UI. HaHTH nOTeHllHan B u,eHTpe. a
TaK1Ke B T01JKax. OTCTOSlIl.lHX OT u,eHTpa lIa paCCTOSlHHSlX rl =
= 20 C:'I H r 2 = 50 CM. 3app.bl cll>eP paBHbI COOTBeTCTBeHIIO
ql = 1,0 IIKn H q2 = - 1,0 HKn. a HX paJl.HycbI paBHbI R 1 =
= 10 CM H Rz = 30 CM.
26,21. Ll.ae KOHlleIlTpll1JeCKlie npOBOJl.Hll.llle cll>epbl paJl.Hycol}
R H 2R 3ap5DKeHbI COOTBeTCTBeHHO 3apSlJl.aMH OJl.HOrO 3HaKa
ql = 0,10 MKKn H q" = 0,20 MKKn. Ha panHoM paccToSlHHH
OT Ka1K.!l.OH H3 ccpep nOTeHu,Han cp = 3,0 KB. HaHTH R.
26.22. lllap pa,nHyca R paBHoMepHo 3apSl1KeH 3.1eKTpH'Ie-
CTBOM C 001>eMHOH nnOTHOCTblO p. HaHTH Mo,nynb HanpSl1KeHHO-
CTII KaK 4JYHKU,HIO paccToSlHHSI OT lleHTpa wapa. DOCTpOHTb
rpa4JHK 4JYHKu,mi E (r).
26,23. 360 HlITOBbIii cnnowlloH wap pa,nHyca R = 5,0 C1>
HeceT 3apSl.n, paBuoMepHo pacnpe,nenellublH C 06'beMHOH n.'IOT-
IIOCTblO p = 10 HKn/M 3 . Onpe,ne.'IHTb HanpSl1KCHHOCTb B TO "I Kax,
OTCTOSlIl.lHX OT lleHTpa wapa Ha pacCToSlHHHX r 1 = 3,0 CM,
r z = 5,0 CM. r 3 = 10 CM. DOCTpOHTb rpa4JHK 3aBHCHMOCTH
E (r).
26.24. lIBe 6ecKOne1Jnble napan.'IeJlbHble nnaCTHllbl paBHo-
Mepno 3apSl1KeHbI C nonepxHocTHOH nnOTHOCTblO 3apSl.na (Jl =
= 1,0 HKnlM 2 H (J2 = - 3,0 HKn/M 2 . Onpe.nenHTb HanpSl1Kell-
HOCTb: I) Me1K,ny nnaCTIlHaMH; 2) Bue nnaCTHH. DOCTpOHTb
rpa(tmK H3:'lenenHH JianpH1KeIiHOCTH B.nonb .'IHHHH, !lepneH-
J1.HKynSipnoH nnaCTHlla:'l.
26.25. PewHTb 3a.:r,a'lY 26.24, ecnH (Jl = (J2=2,65 MKKn/!\t 2 .
26.26. Onpe.n.e.1HTb pa3HocTb nOTeHllHanOB Me1K,ny TO'lKa-
Mil, OTCTOSlIl.lHMII OT 3apSl,na 4,0 IIKn lIa paccTOSlHHHX 16 H
20 CM.
26.27. lIBa 3apH,na no 1,0 MKKn Ka1K,nblu Haxo.n.HTCSI Jia
paccTOSlHHH 50 CM .n.pyr OT ,npyra. KaKYIO pa60TY Ha.n.o cOBep-
WIITb, IlT06b1 c6nH311Tb HX ,no 5,0 CM?
26,28. 3apSlp.bl 0,15 MKKn Ii 3,0 JiKn Haxo.n.HTCSI Ha pac-
CTOHHHU 10 CM .n.pyr OT ,npyra. KaKYIO pa60TY cOBepwaT CHnbl
nonSl, eC.'IH BTOpOH 3apSl,n, OTTanKHBaHCb OT nepBoro, YJl.a.'1HTCH
OT nero Ha paccTmlHue 10 M?
26.29. 3apSl,nbI ql = 0,10 MKKn Ii qz = 1,0 HKJI lIaxo.n.HT-
C':I Ha paCCT051HIHI r = 10 CM .n.pyr OT .npyra. KaKoBa nOTen-
liJlanbliaH 311eprllH :)Toii CIiCTeMbl?
26,30. lIBa 3JIeKTpOna .nBH1KYTCB noon J1.eHCTBHeM CHn 3J1eK-
TpOCTaTH1JeCKOrO OTTa.1KHnaHIUI. KaKYIO CKOpOCTb 01111 6y.nYT
102

.
JlMeTb Ha 6ecKOHetlHO OOJlbWOM paCCTOHHJlH, ecJIH B Halla.'Ib-
Hbl" MOMeHT ;)JleKTpOHbl HaX011.HJlHCb Ha paCCTOHHHl1 , = 1.0 eM
.D.pyr OT .D.pyra H HMeJIH CKOPOCTb. paBH}'lO HYJlIO?
26.31. llBa 3J1eKTpOHa. HaXO){HBWHeCR Ha 6ecKoHeliHo OOJlb-
rnOM pacCTOHHHH 011.HH OT .D.pyroro. HatlHHalOT ,n.BHraTbCR Ha-
BCTpeIJY ,n.pyr ,n.pyry C o,n.HHaKOBblMH CKOpOCTHMH v = 1,0 KMic.
Onpe,n.eJIHTb. Ha KaKoe HaHMeHbwee pacToHHHe C6J1H3HTCR 3J1eK-
TpOHbl.
26.32. MaJlellbKHii rnapHK MaCCO" m = 1,0 r, KOTOPOMY
COO61.l.lHJlJI 3apH.ZJ. q. = 0,15 MKKn. 6porneH H3,n.aJ1eKa co CKO-
pOCTblO V = 1,0 WC B c4>ePY, 3apIDKeHH}'lO 3SpH)l.OM qt =
= 0,30 MKKJI, npH KaKOM MHHHMaJ1bHOM 3HalleHJlH pa;J.Hyca
c4>ePbl rnapHK ,n.OCTHrHeT ee nOBepxHoCTH?
26.33. 3apH.D.b1 q, - 2q, 3q pacnOJlO>KeHbl B BepulHHax
npaBHJlbHOrO TpeyroJlbHHKa co CTOpOHOii a. KaKoBa nOTeH-
I{HaJlbllaR 3HepmR 3TOH CHCTeMbl?
26.34. KaKYIO CKOpOCTb npJl06peJIH t5bl 3J1CKTpOHbl. 0 KO-
TOpblX rOBopHTCR B 3a,n.atle 26.30, eCJIH 6bI HX 6uJlO He ,n.Ba. a
TpH? lIeTblpe?
26.35. 3J1eKTpOH BblJleTaeT Jl3 TOIJKH. nOTeHI{HaJI KOTOpoA
450 B, co CKOpOCTblO 190 wc. KaK}'1O CKOpOCTh OH 6Y11.eT HMeTb
B TOtlKe C nOTeRI{lIaJlOM 475 B?
26.36. npOTOH. JletHI.l.lHH no HanpaBJleHHIO K R.n.py ,n.BYKpaT-
HO HOHH3HpoBaHHoro Heno,n.BH>KHOrO aTOMa reJJHR. 0 HeKOTOpoA
TOIiKe nOJlH C HanpH>KeHHOCTblO E = 10 KB/CM UMeer CKOpOCTb
v = 1,0 KMfc. Ha KaKoe paccToHHue CMO>KeT npOTOH npH6.'IH.
3UTbCR K H,n.py?
26.37. 3J1eKTpOH, neTeBWHH ropH30HTaJlbHO co CKOpOCTblO
vI) = 1,6.10 MMlc, BJleTeJI B O,n.HopoJJ.Hoe 3J1eKTpHIJecKoe nOJIe
C HanpH>KeHHOCTblO E = 90 B/eM, nanpaBJleHHOe BepTHKa1lbHO
BBepx, KaKooa 6y,n.eT no MO,n.Y1l1O H HanpaBJleHHIO CKOpOCTb
3J1eKTpOHa IJepe3 BpeMH t = 1,0 HC? .
26.38. 3J1eKTpoH 11.BH>KeTCR no HanpaBJleHHIO CH.'IOb1X 1IU-
HHH o,n.nopo,n.Horo OOJIH, HanpH>KeHHOCTb KOTOporo E = 120 B/M.
KaKoe paccToHHlle OH npOJIeTHT ,n.o nOJIHOH OCTaHOBKH. eCJlH
ero HaIJa.'IbHaR CKOpOCTb v = 1,0 MM/c? CKOJlbKO BpeMeHH
3.'IeKTpOH 6y,n.eT J1,BHraTbCH ,n.o OCTaHoBKu?
26.39. nbIJIHHKa MaccoH m= 10 Hr nOKOHTCR n OJJ.HOpO.D. HOM
3J1eKTpOCTaTHllecKoM nOJle M€)K)ty nJlaCTHHaMJI C pa3HoCTbIO
nOTeHLlHaJlOB U = 6,0 KB. PaccToRHHe Me>K,lty n.1aCTHHaMH
d = 6,0 CM. KaKOB 3apRJJ. nbIJIHHlrn? KaKoe Ha.n.o npHJlO>KHTb
HanpH>KeHHe K DJlaCTuHaM. lI'f06u n1JlJIHHKa OCTanaCb B
paBHoBecuH, nOTepRB 3apH,n.. paBHbIii sapq,n.y N = 4.0.IOS
3J1eKTpOHOB?
103

 27. npOBO.ll.HHKH H .ll.H3J1eKTpHKH
B 3neKTpHIJeCKOM none
27.1. KaK nepe,'J.aTb BeCb 3apH,'J. npoBo,nHHKa A nO.lloIY H30-
JIHpOBaHHoMY npoBo,nHHKY C (pIlC. 152)?
27.2. KaK nO.llYIJHTb ua ,nBYX nO.'1bIX H30.llHpOBaHHblx npo-
BO,nHHKax 3apH,n, paBHe no Be.llHIJHHe H 3HaKY?
27.3. KaK. HMeH 3.11eKTpHtleCKHH 3apSl.!t. nOJlYIJHTb paBHblH
e\lY no ne.'1UtlHHe 3apH.!t. 110 .!tPyroro 3HaKa?
27.4. nOlJeMY .ll.Ba pa3HoIIMeHll0 3apmKeHHx MeTaJlnHqe- .
CKHX mapa B3alf:\10,neHCTB}IOT ,npyr C ,npyroM C 6o.llbmeH CH.IIOH,
He}f{eJJH 3apH}f{eHHble o,nHOHMeHHO (npH
npOtlHX o,nHHaKOBX YCJIOBHHX)?
27.5. B03MO}f{HO JIH. tlT06b1 ,nBa o,n-
1I0HMeHHO 3apH}f{eHHb1X nppBo,nHHKa
npIITHrHBa.ll,',cb?
27.6. nOJlO>KlITe.llbHO 3ap H}!(eJl Hoe ,
Teno npHTHrHBaeT no,nBerneHHbIil Ha
HHTH mapOBOH npOBo,nHHK. MO)!{IIO .IIH
3aK.IIIOtlHTb OTCIO,na. qTO Teno 3apH:iKeHO
OTpHua:renbHo?
27.7. nO.llO}!(HTeJlbJlO 3apH:iKeHHaH CTeK.IIHHHaH na.llOIJKa
O'ITaJlKHBaeT no,nBemeHHoe Ha HHTH TeJlO. Cne,nyer JIll OTCIO-
)l.a. qTO TeJIO 3apH:iKeHO nOnO)!<HTeJlbHO?
27.8. JlBa paBHblx pa3HoHMeHHblx 3apH,na pacno.'10>KeH Ha
HeH3MellHOM paccTOHHHH ,nPyr OT ,npyra. KaK H3MeHHTcn CH.'1a.
)l.eHCTBYlOl.l.laH Ha 3apH)I,, H HanpH:iKeHHOCTb nO.llH B pa3.11HIl-
HX TOtlKaX, ec.'111 oQa 3apH,na OKPY}!(HTb TOHKHMH MeTa.ll.llHtle-
CKII\iH H30.IIIfpOBaHHbIMH oOOnOtlKaMH, COBna,naIOI.l.lIIMH C 3KBJI-
nOTeHUHa:JIbHblMH nOBepxHOCTHMH?
27,9. no.,lii MeTa.ll.llHileCKHii map A. HMelOl.l.lHH HeOO.llblUOe
OTBepCTHe. 3apH:iKeli nO.llO}!(HTe.llbHO. KaK H3BeCTHO. Ha BHY-
TpeHHcH nOBepxHocTH 3Toro mapa 3apH)J.bI OTCYTCTByIOT. 3a-
pH,nHTCH .IIH MeTaJl.'1HlJeCKIiH map C, eCJIJI Coe,nHHHTb ero npo-
BOJIOKOii C BIfYTpeHHeii nOBepxHocTblO mapa A?
27.10. He3apH:iKeHHblii Mera.ll.llHlleCKHH mapHK, no,nBemell-
HblH Jla llIeJJKOBOH HHTH, nOMCl.l.leH B O,nHopo)l,Hoe 3.'1eKTpHtlecKoe
none HanpH>KeHIIOCTblO E, KaKoBa HanpH}!(eHHOCTb nonH JI..'1H
TOileK BHYTPH mapHKa? 113MellHTcH nH OTBeT B cnYtlae 3apH}!(eH-
Horo lIIapHKa?
27.11. B nOJl.e OTpHuaTeJlbHOrO 3apH,na BHeCJIH nOJlblH Me-
Ta.llJIHilecKHH map. 4TO npoH30ii,ner C noneM 3apH,na? nOHC-
HHTb C nOMOl.Q.blO PHCYHKa.
52 CQ"
PHe. 152
104 '

27.12. nO.l101KHTenbHblH 3apH.!t HaXOJl.UTCH BHYTPII nOJIoro
c4'ePUtleCKOrO npOBOJI.HHKa. 11306pa3uTb C nOMOlllblO CHnOBb!X
nUIUlH 3neKTplltleCKUe no.1H BHYTPII If BHe npOBo.nHuKa. -
27.13. .M.e-rannUlJeCKUe mapbl, 3apn1KeHHble 0.nUHaKOBbIM
gapSl.nOM, lUfeIOT'nOTem.lUanbl20 H 30 B. KaKHM 6y.ne-r nOTeHl.lHan
9TIIX llIapoB, eCJIH Coe.n.UHHTb HX I:'lOBOJIOKOH? (PaccToHHHe
Me.m.ny wapaMH Be.1JIIKO no cpaBHeHHIO C HX paJl,lIycaMIf.)
27.14. .lI.Be napanneJIbHbIe MeTannHlleCKue nJIaCTHHKH pac-
DO.l101KeHbl Ha Heoo.nhllIoM pacCTOHHU" llpyr OT .npyra. KaKue
sapHJ1.bl 6y.n.YT Im.nYl.lUpOBaIIbl Ha no-
sepxHocTHX BTOpOH nnaCTHHKH, eCJIH
nepBoH COO61llHTb nOn01KH.TeJlbHblH 3a-
pH.n. Q?
27.15. 3apH1KeHp.aH Me-rannH'leCKaH
nnaCTHHKa Haxo.n.I1TCH B 3neKTpHIJeCKOM
none. Pe3ynbTHp}'lOlllee none nOK33aHo
sa pHC. 153. 3apHJJ. nJlaCTHHKU q. weBa
OT n.1JaCTHHKH uanpIDKeHHOCTb nO.1JH El'
a cnpaBa - E I' KaKaH CH.1Ja .n.eHcTBye-r
sa n.1JaCTuHKY?
27.16. Ma.1JeHbKHH wap"K, HME-IOIllHH 3apH.n. q = I,Ox
X 10- 8 Kn. HaXOJI.lITCH Ha paCCTOHHHH r = 3,0 CM OT nnocKoH
tde-ran.1JU'leCKOH 3a3eMneHHOH CTeHKH. C KaKoH CII.'JOH OIlU
B3a0.neHcTBYJDT?
27.17. Ha paCCTOHHHH '1 = 2,0 CM OT npOBOJI.mu.eH 6ec-
KOHelJHOH nnOCKOCTU HaXO)1.UTCH 3apH.zt q = 1,0.10- 8 Kn.
Onpe.n.enUTb nOTeHLluan nO.1JH B TOIIKe, OTCTOHJl(eH OT nnOCKO-
CTu Ha paCCTOHHHH'1 HOT3apH.n.a Ha paCCTOHHHU 'z = 3,0 CM.
27.18. Me-rannUtleCKaH nnaCTHHa, paCnOJlO1KeIlIlaH B Bep-
THKaJlbHOH nnOCKOCTU, coe.nIlHeHa C 3cMneH. Ha paccToHHIUI
r = 10 CM OT nnaCTIIHbI nOMern.aIOT mapuK MaccoH m = 0,10 r,
no.n.BellIeHHblH Ha JIHTH Jl,JIHHOH 1 = 12 CM. npH C0061lleHUlI
UlapUKY 3ap::JJI,a q OH npuTHHyncH K nnaCTUHe TaK, qTO HIITb
OTKJIOHUnaCb OT BepTUKanu Ha yron a = 30°. HaHTIf 3apH.I1.
I1IapuKa.
27.19. HeoonbllIoH llIapuK BUCUT Ha.zt ropu301lTa.IJbHOH npo-
BO.l1.mu.eH nnOCKOCTblO Ha U30JIUpYIOll.leH ynpyroii HUTH. noc-
l.Ie TOro KaK wapuKY co061llunu 3apH.n. q = 1,4,10- 8 K.II, OH
onYCTUJlCH Ha Ar = 9,0 MM H ero paCCTOHHue .no npOBO.ll.S1llleii
11.1J0CKOCTU CTano, = 10 CM. HaHTH 1KeCTKOCTb HIITH.
27.20. .llBe napanne.nbHble Me-ranJlIllleCKIIe nnaCTUHbl 3apH-
eHbl TaK, 'ITO npuTHrUBaJOTCH C cllnoH F. H3MeHuTCH nH 31'a
tlLlIa, eCJIII BBecTH MeJK.D.Y HUMH nnacTHHKY H3 .n.H3.1JeKTpuKa?
+
+
+
+
+
+
+
Pue. 153
105

27.21. napaqIHHoBblH mapHK npHTHrHBaeTCH K aapH.)KeH.
HOMY MeTa.1JIHlJeCKoMY mapHKY B B03)1yxe, HO OTTaJIKHBaeTCH
OT Hero B BO)J.e. nOlieMY?
27.22. MeTaJlJIHlleCKHH 3apSl.)KeHHblH map oKpY.)Kell TOJI-
CThlM ccpepH'IeCKHM CJlOeM )1H3J1eKTpHKa. HapHcoBaTb KapTH-
HY CHJlOBbIX JIHHHH 3JIeKTpHtleCKoro nOJUI BHYTPH H BHe )1H-
3.'IeKTpHKa.
27.23. Pa)1HYc MeTaJIJlUlJeCKoro mapa R = 5,0 CM, a TOJI.
J.IJ.HHa CcpepHtlecKOro CJlOH 300HHTa, OKpY.)KalOw.ero map,
d = 5,0 CM. 3apHJJ. mapa q = 6,0.10- 1 Kn. BhlllHCJlHTb Ha-
npH.)KeHHOCTb nOJIH B TOqKax. JIe.)Kaw.HX Ha paCCTOHHHH '1 =
= 6,0 CM H , s = 12 CM OT LleHTpa mapa, H nocTpoHTb rpacpHK
3aBHCHMOCTH HanpJuKeHHOCTH OT paccToHHHH.
27.24. MeTaJlJIHqeCKHH map pa.nHyca R = 5,0 CM, HeC}'llI.HH
3apH)1, paBHOMepHO pacnpe.!l.eneHHblH C nooepxHoCTHOH nJIOT-
HOCTblO a = 2,0.10- 1 Kn/M s . norpY.)KalOT B KepocHH. Onpe-
JJ.eJIHTb BeJmqHHY H 3HaK nOJlHpH3aLlHoHHoro 3apHJJ.a, HaBeJJ.en-
Horo Ha rpaHHLle MeT3J1.'I-.D.H3J1eKl'pHK.
27.25. .llBe BepTHKaJIbHO pacno.'IO.)KeHHbIe nJIaCTHHbI 3apH-
.)KeHbl TaK, liTO pa3HOCTb nOTeHLlHanOB ME!)KJ1Y HHMH paBHa
i\cp = 400 B, nJlaCTHH!.l norpY.)KalOT B Macno. KaKoBa no-
oepxHocTHaH nJIOTHOCTb CBH3aHHblX 3apH.D.OB, eCJIH l.'OJIH-
lIa MaCJIHHOrO cnOH d = 2,0 MM?
 28. 3J1eKTpOeMKOCTb. KOH.D.eHCaTOpbl
28.1. .llBa MeTa.'IJlHlleCKHX mapa -OOJlbmOH H MaJIeHbKHH -
3apH.)KaIOTCH 0.D.JlH3KOBbIM KOJlHtleCTBOM 3J1eKTpHQecTBa. By.
)1YT JlH O.D.HHaKOBhl'dH nOTeHLlHaJIbl m3poB? lJTO npOU30H.D.eT,
ecnu mapbI Coe)J.UHHTb npOBOJlOKOii?
28.2. .llsa MeTaJIJIHQeCKHX mapa - OOJIbmOH H MaJIeHb-
KitH - 3apH.)KaIOTCH )10 O.D.HHaKoBoro no.eHllHaJIa. Ha KaKOM
mape npH 3TOM 6Y.D.eT OOJIbmOH 3apSl.D.? B KaK}'IO CTOPOHY 6Yl1. eT
nepeTeKaTb 3apH.D., ecnH mapbl Coe.n.HHHTb npOBOJIOKOii?
28.3. llBa IeTa.'IJIHQeCKHX 3apH.)KeHHhiX mapa coe,nHHSIIOT
npOBOJIOKOii. nOKa3aTb, 'ITO nocne coe.D.HHeHHSI nOBepXHO-
CTHble nJlOTHOCTH 3apH,noB Ha mapax 6Y.D.YT 06paTHo nponop-
LlHOHaJlbHbl HX pa.D.HycaM.
28.4. KaKHM )10J!)i{eH 6blTb pa.D.uyc mapa, liTo6!.l era eM-
KOCTb 6blJIa paBHa 1,0 «1>?
28.5. BhlQHcnlfTb eMKOCTb 3eMHOro mapa. Ha CKOJlbKO
YBeJIHtlHT nOTeHLlHaJI 3eMJlH aapH.D. q = 1,0 Kn?
28.6. Meran.'mllecKHH map. )1ltaMeTp KOTOporo d = 18 CM,
3apH.)KalOT )10 nOTeHLlHana cp = 10 RE. Onpe.neJIHTb BeJIHqHHY
3apH.D.a mapa.
-106

28.7. N = 1,0.10 3 o,nHHaKoBblx MaJIeHLkHX KaneJIb BO)J.bI,
3apH>KeHHbIX paBHbl:\1If 3apH,nar.IH, CJJIIBalOTCH B O,nHY cepeplllie-
CKYIO Kan.llO. Bo CKOJIbKO pa3 nOTeHIlHaJI 3TOH KanJm 6o.1bllle
nOTeHLlHaJIa MaJIeHbKOH KanJIti?
28.8. D.Ba lllapa, O,nHII pa,nHyca Tl = 5,0 CM C 3apH]J.lJ1\f
ql = 0,80 HKJI, ,npyroil paJ{uyca TI = 10,0 CM C 3apH,noM
q2 = - 2,0 HKJI, Coe,nHHHIOT JI,JIHHHOH TOHKO" npOBOJIOKOil.
KaKoH 3apH,n nepeMecTHTCH no Heu? KaKoB 6YJJ..eT 061.l.lHH no-
TeHllHaJI lllapoB nOCJJe coeJJ..HHeHHH?
28.9. 3apH>KeHHblH,n0 nOTeHllHaJIa qJl = 300 B lllap pa,nH-
yea R 1 = 15 CM coe.nIlHHeTCH C He33pIDKeHHbIM lllapoM .nJIHHHOH
TOHKO" npOBOJIOKOH. nOcJIe coe.nlllleHIIH nOTeHIlHaJI lllapa OKa-
3aJICH CP2 = 100 B. KaKoB pa,nHYC BTOporo lllapa?
28,10. MeTaJIJIHlleCKHH lllapHK pa.nHyca '1 = 1,0 CM, 3apH-
>KeHHbIH .no nOTeHIlHaJIa <PI = 270 B, BHOCHTCH BHYTPb nOJIO-
ro MeTaJIJIHlieCKOro wapa pa,nHyca TII = 10 CM, 3apH)f{eHHoro
,no nOTeHIlHaJIa CPI = 450 B. Onpe,'\eJIIITb nOTeHIlHaJIbi II 3apH-
JI.bl Ha lllapax nOCJIe HX npHKocHoBeHHH.
28.11. MeraJIJIHlJeCKHH lUap pa.nHyca RIt 3apH}KeHHblii .no
HeKoToporo nOTeHllHaJIa, oKpY1KalOT KOHlleHTpllliecKoii cepe-
pHliecKoH npoBo,nHl.l.leH o60JIOQKOH p3.Zl.IIyca R I' KaK 113MeHIIT-
CH nOTeHllHaJI II lieMY CTaHer paBHa eMKOCTb lllapa, eCJIII BHelll-
IIIOIO o60JIoliKY 3a3eMJIIITb?
28.12. npOBO.nHIIK eMKOCTblO C I 3ap>Kell .no noreHllHaJIa
CPIt a npoBo.nHHK eMKOCTblO C I - ll.0 nOTeHllHaJla CPl' npOBOll.-
HHKH y,naJIeJlbl Ha OtIeHb 6oJIbllloe paccToHHlle ll.pyr or .npyra.
KaKIIM 6y,ner nOTeHllllaJI 3THX npOBOll.HHKOB, eCJJH Coell.HHHTb
IIX npOBOJIOKOH?
28.13. npOBOll.HHKH, 3apH>KeHHbIe Oll.HHaKOBblM SapHll.OM,
1I:\lelOT nOTeHllHaJIbl CPl = 40 B II cpz = 60 B. KaKHM 6Yll.er
nOTeHIlHaJI 3THX npoBo.nHHKOB, eCJIH Coell.HHHTb HX TOHKOH
npOBOJIOKOH?
28.14. npOBO,nHHK eMKOCTblO C I = 1,0 MK 3apH1Keli 11.0
nOTeHllHaJIa CPI = 6,0 KB, a npOBOll.HHK eMKOCTblO C-s =
= 2,0 MK-ll.O nOTeHllHaJIa CPI = 12 KB. PaccTOHHHe Me1K,ny
npoBo,nHHKaMII BeJIHKO no cpaBHeHHIO C HX pa3MepaMH, KaKoe
KOJIHqeCTBO TenJIOTbl BbI.neJIHTCH npH coell.HHeHHH 3THX npoBOll.-
HHKOB npoBo.IIoKoH?
28.15. nJIOCKHH KOHll.eHCaTop 06pa3OBaH ll.B)TMH KBa.npaT-
IIbIMII nJIaCTHHar.m, OTCTOHI.l.lHMH ll.pyr or ll.pyra Ha pacCToHHIfII
d = 1,0 MM. KaKoH ll.OJI)f{Ha 6b1Tb lUHpHHa Ka}K.nOH H3 3THX
nJIaCTHtr, 1fI'06bI eMKOCTb KOHll.eHcaTOpa 6bIJJa C = I,D MKC1>?
4e\fY 6Yll.eT paBHa CTOpOHa nJIaCTHHbI ll..'IH nOJlyqeHUH TaKon
w.:e eMKOCTH, ecJJH Me)f{,l{y HUMH nOMeCTHTb reTHHaKc?
107

28.16. I1MclOTcH J].Be MeAllbie nJIaCTHHbl, JIHCTOK CJIIOJ].bl
TOJII.l.lIIHOH 0,10 Ir.f, KBapLleBaH nJIaCTHHKa TOJIW.IIHOii 2,0 MM
H nJIaCTHHKa BOCKa TOJII.l.lHHOH 1,0 CM. KaKYIO H3 nJIaCTHH HaJ].O
B3H fb J]..'IH nOJIY'lemHI lIaU60JIbllIeii eMKOCTH KOHJ].cHcaTopa?
28.17. 3T3JIOH eMKOCTblO 1,0 r.IKO J].CJiaCTCH H3 TOIIKIIX JIH-
CTOtJh.OB MeTaJIJla, npOCJIOCHIIblX JIIICTO'lK3MH CJIIO.D.b1 TOJII.l.lJlHOii
0,10 MM. K3KOBa AOJIL!)1J3 6bITb nonepXHOCTb TaKoro KOHJ].eHca-
Topa?
28.18. nJIOCKliH I<OHAeHcaTop, MC>I<.n.y 06KJ1:JJ].KaMH KOTO-
pore Ha>"O.'UITCH CJI10.:i,HHaH nJiaCTJIIIKa, npllcoeAlllleH K aKhY-
MYJISITOpy. 3apSlJI KOIlJ].ellc8Topa p;:ncII qo = 14 MKKJI. KaKoii
3apSill npoii.n.er 'lepe3 ahK)'MYJIHTOp npll YAaJICHHH nJIa.
CTHIIKII?
28.19. LlB3 o.n.lfllaKOBbiX llIapliKa AliaMeTpo:\1 d = 1,0 CM
Ka)f{AbIi'1 33pH)f{CIIbl O,1.IIH AO nOTCHLlUaJla CPl = - 6,0 KB,
J].pyroi{ - J].O norellLllla"la CPz = 6,0 KB. Bbl'lIlCJIlITb ClI.'lY
npHTmKemlH MCJI<jlY 9TIIMH lllapllKaMH I1a paccToHHIUl R =
= 1,0 M.
28.20. C KaKoH CHJIOH D3aIlMo;J.cHCTBYIOT nJIaCTlfllKH nJIOCKO-
ro KOIIJl,CHC3TOpa 1I.'I01.l.l3AblO S = 0,010 M I , CCJIII pa3HocTb no-
TeHLlllaJIOB Me>I<JI.Y IIHMU V = 500 B II paccToHHHC d = 3,0 MM?
28.21. nJIaCnUlbl nJIOCKOre KOIIJ].cHcaTopa HMelOT 3apH,lJ.bI
+ Q U - Q. KaK U3MCIIIITCH CUJla B3anr.lollciicTDHH 9TIIX nJIa-
CTIIH, eCJIII paccTomme Me)f{J].Y IUlMIi YBe"lH'lItTb B TPH pa3a?
28.22. PelllllTh 3aJ].a'lY 28.21, CliHTaH, liTO nJlaCTliJlbI KOH-
.neHcaTopa npHcoeAlllleHbI K 6aTapce aKKYMYJIHTOpa, I
28.23. KaK H3MelllITCH eMKOCTb Co p.JIOCKOrO KOH,lJ.CHCaTOpa,
CCJI1f Men<.a.y cre 06KJIa;J.KaMIi nOMeCTIlTb 1I.'IaCTI:IHI<Y: 1) CTCK-
JIH IIIIYIO; 2) MeTa.'l.ll1tJCCKYIO. To.ll.l.llllla Ka)f{}J.oil nnaCTIIHKH
paBlla nOJlOBHHe paccToSlIIIIH Me)f{AY o()KnaAKaMH.
28.24. TOIIKaH MCTa.'l"lHtJeCKaH n..'IaCTIIIIK3 nOMel.l.lella Me)f{-
AY 06K.'laAKaMII n,,10CKoro KOllllellcaTopa napa.l.'leJIbHO o6eltM
IlJIaCTlIHI{aM. KaK 3TO DOBJIHffeT lIa eMKOCTb? liTo npOlI30HJ].CT,
CC.'l1l 3TY n.'I3CTlIIIKY COCAIlHIITb C OJ].HOIl
 9 113 O()K"la,IJ.Oh.?
 ,J 28.25. I-laihll eMKOCTb KOH.i1.eIlCaTO-
pa, H300pa>l;:eHHoro 'lla pIlC. 154. nJIe-
I.l.la,lib Kaw.;J,oH nJIaCTHHbI paBHa S, a
Pile. 154
paCCTOffHlte Me)K,lJ.Y n.'IaCTHHaMIl paD-
110 d.
28.26. 1(0llAellcaTop, 3apH)f{eHllbIH AO HanpmKeHHH VI =
- 100 B, coeAHHHeTCH C KOHJ].eHcaTopoM TaKOH)f{e CMKOCTII, HO
3apmKeHHblM AO HanpSl)f{ellHH VI = 200 B OAHU pa3 OJ].HOHMeH-
110 3apH>Ke1lHblMH 06KJIAKaMIIJ J].Pyroit - pa31:'HMeHHO 3apsr-
108

)i{eltHblMH, KaKoe HanpH>KeHUe yctaHoBHTCSI Me}K;'1y 06K.1Ja,nKa-
MJf B o60Hx CJIYllaSlx?
28.27. npOCTpallCTBO M.ny nJiaCTHHKaMH nJlOCKOrO KOH-
,u.ellcaTOpa 3anOJIHeHO .nn)'MSi CJIOSIMIi ,nH3J1eKTpHKoB: cpap4x>pa
TOJlI.l.lHHOH d 1 = 1,0 CM H napa4:1l10M TO.'II.l.lHIIOH d z = 2,0 CM.
Pa3HocTb nOTellLlHaJIOn MCJK;'1Y C6KJIa.nKaMH U = 2,1 KB.
Onpe,neJlHTb nanpIDKeHHOCTb nOJUI n na.neHJie norenllJia.'Ja B
KaJK.D.OM H3 CJJoeB.
28.28. BYMara np06HBae-rcSi npH Hanp$!>KenHOCTII nOJlSl
E = 18 KB/cP.f. !lBa nJlOCKHX KOHAeHcaTopa c H30JlHPYIOlU.HM
CJloeM 1f3 9TOH 6YMaril TOJII.l.lHHOH d = 2,0 MM, C.D.HH eMKOCTblO
C 1 = 1200 nfl>, .D.pyroH eMy.OCTblO C z = 400 nfl>, coe,nHHeHbI
nOCJIe.nOBaTeJIbHO. npH KaKOM HaHMCHbllIeM nanpHJKeHHH 6y,nCT
np06HTa 3T3 cHCTta?
28.29. !lBa O.D.HHaKOBblX llIapa y,naJleHbI Ha OlIeHb 6oJIbllIOe
pacCTOSlIIHe ,npyr OT ,npyra. nOJle nepBoro llIapa o6.na.naer
5Heprneit WI = 1,6 M.lI.>K, a nOJIe Broporo - 3ueprHeit
\l.z = 3,6 M.lI.>K. KaKoe KOJIHlIeCTBO TenJlOThl Bbl,neJIHTCSI npH
coe)J.HHenHlI 3THX llIapoB npOBOJIOKOH?
28.30. 1130JIHpoBaHHhlit MeTaJlJIHllecKHH llIap pa.D.Hyca r =
= 5,0 CM 3apHJKeH ,no noreHLlHaJia cp = 10 KB. HaHTIi nJlOT-
HOCTb 9HeprHII y nOBepXHOCTH mapa.
28.31 B03MO}KHO Jill YBeJIIIIIHTb 3Heprmo 3apSl>KeHHOrO
pa3,nBII>KHOrO KOH,neHcaropa, He H3MeHSISI ero 3apH,na?
28,32. nJIOCKHii B03.nYllIHblH KOH.D.enCaTop eMKOCTblO C =
= 20 ilfl> 3ap$!JKeH .D.O pa3HOCTli nOTeHLlHaJlOB U = 100 B
KaKYIO pa(50TY Ha,no cOBepllIHTb, 1JT06hl B,nBoe YBeJlIIIlHTb paG-
TOSlHHe Jde}f{)l.y OOKJIaJlKaMII?
28,33. Me>K,ny 06KJIa,nKaMH n.'1OCKoro KOH,a.eHcaTopa Haxo-
AHTCSI napa<lJHHOBaSi nJlaCTJlHKa. EMKOCTb KOH,l:leHCaTOpa C =
= 4,0 MKfl>, ero 3apSIJI. q = 0,20 MKJI. KaKYIO pa60TY HYJKIIO
cOBepllIHTb, IlT06b1 BblTaro.HTb nJl3CTHHKY H3 KOHJleHC3Topa?
28.34. nJlOCKHH KOH,l:leHcarop, Hano.noBHHY 3ano.'IHeHHblH
E )CKOM, 3apH,l:lHJlH ,no HeKOTopoil pa3HOCTH nOTeHLlHaJlOB. HaH-
TII pacnpe,l:leJIeHHe 3lfeprHII B B03.nYlliHOM 3a30pe II B BOCKe.
28.35. HaitTH eMKOCTH KOH,neHcaTOpHblx ooTapeH, 11306pa-
>KeHHblX Ha pHC. 155, a, 6.
26.36. HaHTH eMKOCTb CHCTeMhl KOH)l.eHCaTOpoB, BKJIlOlleH-
Rb!X Me}f(JlY TOIiKaMH A H B, KaK nOKa3aHO Ha pliC. 156.
28.37. BaTapeSi 113 tleTbIpex o,nHHaKOBblX KOH)l.eHCaTOpoB
BKJllOlieHa O,l:lHH pa3 no cxeMe pliC. 157, a, JlPyroif pa3 - no
CXeMe pliC. 157,6. B KaKON CJIYIJae eMKOCTb ooTapeu 6y,ner
Cio.'Ibwe?
109

28.38. KaK H3eHHTCH 3apHJI. n pa3HOCTb nOTeH'IlllaoB oC>-
KJlaJI.OK KOHJI.CHcaTOpa C a (pHC, 158) npH npo6oe KOHHCaTo.pa
C'J.? Bo CKOJIbKO pa3?
28.39. B JleKOTOpOH uenu HMeJICH ytlact'oK, H306pa>KeJlHblfl
H3 pHC. 159. EMKOCTb KOH.'I.eHCaTOpa C = 10 MKc1>, ero aapH.:I,
q = 40 MKK.'1 Ii 3LlC HCTOIlHHKa 8 = 1,0 B, Haihlf pa3HOCTh
nOTeHllllaJIOn Me>KJI.Y TOQKaMH A If B.
0' ) ,. , .
 r, c J "r "J . . Z'
-c: -£I:t- 
C z £t C z c.
Puc. 155
Pnc. 156
,
28.40. Ha YlJaCTKe nenlt (puc. 160) 8 1 = 1,0 B, 8'J. =
= 2,0 B, CPA - CPB = 3,0 B, C 1 = 20 MKc1>, C 2 = 30 MKc1>,
C 3 = 60 MK<1>. HaHTH HanpH>KeHHe Ha l\.a1KJI.OM KOHJI.eHcarope.
oJ
1 Fcc Jj
HH
5)
c .c c fJ
o H H
1 c n z
u y
r T CJ
PHC. 157
PHC. 158
28.41. Ha YllaCTKe nenlf (pltc. 161) 8 1 = 1,0 B, 8 2 =
= 2,0 B, C 1 = 10 MKc1>, C.. = 20 MKc1>. HaihH 330HJI. KOH;J.ell-
caTopa C 2 , 3HaH, liTO 3apHJI. KOHJI.eHCaTOpa C 1 'paBeH ql =
= 10 MKKJI.
PRe. 159
A C, C z C J 8
HHt-Jr-;-
t, l,
Pile. I GO
,( - + 8
-.-!r- U -:'_-
28.42. HaihH 3apSlJI. K3>KJI.0ro KOHJI.eHCaTOp3 B LlenH, nOKa-
3aHHOH H3 pHC, 162.
28.43. OnpeJl.eJIHTb pa3HOCTb nOTeHLlH3JIOB Me>K.ZlY TO'lK3MH
A H B B cxeMe, H30opIDKeHHoH H3 puc, 163.
110

£1 c,  1J
ty- C'yr3 CZ
'z
e
PHC. 161 Puc. 162 Puc. 163
28.44. Onpe)J.eJIHTb pa3HocTb nOTeHlHanOB MeJK.llY TOIlKa-
MH A H B B cxeMe, H306paJKeHHOH Ha pHC. 164.
28.45. Ha cxeMe, H306pa)KeHHOH H3 pHC, 165, 8 = 0,30 KB,
C = 100 n<%>. CHallana 3aMblKaJOT KJlIOIl KI' 3aTeM KJlIOIl KI
pa3MblKalOT H 3aMblKaIOT KJIIOIJ Kz. KaKHe 3apH.IU>I npOTeKYT npH
310M B YKa3aHx CTpeJIKaMH HanpaBneHHHX?

D-I-;;K Z
I'T{R
lC"J... z
PHC. 164
PHe. 165
.46. Onpe)J.eJIHTb, KaKoH Teller 3apH)J. llepe3 HCTOIJHHK
3.il.C H npOBO)J.HHK, KOTOpbIM 3aMblKalOT TOIJKH A H B (CM.
pHC. 163), ecnH C 1 = C 2 = C 8 = CO, C, = 2C o .
3aAaqH K rnaBe VIII
1111.1. J1.Be npOBOASll.Q.He C4JePbl )J.HaMerpaMH D = 5,0 MM
'\\t = 2,5 MM coeAHHeHbl HenpoBOAHI.qeH npY)KHHOH )KeCTKO-
CTblV k = 100 HIM AJlHHoA 1 = 10 CM, O)J.HoA H3 c4Jep co06-
lllalOT 3apH.D. Q. 3aTeM C4JePbl CoeAHlUIlOT TOHKHM npoBoAHHKOM.
PacCToHHHe Me)!{.llY c4JepaMH CTaHOBIiTCH paBHblM L = 10,5 CM.
BaHTH 3apHA Q, ecJIH )J.O C006ll.leHHH 3Toro 3apHAa CHna HaTH-
)f{eHHH npY)KHHbl 61olJ1a paBHa HY.,IO.
VII 1.2. OnpeAenHTb cHny B3aHMO-
AeHcTBHH ABYX )J.HnoneA (pHC. 166),
HaXOAHI.qHXCH H3 paccToHHIIH r > I
Apyr OT APyra.
VII 1.3. .il.Be MeT3JIJIH1leCKHe nna-
CTHHbI nnOll.la.D.blO S = 10 CM 2 YKpen-
JleHbl napanneJIbHO APyr APyr}' Ha pac-
U 9 .... +q
-'I -1/
r
Pi«':. 166
111

CTOHHHH I = 1,0 CM: OAHa - Ha H30nHpYlOllleH nOACTaBKe,
ApyraH - H3 npY)l{llHe JKeCTKOCTblO k = 0,25 HIM (pHC, 167).
li3onHpoBaHHoH n.'IaCTHHe coo6111unH 3apHA q = 3,0 HKJI.
t.IeMY paBHa pa3HOCTb nOTellHanOB MC>K.D.Y nnaCTImaMH?
Vll1.4. OnpeAMHTb, KaKaH 311eprHH 3anaceHa B 6aTapee
KOIlAellcaTopOB, H306pa>KeHHblX lIa pHC. 168.
r
--x-
:5124
L
C Y2t T
PHC. 167
PHC. 168
Pac. 1«39
V1I1.5. .Me>K.D.Y nnacnlH3MH 1 H 2, pacno.'O>KellllblMH Ha
He60nbwoM paCCTOHHHH Apyr OT Apyra, pa3110cTb nOTellH3nOB
l1o = 120B. K 3THM nnaCTHH3M nOAHecnH ABe nnaCTHHbl H3
T3Koe )Ke paCCTOHHHe (pHC. 169). t.IeMY paBHa p33HOCTb nOTeH-
lluanOB Me)KAy.nnacTHHaMH 1 H 4, ecnH nnaCTIfHbl 3 H 4 COelll!'
HHnH npoBoAHHKOM, a 3aTeM npoBoAHHK y6panH?
f
...,
*
. -
PUC. 170
PHC. 171
V1I1.6. .il.Be MeTannHlJeCKHe nnaCTHHbl, HMelOlllue 3apH.llbi
qt H Q2' nOAHeCnH napaJInenbllO Apyr Apyry. OnpeAe.'1J1Tb, KaKue
SapHllbl HaBe.n:YTCH Ha nOBepxHOCTHX nnacnlH.
VIII. 7. .il.Be MeTan.'IHlJeCKHe n.'IaCTHHbl pacnOnOJKeHb[ H8
pacCToHHHH L .n:pyr OT JJ.pyra H coeJJ.JlHeHbl MeJKAY co60ii
npoBoAIIHKOM. OAlla U3 nnaCTIfH 3a3eMneHa. MemAY nnaCTIIHa-
MH Ha pacCToHHIfH 1/3L OT OllHOH H3JfOAIITCH TOHKaH lIenpoBoAH-
maH nneHKa. Ha KOTOpOH paBHoMepHo pacnpe.u.eneH 3apH..1: Q
(pHC. 170). OnpeAMlfTb, KaKoH 3apHA nOTeqeT no npoBoAHHKY,
ecnH nneHKY nepe,llBHHYTb Ha paccTOHHHe 1/3L K ApyroH nna-
CTHHe.
112

VII I. 8. llBa wapHKa C 3apHJlaMII q = ..)0 HI(;J Ka}l(,lJ,blH 3a-
KpenJleHbl Ha Jl8Yx HenpoBO,!J.HIllHX CTep)KHlIX H YKpenJIeHbl
Me>K)J.Y COOOH HenpOBOJlHllleii HHTblO (pHC. 171). CTep)KHH MorYT
BpaJ.U.aTbCSI B nnOCKOCTH pHcYHKa BOKpyr TOqKH 0 6e3 TpeHHH.
JIJIHHa HHTH H crep:Hmeii O.ll.HHaKOB3 H paBHa 1 = 5,0 CM, llla-
pHKI! nOMem.alOT B O,!J.HopO,ilHOe 3JleKTpHIJeCKOe nO.'Ie HanpH>KCH-
HOCTbIO E = 100 KB,'M, HanpanJleHnOe ncpneH,!J.HKY.llHPHO nliTH
B nnOCKOCTH pIlCYUKa. B HeKOTopblH MOMenT BpeMellH HIITb
nepe>Kl1raIOT. npeHe6peraH JlellCTBlieM CHJIbI TH>KeCTII, naHTH
CfJIY HaTH>KeHHH CTep>KHeIi B MOMeHT, KorJ),a 3apHJI.bI HaXOJlHTCSI
Ha 0Jl80H npmfOH C OCbIO BpallleHHH.
f nAB A IX. nOCTOSl"Hbin TOt(
 29. CHJla TOKa. 3aKoli OMa .lI.JlH yqaCTKa u.enH.
COe.ll.HneHHH npOnO.ll.HHKOB
29.1. t.IeMY paBna CIIJla TOKa B npoDoJlIIHKe. eCJlH 3a
1 MHH qCpe3 CelJeHlle npoBo,!J.IIHKa npOTeKaeT 30 MKJI 3JIeKT-
pHlIecTBa?
29.2. Ha KOH,n:eHcaTop nepeMcnnoH eMKOCTH nOJlaHO HanpSl-
>KCnHe U = 100 B. KaKoH CHJIbI TOK TelIeT no npoBo,!J.aM, eCJIH
eMKOCTb KOHJ),encaTopa MeHHIOT paBHoMepHo co CKOpOCTbIO
l:1C / M = 10 H<I>/C?
2913. TIo npoDo;J.Y TeqeT TOK CHJIOH I = lOA. HaHTH Maccy
3J1eKTpOHOB, npOXO,!J.HIllHX Qepe3 nonepe'lUoe ccqeWte 3TOro
npOBOJla 3a BpeMSI t = 1,0 IJ.
29.4. 3.'ICKTpHlIecKaH JJ.enb COCTOHT H3 .noyx nOCJleJlOBa-
TeJlbHO COeJlHHeHHbIX KYCKOB Me.llHOrO npOBOJla ce'leHIIHMH
SI = 2,0 trIM! H S2 = 3,0 MM 2 . CpaBHHTb CKOpOCTH ynopSl)J.o-
IICHHoro JlBH>KeHUH 3JIeKTpOHoB B npOBO.ll.ax.
29.5. no npOBOJlHHKY TeIICT TOK cHnoH 0,20 A, pa3HOCTb
nOTeHJJ.HaJlOB Ha KOHuax npoBo.aHHKa 7,0 B. t.IeMY paBHo co-
npOTIIBJleHlle npOBOJlHHKa?
29.6. Onpc;J.eJmTb nnOTHOCTb TOKa, TeKYlllero no MOTKY
TonKo", MeJ1,HOH npOBOJlOKH JlJlHHOH 1 = 10M, Ha KOTOpblH nOJla-
HO HanpH>KCHHe U = 17 MB.
29.7. OnpeJlenHTb conpoTHBneHHe MOTKa CTaJlbHOH npoBo-
JlOKH JlHaMeTpO\f d = 1,0 MM, Macca KOTOporo m = 300 r.
29.8. HHXpofoBaH CnlIpaJib HarpeBaTeJIbHOrO npHoopa
J),OJI>Klla Ht.feTb cOnpOTHBJIeHHe R = 30 OM npH TeMnepsType
HaKa.la t = 900° C. CKOJIbKO MeTpOB npOBOJIOKH HaJlO B3HTb
JlJIH H3rOTOBJIeHHH Cm-lpaJlH, eCJIH nJlOUI.a.D.b nOnepeqHOrO celIe-
BUH npOBOJIOKH S = 0.30 MM 2 ?
113

29.9. BOJIb4JpaMoBaH HHTb 9JleKTpHqecKoH JIaMnI>l npHTeM-
nepaType t 1 = 2000" C mleer cOnpOTHBJIeHHe RI = 204 OM.
Onpe.n.eJIHTb ee conpOTHBJIeHHe npH TeMnepaType t l = 20° C.
29. to. ]1.0 KaKoH TeMnepaTypbl HarpeBaercH HHxpoMoBaSi
9JIeKTporpeJIKa, eCJIH 1f3BeCTHO, 1fT0 TOK, npoxo.n.HJ.I.J.HH qepea
OGMOTKY B MOMeHT ee BKJIIOqeHHH (t l = 20° C), B n = 1,09 pa-
sa npeBblWaeT pa60qHH TOK?
29.11. KaKoe KOJIHqecTBO JIaMnOqeK, paccIIHTaHHblx Ha
6,3 B, Ha.n.o B3f1Tb AJIH e;rOqHOH 3JIeKTpOrHpJIHIIJI,bl, 1fTOObI. ee
MO>KHO 6b1JIO BKJIIOqHTb B ropo.n.CKYIO OCBeTHTeJIbHYIO CeTb C Ha-
npIDKeHHeM 220 B? .
29.12. ]1.yroBoH 4x>Hapb, Tpe6YIOIllHH AJIH CBoero nHTaHHH
HanpHJKeHHe U 0 = 40 B H CHJIY TOKa J 0 = 10 A, BKJIIOqeH
B CeTb C HanpHJKeHHeM U = 120 B qepe3 peocTaT, H3fOTOBJIeH-
HhIH H3 KOHcTaHTaHoBoH npOBOJIOKH CeqeHHeM S = 2,0 MM 2 .
Onpe.n.eJIHTb cOnpOTHBJIeHHe peocTaTa H .n.JIHHY npOBOJIOKH, tie-
o(SXO.n.HMOH AJIH ero H3fOTOBJIeHHH.
29.13. )l<eJIeaHblH CTep)f{eHb coe.n.HHeH nOCJIe.n.OBaTeJIbHO C
yrOJIbHbIM TaKoH )f{e TOJIIllHHbI:. TIpH KaKOM COOTHoweHHH HX
AJIHH cOnpOTHBJIeHHe TaKoH KOM6HHaLlHH He 3aBHCHT OT TeM-
nepaTypbl?
29.14. B CeTb C HanpHJKeHHeM U = 24 B no.n.KJIIOqHJIH .n.Ba
nOCJIe.n.OBaTeJIbHO coe.n.lfHeHHbIX peaHCTopa. TIpH 3TOM CHJIa
TOKa CTaJIa paBHOH J I = 0,60 A. Kor.n.a peaHCTopbl no.n.KJIIO-
IIUJIH napaJIJIeJIbHO, CYMMapHaH CHJIa TOKa CTaJIa paBHoH J:I =
= 3,2 A. Onpe.zr.eJIHTb conpOTHBJIeHHH peaHcTopoB.
29.15. TIpH nOCJIe.n.OBaTeJIbHOM no.n.KJIIOqeHHH K CeTH JJ.BYX
npoBo.n.HHKOB CHJIa TOKa B 6,25 pa3a MeHbIIre, qeM npH napaJI-
leJIbHOM no.n.KmoqeHHH 3THX npoBo.n.HHKOB. Bo CKOJIbKO pa3
'TJJHqaIOTCH conpOTHBJIeHkH npoBo.n.HHKOB?
29.16. 3JIeKTpHqeCKaH llenb COCTaBJIeHa H3 Tpex npoBo.n.HH-
KOB o.n.HHaKoBoH AJIHHhI H c.n.eJIaHHblX H3 o.n.Horo MaTepHaJIa.
TIpoBO.n.HHK CeqeHHeM SI = 3,0 ml coe.n.HHeH nOCJIe.n.OBaTeJIb-
HO C napaJIJIeJIbHO coe.n.HHeHHblMH npoBo.n.HHKaMH CeqeHHHMH
SI = 2,0 MM 1 H S3 = 4,0 I. Pa3HocTb nOTeHLlHa.10B Ha KOH-
nax LlenH U = 12 B. CHJIa TOKa, TeKym.ero qepea npoBO.II.HlfK
CeqeHHeM Sit paBHa /1 = 1,0 A. Onpe.n.eJIHTb conpOTHBJIeHUe
KaJK.n.oro npOBo.n.HHKa, CHJIY TOKa, TeKym.ero qepea KaJKJI,blH
npOBo.n.HHK, H na.n.eHHe HanpH)f{eHHH Ha KIDK.n.OM npoBo.n.HHKe.
29.17. KaKHe cOnpOTHBJIeHHH peaHcropoB MOJKHO -noJIY-
qHTb, HMeH B CBoeM paCnOpHJKeHHH Tplf pe3Hcropa cOnpOTHBJIe-
HlfeM 60 OM KaJK,ll.b1H?
29.18. KaK H3MeHHTCH nOKa3aHHH Bo.1bTMeTpa npH nepe-
Mew.eHHH nOJI3YHK3 peocTaTa BnpaBO (PHC. 172)?
114

29.19. OnpeAeJIHTb conpOTIiBJIeHlle peocraTa, nOO130.'151IO"
mero YMeHbillliTb TOK B n pa3 (pIIC. 173).
29.20. nOCTpOIiTb rpaq>HK 3aBIICIi!\IOCTH o61l1.ero conpoTIIB-
.'1eHHH R J.{enll OT oot!J>OTIiBneHHH , npaBoii lJaCTH peocTaTa
(pnc. 174, a-e).

Puc. 172

P.IC. 173
29.21. B K3KHX npeAe.'1ax M01KHO perYJIHpOBaTb HanpH1Ke-
HHe B CXCMax H3 pHC. 175, a. 6.
29.22. Ha BXOA J.{enO'lKH H3 pe3HCTopoB, ncr<a3aHlioH Ha
pHC. 176, a, 6 noaHo :aanpH1Kelilie U o. Onpe;J.eJllITb H3npH1KeHlie
Ha BblXOAe. KaKoe HanpH1KeHHe 6YJJ.eT lIa BXO;J.e, ec.nll H<l BbI-
XOA nOAaTb HanpH1KeHHe U 01
aj
 r-<>
K
6} 6)
LgJ
K
Pue. 174
29.23, Onpe;J.e.'1HTb conpOTlIBJIeliHe J.{eneii, nOKa33HHblX Ha
pHC. 177, a-;:,
29.24. Onpc;J.enHTb COnpOTlIBJlennC R npoBo.'IOtlllbiX eeTOK
(pHC. 178, a-e). COnpOTlIBJlCHHe ha1K)).oro 31:1eHa paello r.
t' & 6 J
U, u.
l!. D
PHe. 175
/1)
/J
 Q
5) R R /J

PHe. 176
29,25. KOf)).a na K.'1et;IMbl AB (pHC. 179) nO.i].aJlH HanpH)Ke-
Jme, 3apHA lIa KOH)I,eHCaTOpe C OKa33J1CH panHblM UYJlIO. Onpe-
AemlTb conpOTHBJleHHe pe:mcTOpa R:J:'
29.26. 3neKTpH'leCK3H WIHTKa nOAKJllOlJeHa K ceTH C H3-
npSl1KeHUeM U 0 = 220 B C nOMOblO npoBoAoB, II\fCIOIllHX co-
lla
- -

"'RR 
R R R
t.)R

Puc. 177
npOTHBJIeHHe r = 5,0 OM, npH 3TOM n8npH1KeHHe Ha nJIIfTKe
paBIIO VI = 210 B. t.JeMY 6y.ne-r paBHO Hanp5u«eHHe Ha nmlT-
Ke, eCJIH K neu no.nKJIIOHTb napaJIJIeJIbHO TaKYIO }f{e nJIHTKY?
29.27. Onpe.neJIHTb, KaKoii CHJIbI TOK H.neT qepe3 aMnepMeTp
(pHC. IBO), eC.'!H V = 15 B, Rl = 5,0 OM, R, = 10 OM, Ra =
= 10 OM, R. = 5,0 OM.
aJ 61 @ 8JBHYT P eHHHMcon p O'1'HBJIe-
;sf A HHeM aMnepMeTpa npeHe-
6peQb.
29.28. .IDmepMeTp co-
npOTHBJIeHHeM r = 100M
lJ DJ eJ paCCIJHTaH Ha CHJIY TQKa
fW   10 = 30 MA. KaKHe )l.06a-
BOIJHble COnpOTHBJIeHHH RI'
R 2' R a, R. Ha.no B3S1Tb,
'ITOC)bI MO)f{UO 6b1JIO H3Me-
pSlTb nanpH)KeHHe U B Qe-
Tblpex npe.n.enax: 3, IS, 75
H 150 B?
29.29. TIapaJIJIeJIbHO a:o.mepMcTpy, HMelOIU.eMY conpoTHB-
JIeHHe r = 0,020 OM, nKJIlOIJeH Me.llHbIii npoBO.nHHK )l.JIIIHOH
1 = 20 CM H ceqemleM S =3,4 MM 2 . Onpe.lleJIHTb CHJIY TOKa B
Llenlf, eCJIH 8;o,mepMeTp nOKa3bIBaeT 1 A = 0,30 A.
29.30. Onpe.n.enHTb nOKa3aHHSI BOJIbTMeTpOB, nO.!l.KJIIOIJeU-
HbIxKnoTeHLlHOMeTpy conpOTHBJIeHHeM R = 100OM(pHc.IBI).
HanpH1KeHHe V = 60 B. TIo.n3YHOK nOTeIlLlHOMeTpa Haxo.nHT-
PHe. 178
Am
Bm Rx
PHe 179
R R

[H '
U R
_ v,
Pue 180
Puc. 181
116

CSI nOCepe.ll.HUe. ConpOTlIBJIe-
BliSl BOJIbTMeTpOB rl = 60 Gr.f.
r s = 40 OM.
29,31. Bo.'1bTMeTp, BliJIIO-
qeHHblH nOCJI€.lI.OnaTeJIbUO C co-
npOTIIBJleHlleM R 1 = 70 Gr.'.
nOha3b1BaCT H3npSUKeHlle VI =
= 100 B npH nanpSUKemHl n U.ClIl1 V = 240 D. 41'0 nOKaJKeT
BOJIbTMeTp, ecJIH cro BK.rIIO'lIlTb nOC'IC.lI.OBaTc.1bIlO C COnpOTlIB-
JICuneM R 2 = 35 ROM B TY )liC CCTb?
29.32.. Ha pIlC, 182, a, 6 11306paJKCHbl cxe:o.ll>1 .lI.JISI H3l\fCpe-
I1IfH conponm.1eHIHI. KaK)'IO 113 nllx CJICJl.YCT npe.ll.1I0'leCTb, .Kor-
.ita H3MepSlC!lfOe conpOTIIB.'leHIIe nemmo? KOr.!l3 OHO MaJIO?

PIIC. 182
 30. 3aKoH Ol\la .lI.JUI 3all1KIIYToH LlenH
30.1. K 6aTapeHKe C 3ll.C 4,5 B If BHYTPCHHIIM COnpOTlIB-
JlCHHCM I,D OM nO.ll.KJlIO'lIlJlIf pe311CTOp conpOTHBJIeHHCM
8.0 Gr... KaKoii CHJIbi TOK TC'le-r B Llenll? 4eMY paono nanp$l-
JKeHHe Ha BUelliHeM conpOTIIBJICHIIH?
30.2. B LlenH, COCTOSll1l.eii 113 HCTOIJHIIKa TOKa c 3ll.C 8 =
= 6.0 B, BHYTpenHHM cOnpOTIIBJleHHeM r = 2,0 OM H BHelllHHM
COnpOTHBJIeHHCr.r, H.lI.eT TOK CHJIOH 11 = 1,0 A. KaKoil CHJIbi TOK
nOH.lI.eT no LlcnH. eCJIII BHCllIHce conpOTHBJICIlHe YBeJIH'UiTb B
n = 2,0 pa3a?
30.3. K 6aTapeHKe C 3ll.C 8 = 3,0 B nO.ll.KJIIO'lIlJIH pe-
3I1CTOj> cOnpOTHBJIeHIfCM R = 20 01\1. na.ll.elme HanpHJKCIUlH Ha
pe3HCTope OKa3aJIOCb V = 2,0 B. OnpeJl.emlTb TOK KOPOT-
Koro 3aMblKaHlUi.
30.4. Kor.na K HCTOq»KY TOKa nO,!J.KJIIOqIlJIH pC3HCrop con.
POTlIB.rlcHueM RI = 5,0 UM. CIIJla TOKa CTaJla 11 = 1,0 A, a
KOr.ll.a nO.ll.KJlIOlJlfJm pe3l1CTCp conpOTHBJIeUl!eM R:. = 15 OM,
TO 1 2 = 0,50 A. Ofc.lI.eJIlITb 3D.C IICTO'lHIIKa TOKa Hero
BHYTpCHHee conpOTHBJICIlHe.
30.5. nOCTpOI!Tb Jl.JIH nenl!, COCTOHl1l.eH 113 IfCTOIUlHKa TOlia
C 3LLC 8, BHYTpeHHm.1 conpOTHBJIClmeM r H 13HelllHIIM co-
npOTHBJICHHe:\1 R, rpaHKH 3aBHCHMOCTeii TOKa B Llcnll H Hanpn-
lKeHHSI Ha 3aJKIIMax IICTO'lHIIKa OT BHelllHero conpOTIIBJIeHHSI.
30.6. Bo CKOJIbKO pa3 Buellince cOnpOTIIBJICHlle IIcrollHIIKa
TOKa ,!J.OJI>KHO 6blTb 60JIbUie BHYTpeuncro. tIT06b1 np" paCGeTaX
(npeue6pcraSi BIIYTpellHI!M conpoTHB1eHHeM HCTO'lHHKa) 01llH6-
Ka He npeBbllllaJla 1,0%.
30.7. I..J.enb COCTOHT H3 aKKYMYJIHTOpa C BHYTpeHHHM co-
npOTHBJICHHeM r = 5.0 OM H HarpY3KII R = 15 OM. ITpH no:!.-
117

JUIlOqeHlH1 K HarpY3Ke HeKOTOpOrO pe3J1CTOpa napa.'1JIenbHO, a
3aTeM nocneAOBaTeJ1bHO TOK lIepe3 3TOT pe3HCTOp lie MeHHeT-
CH. 1..JeMY paBIIO conpOTIIBJleHlle pe3l1cTopa?
30.8. K reHepaTOpy nO.!J.KJllOlIeHO n = 100 JlaMn, CoeAH.
HeHHblX napanJle.'1bHO, HMelO111HX COnnOTJlBneHHe R = 1,2 K1
ha)lo..1.aS1. HanpH)lo.(,lIl1e Ha .1amax U = 220 B. BHYTpellHee co-
npoTIID.'ICHHe rellepaTopa r = 6,0 OM. OnpeAenHTb 3LlC reHe-
paTOpa.
30.9. OnpCAeJlIITb naAelme HanpSlJKeHIIH Ha pe3HcTopax 11
IICTOIJIIHKE' TOKa, a T'U{>Ke CHJlbI TOKon lIepe3 HHX, eCJI}I
Rl = 6,0 OM, R 2 = 12 OM, R3 = 5,0 OM, r = 3-,0 (».1, <1 =
12 B (pnc. 183).
R,
H, 
R, £r
',r
Rz
£, r f,r
PIIC. 183 PHC 184 PHC. 185
30.10. KaKoBa Ao.'1>KHa 6blTb 3LlC 6aTapeH B CxeMe, 1130-
6paJKeHHOH Ha pHC. 184, IJTOObI HanpSlJKeHHOCTb nonH B nno-
CKOM KOIIAeHcaTope 6bIna E.= 2,0 KB/M? ConpoTHBnCHlle
r = Rl = R'I.' PaCCToHIIHe Me>K;ty nnaCTIIHBMH KOH.!I.eHCaTOpa
d = 5,0 MM.
30.11. KorAa napanJlenbHO KOHAeHcaTopy, nOAKJllOlIellHOMY
K 3aJKIIMaM 6aTapeH, nOAKJlIOHnH pe3HCTOp conpoTHB.'1eHHeM
R = 15 OM, 3apSiA Ha KOIIJ].eHcaTOpe YMeHblllllncSi B n =
= 1,2 pa3a. t.JeMY paBHO BHYTpeHHee conpoTHBneHlle 6aTa-
peH)
30.12. OnpeAe.'1HTb 3apHJJ. Ha KOHAellcaTope eMKOCTblO
C = 1,0 MKcI> (pIlC. 185). 3.l1.C IICTmmllK3 TOKa <1 = 6,0 B,
BHYTpellHee COnpOTJIDJleUHC r = 5,0 OM, Rl = Rz = R3 =
= 20 OM.
30.13. Onpe.Zle.1HTb 3apH.Zl Ha KOH.ZleHeaTOpe C = 15 MKcI>
B exeMe, nOKa3aHHoii Ha pHC. 186. Rl = R. = R. = 12 OM,
Rz = Rr. = 18 OM, 3LlC HCTOqHHKa TOKa 8 = 7,5 B, BHY-
TpeHHce eonpOTliBneHlle r = 1,0 OM.
30.14. OnpeJl.eJlIITb, KaKoii 3apH;t npoTeqeT qepe3 conpo-
THBJleHlle R 2 nocJle pa3\fbIKaHlfH KJIlOqa K (pHe. 187), ecnll
Rl = R'I. = Rs = RI = R = 20 OM, 8 = 100 B, r = 10 OM,
C = 10 Mh<!>.
liB

30.15. Onpe)J.eJlHTb p33HOCTb nOTeHl.{H3nOB Me)f{)J.Y TOIIK3-
alH A H B B LlenH, H306pIDKeHHoH H3 pHC. 188.
30.16. Onpe)J.eJIHTb p33HOCTb nOTeHLlH3JIOB Me2K,lJ.Y TOIJKaMH
A H B B uenH, H300p3JKeHHOii H3 pHC. 189.
30.17. I1CTOIIHHK TOK3 C 311C 8 = 3,0 B H BHYTPCHHHM
conpOTHBneHHeM , = 5,0 OM nO)J.KJIIOIIHJIH K KJIeMMaM A H 8
HeKOTOporo YCTPOHCTB3, npHlleN DJIIOC HCTOIIHHK3 npHcoe)J.H-
HIIJIH K KJIeMftle 8, a "IHHYC - K KJIeIle A. DpH 3TOM lIepe3
@ C, A C z
r''
R, C R.
t,r f.,r e,r
Puc. 186 PIIC. 187 Puc. 188
HCTOIIHHK B H3np3BJIeHHU OT KJIeMMbI A K KneMMe 8 nOWeJl TOK
CHJIOH 11 = 1,0 A. Kor)J.3 nJIIOC HCTOIIHHK3 nOKJIIOIIHJIH K KJIeM-
Me 8, 3 MHHYC - K KJIep.1Me A, TO lIepe3 HCTOIIHHK nOllIeJI TOK
I Ii = 0,60 A B H3np3BJIeHHH OT A K B. OnpeJJ.eJlHTb n3npHJKeHHe
Ha HCTOIJHHKe B nepBoM H BTOpOM CJIYIJaHX.
2C A C ,r,
T l/ R 4 1 ''i AtJ-
ZR c 2R .
8 r I n l
&z.'Z
,R
Puc. 189 PIIC. 190 Puc. 191
30.18. Onpc.J.CJIIlTb 311C If BHYTpeHHee conpOTHBJleHHe
YCTpoikTB3, onllc3HIIoro B 33)J.311e 30.17,
30.19. Onpe.n.e..1HTb p33HOCTb nOTeHLlH3.'10B Me)K)J.Y TOIIK3-
MH A H 8 (pHC. 190). 311C HCTOIIIIHKOB TOKa 8 1 = 1,0 B
H 8'1. = 1,3 B, BHYTpeHHHe conpOTHBJleHIIH '1 = 3,0 0:.1 H
':a = 5,0 <»'1, BllelliHee ConpOTHBJIeHHe R = 7,0 I.
30.20. AKKYMynHTOp C BHYTpeHHHM conpOTHB.TleHHeM r =
= 2,0 OM H 311C 8 = 3,5 B n0]1.33pIDKaeTCB OT ceTH C H3npB-
>KeHHeM U = 12 B. K3Koe Orp3HHII1IB31OIllee COnpOTHBJIeHHe
R H3)J.O nOCTaBHTb, IJT06b1 CH.13 TOKa B LlenH He npeBbUU8JI3
119
...- -

1= 1,0 A? KaKoe HanpH1KeUHe VI 6y.neT npH 3TON Ha KJ1eM-
AffiX aKKYMynTOpa?
30.21. KaKoe conpOTHBncHue R Ha;J.O no.nKJIJOlJ1iTb Me1K.nv
TO'lKaMH A II B, 'ITo6bl TOK lJepe3 6aTapcJO C 3D.C 8" = 4,013
Ii BIIYTpeHHIiM conpOTliBJIeHlieM '7. = 3,0 OM 01,1.1 paBeH HY-
JIJO (pliC. 191)? 8 1 = 6,0 B, '1 = '2'
30.22. D.B3 HCTO'lHUKa TOKa C 3D.C 8 1 H 8 1 H BHYTpeHHH-
Mil conpOTHBJIeHHHMU '1 li '" Coe.nHIICIIbl napan;ICJIbIlO. Onpe-
.nenUTb 311C no.nYlJeHHoro HCTO'lHHKa TOKa (HanpSl1KeHUe Ha
KneMMax liCTOIJHliKOB). KaKOU Clinbl TOK TelJeT lJepe3 con po-
THBneliHe R, ecJ.1U ero no.nKJ1JOllliTb K KJIeMMaM liCTO'lHHKOB?
30.23. Onpe.ne.'1HTb 3LlC Tpex napaJIJIeJIbHO coe.nHHeHHblX
HCTOIlHUKOD TOKa. -
30,24. TpH o.nUHaKOBblX ooTapeli C BHYTpeHHHM conpOTHB-
neHHeM' = 6,0 OM 3aMKHYJIH, O.nHH pa3 Coe,!J.HHliB napaJlJIe.JIb-
HO, a .nPyroH pa3 - nOCJIe.noeaTeJIblIO Ha HeKOTopoe conpo-
THBJIeHHe. npli 3TOM Clina TOKa B o6<mx cnYllax 6b1JIa o.nu-
HaKOBa. Onpe.neJlHTb BHeUIHee conpOTIiB.'1eHHe.
30.25. HecKo.nbKo O,llHHaKOBblX HCTOIJHHKOB TOKa coe.nu-
HeHbI nOCJIe,!lOBaTenbHO Ii saMKHyrDI HaKopOTKo. Onpe.neJlHTb
HanpSl1KeHHe Ha HCTOtlIlHKe TOKa.
30.26. TpIl HCTOtlHIIKa TOKa C 3LlC 8 1 = 1,0 B, 8 z =
= 2,0 B li 8 3 = 3,0 B U BHYTpeHHHMu cOnpOTHBJIeHHHMII
COOTBeTCTBeHHO'1 = 1,0 OM, '2 = 2,0 OM H '3 = 3,0 OM coe-
AHlIeHbl noc.'1e.noBaTeJIbHO H 3aMKHYTbI HaKopOTKO. Onpe.ne-
JIHTb cHny TOKa B llenH Ii na.nCHHe lIanpHeHIISI Ha Ka1K,llOM H3
HCTO'lHHKOB. t.JeMY paBHbI cuna TOKa H na.neHHe HanpH1KeHHSJ,
ecmr Bee Tpll HCTOIJHHKa HMelOT o.nHHaKOBYJO 3LlC, paBHYJO
2,0 B?
30.27. D.aHb[ .nBa HCTOtlHJlKa TOKa c 3LlC 8 1 = 4,0 B H
BHYTpeHlIliM conpOTIrBneHHeM '1 = 2,0 OM H S" = 5,0 B,
'" = 4,0 OM. npH KaKOM BHel11HeM conpOTHBJIeHHH TOK lJepe3
STO conpOTHB.'1eHHe He 3aBJICHT OT cnocooa coe,llHHeHH 3JIe-
MeIlTOB? KaKYJO MaKCHM3.'1bHYJO CHJIY TOKa M01KHO nO.IIYtlUTb
tlepC3 pe3HCTOp conpOTHBJleHUeM R = 12 OM?
30.28. EMKOCTb O.nHOro aKKYMynSlTOpa 50 A . Il. Onpe.ne-
JIUT!> eMKOCTb qeTblpeX TaKHX 8KKYMymnopoB, BKJIJOqeHHX:
a) nOCJIe,llCBaTe.'1bHO; 6) napaJIJIeJIbHo.
30.29. D.Ba aKKYM)'JIHTOpa eMr<OCTbJO 60 U 65 A . tl Coe.nH-
HeHbl nocne;J.OBaTeJlbHO. Onpe.n.eJIHTb eMKOCTb TaKOH 6aT8pe1l
aKK} My.'1HTOpOB.
30.30. B Llenu, nOK83aHHOH Ha pHC. 192, TOK qepe3 raJlb-
saHOMeTp He TelJeT. Onpe.neJlHTb, qeMY paBHO conpOTlrBJleHHe
Rz. R = 9,0 OM, 8 1 = 15 B, '1 = 2,8 OM, 8" = 2,7 B.
J20

30.31. 3apH)1. Ha KOH,neHcaTope C paBeH HYJIIO. KaK no,n-
'UOl.leH JlCTOtj]IHK TOKa 8 2 H qeMY paBHa ero 3D.C? R 1 =
-= 12 OM, R. = 6,0 Ct.1, Ra = 3,0 Ct.1, Rc = 15 cn..1, 8 1 =
5,0 B, T 1 = 1,0 Ct.1 (pHC. 193).
30.32. CxeMa COCTaBJIena H3 celom O)1.lfIlaKOBbiX IfCTO'lHH-
!tOB TOKa C 31I.C 8 = 4,0 B If BHYTpeHHIIM cOnpOTHBJIeHHeM
 R1(
£.1
R R
£/rr,
&"r;
W$t9
a 6 6 c:
PHC. 192
PIIC. 193
PHC. 194
,= 3.0 OM, qeTblpex o,nHHaKOBbiX KOH)1.eHCaTOpoB eMKOCTblO
C = 100 n<1> H conpOTHBJIeHHH R = 1,0 OM. Onpe)1.eJIHTb 3a-
I pH,lllla BepxHeif f!JIaCTHHe Ka>l<,llorO KOH,neHcaTopa (pHe. 194).
 31. Pa60Ta H MOW.HOCTb TOKa
31.1. KaKYIO pa60TY npOH3BeJI 3JIeKTpHqeCKHH TOK, eCJlH
lIepe3 CCqeHHe npOBO)1.HHKa npolIIeJI 3apH)1. q = 1,5 K.n II na-
AeHHe HanpH>I<eHHH H8 npOBO;J.IUIKe U = 2,0 B?
31.2. 3a BpeMH t = 10 C IJepe3 npoBo)1.HHK, na)1.eHHe HanpH-
>KenHH lIa KOTOpOll1 U = 12 B, npolIIeJI 3apH,ll q = 24 KJI. On-
pe,aeJllfTb pa6oTy, cOBeplIIeHH}'IO TOKOM. MOUlHOCTb TOh, co-
OnIBJIeHHe npoBo,nHHKa.
31.3. DOCTpOHTb rpa«l>HKH 3aBHcHMoCTeH MOHOCTH, BbI-
ie.lrHeMoH Ha cOnpOTHBJIeHHH: a) OT HanpH)f{eHHH npH nOCTO-
BIIHOM eoripoTHBJIeHHH; 6) OT .conpOTlIBJIeHHH npH nOCTOHHHOM
BanpH>I<eHIIII. KaK Ha,no H3MeHTb conpOTHBJIeHHe, qTo6bl 3a-
8 _I1MOCTb MO1I0eTH OT HanpJl>l<eHHH CSb1JIa JIHHeHHoii?
31.4. Ha O)1.HOH JIaMnOIJKe HanHcaHO 127 B, 60 BT, Ha BTO-
M" - 220 B, 60 BT. KaKaH MOHOCTb 6Y)1.eT Bbl;J.eJIHTbCH B
I\a)f{!J.OH 113 JIaMnOlJeK, eCJIH nepBYIO BCTaBHTb B eeTb e HanpH-
HHeM 220 B, a BTOp}'lO - B ceTb C HanpH>I<eHHeM 127 B?
31.5. LIBe JIaMnOIJKH eOnpOTIiBJIeHHHMH R 1 = 180 OM H
P = 360 0\1 no,nKJIIOIJHJIH napaJIJIeJIHIO KeeTH C )fanpH>I<e-
reM U = 120 B. KaKaH MOll.lHOCTb BbilleJIHeTCH B Ka)f{)l.oH H3
o\ctMnOlJeK? KaKaH 6y)1.e:I' Bbl)1.eJlJlTbCH MOlllHOCTb, t:CJlH JIaM-
( KH nO)1.KJI.IOIJHTb nOCJIe.lloBaTeJlbHo?
121

....
31.6. neperopeBlIIyro CnHpaJIb 9JIeKTpHQeCKoro YTIOra
MOIIJ.HOCTblO 300 BT YKOpOTHJIH Ha 1/&. KaKOH CTaJIa npH 3TO
ero MOID.HOCTb?
31.7. nOJIOBHHY HarpeBaTeJIbHOH CnHpaJIH, nO,llK.mOllelI-
HOH K ceTH, onYCTHJIH B BO,ny. KaK H3MeHHJIaCb npH 3TOM MOil{-
HOCTb, BbI;J.eJ1HeMaH BeeH CnHpaJl'blO? llaCTblO, norpy:meHHOH
B BO,ny? OTKpbITOH 1laCTbIO?
31.A. npH60p HMeeT TPH HarpeBaTeJ1bHble CnHpaJIH no
120 01.1 Ka)KJ\.aH. KaKHe MOIIlHOCTH MO:mHO nOJIYIlHTb, HCnOJIb-
3YH pa3JIHIJHble COC,'J.HHeHHH CnHpaJIeH? HanpH:meHHe B cen!
120 B.
31.9. KaKoe ,nonOJIHHTeJ1bHOe cOnpOTIfBJIeHHe Ha,110 nOCTa-
BHTb. K JIaMne MOID.HOCTblO P = 300 BT, paCClffiTaHIfOH na Ha.
npH:meHHe V = 110 B, QTo6b1 npH HanpH:meHHH B CeTH VI =
= 127 B JIama pa6OT2JIa B HOpMaJIbHOM pe)KHMe?
31.10. KaKoe HanpH:meHHe lIa,no nOMep:mHBaTb 13 CfTH II
K2KaH Mow.iIocTb ,llOJIJKHa nOTpe6JIHTbCH, QTo6b1 nHTaTb TOKO
n = 30 JIaMn MOID.HOCTbIO no P = 60 BT, coe,llHHeHHblX na-
paJIJIeJIbHO, npH HanpSUKeHHH V = 120 B, ecJIH conpOTHB.'Ie-
HHe npoBo,noB, no,ltBO,llSIIIJ.HX TOK K JIaMnaM, r = 4,0 OM? Ka.
KOB Ko3<!xPHI.1:HeHT nOJIe3HOrO ,lleHCTBHH .9JIeKTpOCfTH?
. 31.11. 3neKTpODJIHTKa MOIIJ.HOCTbIO P = 1,0 KBT, pac-
CIJHTaHHaH Ha HanpSUKeHHe V = 120 B, no,nKJIlOlleH8 B ceTb C
HanpH:meHHeM VI = 127 B. ConpOTHBJIeHHe nO,llBO,llSIIIJ.HX
npoBo,noB r = 4,0 OM. KaKaH MOID.HOCTb BbI,neJIHeTCH nJIUT-
KoA? napaJIneJIbHO K nJIHTKe no,nKJIlOIlHJIH BTOp}'lO T8K}'IO :me.
KaKaH MOIIJ.HOCTb CTaJIa BbI,lleJIHTbCH .llBYMH nJIHTKaMH?
31.12. B CeTb C HanpH>KeHHeM V = 220 B C nOMOIIJ.blO npo-
BO,nOB COnpOTHBJIeHHeM r = 5,0 OM no,nK,lllOQeH peocTaT. Dpn
KaKoH CHJIe TOKa Ha peOCTare BbI,'].eJIHeTCH TaKaH JKe MOID.HOCTb,
KaK H npH CHJIe TOKa /1 = 2,0 A? KaKaH llaCTb pacxOJI:yer.mii
.9HeprHH BbI,neJIHeTCH B peocTare B TOM H ,npyroM CJIyqaHx?
31.13. /t10ID.HOCTb, BbI,neJIHeMaH Ha pe3HCTOpe, no,nKJIlOtJeH-
HOM K HCTOIlHHKY TOKa c 31I.C 8 = 3,0 B H BH)'TpeHHHM conpo-
TIIBJIeHlleM r = 1,0 OM, paBHa P = 2,0 BT. Onpe,lleJIHTb ClfilY
TOKa B u.enH. .
31.14. 31I.C HCTOIlHHKa TOKa II = 2,0 B, BHYTpeHHee co-
npOTHBJIeHHe r = 1,0 OM. Onpe,neJIHTb conpoTHB.'leHHe BHew-
HeH [{enH, eCJIH B Heii BbI)I.eJIHeTCH MOIIJ.HOCTb P = 0,75 BT,
31.15. KaKoe KOJIHQeCTBO .9HeprHH 3anaCeHO B aKKYMYJUI-
TOpe eMKOCTLIO 50 A . q, HMelOw.eM 31I.C 8 = 12 B?
31.16. MCTOQHHK TOKa C 31I.C II H BH)'TpeHHID.f conpoTHB-
JIeHHeM r 3aMKH)'T Ha peocTaT. nocrpOHTb rpa4>HKH 3aBUCU-
MocreA MOIIlHOCTH, BbI)I.eJIHeMOA HCTOqHHKOM; MOW.HOCTH, Bbl-
122

.u.eJlSle.IOH Bo BllenIHeii LlenH, Ko34xPJIJ-UleIlTa nO.'1e:3II0ro .neHCT.
BIfS1 HCTOtJlIHKa OT CIIJIbi TOKa B LlenH. TIpH KaKOH CIIJIe TOKa
-.10111HOCTb, BblJJ.eJIS1eMaJi BO BHenIHeH LlenH, 6YJJ.eT nallOOJIbllIeii?
31.17. K aKKYMY.'lSlTOpHOH 6aTapee C DH}TpeHHIIM con po-
'I"IIB.leHHeM r nOJJ.KJIlOtJeH pe3HcTop conpoTHB.leHHeM R. Co
BreMeHeM 6aTapeJi caJJ.IITCSl - YMeHbllIaeTCJI ee 31IC. nOCTpO-
IITb rpa4>HKII 3aBHcIIMOCTeH: MOlllHOCTH, BblJJ.eJIS1eMOH HCTO'!-
HHKOM, MOllllIOCTH, BblJJ.eJIS1eMOH BO BHeuilieH Llem-l, K03<f>cPH-
LlHeHTa nOJIe3110rO JJ.eiicTBIiSl HCTOIJHHKa OT 31IC HCTotJlIHKa
iOKa.
31.18. I1CTOIJHHK TOKa C 311C c8 H BHYTpeHHIIM conpOTIIB-
neHHe:l1 r 3aMKHYT na peocTaT. nOCTpOHTb rpatPHKH 3aBllCII-
MocTeH: CHnb! roKa, lIanpJl:H<ellllSl, MOlllHOCTH DO DHelIIueH Lle-
nH, MOlllHOCTH, BblJJ.enSlCMofl HCTOIJHHKOM, MOlllH, OCTII BbJ.ne-
nSJlOllleHCS1 BHYTPH HCTOIJHHKa, II KIUl HCTO'iHHKa OT BHellIHe-
ro COnpOTHBJIeHHJI. npH KaKOM BHeWHeM conpOTIIBneHIIH DO
BHeWHeH LlenH BbI,XlenS1eTCJI IIlaKCHMaJIbHaH MOlllHOCTb?
31.19. HCrotJHHK TOKa C 31IC 3aMKHYT Ha peocT3T. npll
cline TOKa II = 0,20 A H 1 2 = 2,4 A H3 peocT3re BbIJJ.eJISleTCH
O;J.HHaKOBaH MOlllHOCTb. npH KaKOH CHne TOKa Ha peOCTaTe Bbl-
.
Jle.1S1eTCJI MaKCHManbHaSl MOlll.II0CTb? 1.JeMY paBHa CHna TOKa
KopOThoro 3aMb!KaHIISl?
31.20. OnpeJJ.enHTb cHny TOKa KopOTKoro 3aMblKaHHS1 6a-
Tapen, ecnll npH cune TOKa /1 = 2,0 A BO BlieWHeH LlenH BLI-
Ae.lIS1eTCJI MOlllHOCTb PI = 24 BT, a npH cline TOKa 1 2 = 5,0 A-
MOlllHOCTb P 2 = 30 BT,
31.21. no )'cnoBIlIO npeJJ.bi;J,YIUCH 3aJJ.atJII onpeJJ.eJIHTb MaK-
CIIManbHYIO MOlllHOCTb, KOTopaSl MO)KeT BbIJJ.eJIHTbCJI B9 BHelII-
Hef! LlenH.
31.22. MaKcliManbnaH MOlll.HOCTb BO BHelIIHeH UfnH paBHa
p..auc = 12 By npll CHne TOKa I = 2,0 A. Onpe.neJIlITb 3.lI.C
H BHYTpeHHee COnpOTHBJIeHlle nCTotJHHKa TOKa,
31.23. npH nOAK.llOlJeUHII K HCrotJHHKY TOKa C 3.QC 8 =
=== 15 B conpOTHBneHHH R = 15 OM Kn1I HCTOIJHIIKa 1') =
::: 751}o. KaK}1O MaKcHManbllYIO MOlllHOCTb BO B-HellJHeii LlcnH
I.!O:H<eT BblJJ.enHTb JJ.aHHblH HCTOtJHHK?
31.24. npH H3MelleHHH BHellJHero COnpOTlIBneHHH C R 1 =
= 6,0 OM ,XlO R 2 = 210M KfI.lI. cxeMbi YBcnHtJlIJICJI BJJ.Boe.
l:IellIY paBlio BH}'TpeHHee COnpOTHBJIeHHe HCTOIJHHha TOKa?
31.25. npH KaKOM COnpOTJlBJIeHHH MOIUHOCTb, Bbl)1.enS1CMaH
eo BHellJHeH Llcml, TaKaJl >Re, KaK II npH conpOTHBneHHII R 1 =
= 10 OM. 1.JeMY paseH KfI1I B Ka>K,lJ.OM CJIYlJae? BH}'TpeHHee
conpOTHHnellHe HCTotJHHKa TOKa r = 2,5 OM.
123

.......
31.26. KorJ).a bO BHCUJHeH LlenH BblJl.CJIS1eTCS1 MOllllIOCTb
PI = 18 BT, KIlll UCTO'lHUKa TOKa ''11 = 64%. npH Jl3MCHe_
IIHH BHeUIHero conpOTUD.'JeHHS1 KnLl IICTOQHHKa CTaJI 1]2 - =
= 36%. KaKaSi MOlllHOCTb Bbl.ZlCJISleTCSI npll 3TOM BIIYTPII IIc-
TO'lHHKa TOKa?
31.27. npH 3aMbiKalllllf aKKYMy.'1S1TOpa cnaQaJIa Ha pe-
3UCTOP conpOTIIBJIeHHeM RI' a 3aTCM Ha R 2 MOUlHOCTb, BbI!l.e-
JISlelan na 3Tnx pC311cTopax, B ooonx c.'1yqaS1X OKa3aJIaCb OJl.I1-
HaKoBoit OnpCJleJUlTb BHYTpcHHec cOnpOTHBJIeHHC aKKYMY-
JIS1Topa.
31.28. 1I.Ba COnpOTlfBJICHUSI no R = 10 OM nOJ).KJllot!aIOTCSI
K HCTOIJHIIKY TOKa C 31I.C 8 = 3;0 B CHaqaJIa nOCJ1eJlOllaTCJIb-
110, a "3aTeM napaJIJIeJIbHo. B OOOHX CJIYQaS1x. Tcn 'JonaS1 Mom.
HOCTb, DbI.lleJIS1eMaSi KaX<J).bIM COnpOTlfBJ1CHlICM, OKa3aJIaCb O.!l.H.
lIaKOBoiL 4eMY paBna CIIJla TOKa D KaX<JlOM c.'IYIJac?
31.29. oaTapcSI COCTOlfT H3 n = 3 noc.'1eJlODaTC.'JbHO coe-
;J.IIHeHllblX IICTO'lHHKOB TOKa C 31I.C 8 = 2,0 B II BnYTpcHHmf
conpOTHBJlCnHeM r = 3,0 B Ka)KJlWf. 4eMY paDlia MaKCIiMaJIb-
HaSi MOlllHOCTb, BblJleJIS1CMan BO BHeWHeH LlcnH TaKoil 6aTapcH?
KaKYIO MaKCIiMaJIbHYIO MOIllHOC1'b BO DHeWHe" Llemf MOn;:HO
nOJlY'lHTb, CoeJ1.HHHB 3J1eMeHTbI napaJIJICJIbHO?
31.30. N O}J.HllaKOBblX 3JIelltelITOB c 3lI.C G II DHyrpellIIIIM
cOnpOTIIBJIeHUeM r Ka)KJ1,bIH coeJllllleHbI nOCJIeJlOBaTeJIbHO II 3aMK-
HYTbI HaKopOTKo. KaKoe KOJIH'leCTBO TenJIOTbi BblJleJIS1eTCSI D
e)lHHIILlY BpeMeHH?
31.31. AKKYMYJIS1TOp C 31I.C 8 = 8,0 B II DHYTPCHHIIf
COnpOTHBJIeHHeM r = 10 <>..t 3apS1)KaeTCSI OT nOJ).3apSl}J.Horo
YCTpoHcTBa HanpS1:H<eHUeM U = 12 B_ KaRan MOlllHOCTb pac-
XOJlYCTCH BHYTPH Ha Bbl)J.eJIelilie TenJIOTLI? KaKYIO MOllllIOCTb
aKKYMYJIHTOp nOTpcMS1eT OT CeTH?
31.32. AKKYMYJIS1TOp nOJ13apSln;:aloT OT ceTIf C lIanpn)Ke.
HHeM U = 15 B. 31I.C aKKYMYJIS1TOpa 8 = 12 B, DIIYTpellJ1e
conpOTIIBJIeHIlC r = 15 Or.1. OnpeJl.eJIIITb, KaKaS! QaCTb 3l1ep-
rHII, nOTpewuieMoH OT ceTH, UJl.eT Ha nO)l3apn1I.KY aKK)""YJIS1TU-
pap 4eMY OHa panHa?
31.33. npH nOJl3apS1JlKe aKKj"MYJIHTOpa C BIIYTpemIH\f co-
npOTHBJIeHUCM r OT 3apS1JlHOrO YCTpoiicTDa C lI:mpfl:H<eHUeM U
3lI.C aKKYMYJISITOpa nC:;BblWaeTCSI. nOCTpOHTb rpat}mhll 3aB!!-
cHMocTeH: MOIllIIOCTH, narpe6.'1SIeMOii OT 3apS!Jl.I!Oro YCTPOHCTDii,
MOIllHOCTU, paCXoJl.yeMoH Ha nOJ1.3apS1JlKY aKKYMYJISITOpa, MOUl-
IIOCTH, pacxoJlyeMoii lIa TenJIO, Kn.a 3apn;:J.Horo YCTPOHCT133
01' 3.lI.C aKKYMYJIS1Topa. npH KaKOM 3I1a'leHHH 3LlC MOIllHOCTl>,
pacXOJlYeMaH Ha nO)l3apSlJ1.KY, MaKCIIMaJIbHa?
12t

31.34. OnpeJl,eJIIITb 3ilC aKKYMyJlSlropa, nUJI,3apSUKae\fOrO
aT CeTH C HanpS1>KeHHeM U = 12 B. eCJIH nOJIOBHHa nOTpe6-
.:IS1eMOii aKKYMYJIS1TOpOM 3HeprHH pacxoJl,yercSI Ha Ten-
nOTY.
31.35..lI.Ba aKKYMYJISITOpa C 3lI.C, paBllblMH 8 1 =
= 8,0 B H III = 3,0 B, CoeJl,HHHJIH napa.1J.'IeJIbHO. npH 3TOM
nOJJY'IHJIOCb, qro OJl,HH 8KKYMYJIHTOp no.n.3apSl>KaeT .n.pyroii
R MOlllHOCTb, paCXOJ1.yeMasr ua nOJl,3arMKY. P = 1.5 BT. Ka-
KOU CHJlbI TOK Te'leT qepe3 8KKYMYJ1SITOpbl?
31.36. B CeTb nOCTOSlHHoro TOKa C HanpS1>KeHlleP-1 U =
= 110 B BKJllO'IeH 3JIeK1'poMOTop. ConpOTHBJIeHHe 06MOTKH
9JIeKTpOMoTopa R = 2,0 OM. MOTOp nOTpe6JIS1eT TOK CHJIoii
1= 8,0 A. OnpeJl,enHTb MOlllHOCTb, nOTpeooS1eM)'lO MOTOPOM.
lIeXaHHqecKYJO M011l.HOCTb H KI1lI. MOTOpa.
31.37. 1.Iepe3 3JIeKTpoMOTop. nOJl,KJIIO'IeHHb!H K ceTH C Ha-
npIDKeHHeM U = 12 B, Teller TOK CHJIoii I = 6,0 A. Onpe.n.e-
.l!HTb MOlllHOCTb Ha BaJIY MOTOpa, ecJIH npH nOJIHOM saTopMa-
)KHBaHHH HKOpsr no ltenH TeIJ:eT TOK CHJlOH J 0 = 30 A.
31.38. MOTOp, nOJl,KJllOlIeHHblH K H C HanpIDKeHHeM U =
= 220 B, pa3BHBaeT MOlllHOCTb P = 3,0 KBT. ConpOTHB-
JleHHe 06MOTKH J.fOTOpa R. = 4,Q OM. Onpe;J.eJIHTb CHJIY TOl<a,
nOT}>e6J1S1eM)'lO MOTOpOM.
31.39. 8JIeKTpOMOTOp no.n.KJIJOlIeH K CeTH C HanpS1>KeHHeM
U. ConpOTHBJleHHe 06MOTKH HKOpSl MOTopa r. nOCTpOHTb rpa-
cIIHKH 3aBHcHMoCTeH: MOlllHOCTH, nOJlYIJ:aeMOH MOTOpOM, Mexa-
HHIJ:eCKOH MOlllHOCTH, MOlllHOCTH. pacxo.n.yeMoH Ha TenJIOTY.
KIUJ. MOTOpa OT CHJIbI TOKa, TeKYlllero 'Iepe3 MOTOp. npH Ka-
KOH CHJle TOKa MOTOp pa3BHBaer MaKCHMaJIbH}'IO MeXaHH'IecKYIO
MOIIJ.HOCTb?
31.40. npH CHJIe TOKa 11 . 10 A 3J1eKTpOMoTOp pa3BHBaer
MOlllHOCTb PJ = 0,50 KBT. npH II = O A - MOlllHOCTb Pz=
= 0,80 KBT. Onpe.n.eJIHTb KIln. MOTopa npH .n.aHHblX 3Haqe-
8HSlx TOKa. KaKoH CHJlb! TOK Teller lIepe3 06MOTKY JlKOpH, eCJIH
9J!eKTpoMOTOp SaKJIHHHT?
31.41. 1.Iepe3 KaKoe BpeMSI saKHnHT 200 r BO,nbl,,- ecnlf 'Ie-
pe3 KHnHTHJIbHHK TelJeT TOK cHnoD 0,50 A npH HanpSl>KCUIiH B
teTH 220 B? HaIJ:aJIbHaSl TeMnepaTypa BOJ].bI 200 C. ,
31.42. K KOHLlaM CBHHltOBOH npOBOJlOKIJ JI,JIHnOH I = 1,0 M
bpHJIO>KeHa pa3HocTb nmeHLlHaJIOB U =10 B. CKOJlbKO Bpe-
IleHH npOH.!I.eT C Ha'laJIa nponycKaHIU\ TOKa .11.0 MOMeHTa, Kor.n.a
tBHHeLl Ha'lHeT nJIaBHTbCSI? HallanbHaSl TeMnepaTypa CBHHLla
Ie = 20° C. nmepeii TenJIOTbi B oKpY>Ka1Oll\.ee npOCTpaHCTBo
I1peHe6peQb.
31.43. Ha CKOJIbKO HarpeercSl MeJ1,Hblii Crep>KeHb S3 I:IpeMSI
125

T = 50 C, ecnH no He:l.tY TeqeT TOK n.1OTHOCTbJO j = 4,0 A/MM"1?
nOTepen TenJIOTbi B oKpYJKalOlllee npocTpaHcTBo npeHe6pe'lb.
31.44. OnpeJl,e.TIHTb MOlllHOCTb lIarpeBaTe.1S1, eenH Ha HeM
MOJKHO BCKHnS1TUTb 3a BpeMS1 T = 10 t.1III1 BOJl,Y 06"Le\toM V ==-
= 2,0 n. HaQa.'IbHaS1 Ter.mepaTypa BO;J.bI t = 20° C. Knn. Ha-
rpeBaTe.TIS1 1J = 751}o.
31.45. C nOMolllbJO HarpenaTe.lbHoil cnJlpaJIJI conpoTIIB-
JIeHHeM R = 2,0 OM, nOJl.KJlIO'leHHOii K 3KKYMynS1Topy C 3D.C
8 = 36 B, HarpeBalOT BO.n.y Maccoil m = 500 r. 3a BpeMSI T ""'"
= 10 MHH BOJ\a Harpenacb Ha !!.t = 29° C. OnpeAeJIJlTb BHYT-
peilHee cOnpOTHBJIeHlle aKKYMYJISITOpa.
31.46. 3JleKTpHIJeCKJlH 'laiiHHK HMeeT )J.Be HarpenaTeJIbllbIe
cnHpanH. npll BKJlIO'lCHIiH OJl,HO" 1f3 HHX BOJl,a B qaHlIIlKe 3a-
KllnaeT qepea t. = 8,0 MIIII, npH BKJIiolJeHHH ApyroH - qepe3
t 2 = 24 MIIH, 4epe3 KaKoe Bpe:UJI 6YAeT 3aKHnaTb B qaiiHIIKe
DOJl,a, eenH cnupa.'IH Coe;I.UIIHTb: a) noeneJ\OBaTeJIbHO; 6) na-
paJIneJIbHo?
31.47. KaKoe KOJIUqecTBO HeTH C)I{lIraeTCSI Ha SJIeKTpO-
CTaHLI.IIU, qToGbl no TeneBII30py MOlllHOCTblO 250 BT nOCMOTpeTb
l,5-qacoBoH anbM? O.J:uTaTb KIllJ. sneKTpocTaHLlHH 35o.
31.48. Tpa'ltBaii MaCCO" m = 22,5 T ABH)I{eTCS1 co CKOpO-
CTblO V = 36 Ut,'q no ropH30HTanM'oMY nYTH. K03qxtJULlHeHT
TpeHtfJl J!. = 0,010, HanpSl)l{eHHe B JIHHIIH U = 500 B, KnLl
ABHraTeJIS1 U nepeJl,a'lH 1J = 75%. OllpeJl,eJIHTb CIIJIY TOKa,
npoXoJl,S1111erO lJ.epe3 ADllraTe.'Ib. C KaKOH CKOpOCTblO 6YJI,eT
Jl,DHraTbCS1 TpaMnaH Bnepx no rope C Yh..l0HOM 0,030, pacxoJl,)'51
TY )I{e MOlllHOCTb?
31.49. 9.1eKTpoBo3 Maccoii m = 300 T ABII)I{eTCS1 BIIH3 no
rope co CKOpOCTbJO v = 72 KM!'l. YKJlOH ropbl COCTaBJIS1eT hI
1Ia Kanc,b1e 100 r.t nYTIf. Ko3<}xPIILI.UeHT conpOTHBJIeHII5I Jl,BH)I{e-
111110 J!. = 0,020, HanpS1)1{eHHe B JIHHHIl U = 3,0 KB, KnJ
SJleKTpOB03a 1) = 80 %. OnpeAe.TIHTJ cuny TOKa, npOXOAS1111e-
ro qepe3 MOTOp 3JIeKTpoBo3a.
31.50. 3neKTpOJl,BJlraTenb nOJl.'bC:\lHoro Kpalla. pa60TaeT no"l.
lIanpS1)1{ellUeM U = 380 B H nOTpe6JIS1eT TOK CH.10H I = 20 A.
OllpeJl,eJIHTb conpOTHBJIeliHe 06MOTKH MOTopa, eenu rpY3 Mac-
COH m = 1,0 T KpaH nOJ\lIIfMaeT Ha BblCOTY h = 19 M 3a DperMI
t = 50 c.
 32. 3.neKTpH"IeCKHH TOK B pa3nHIJHblX cpe.ll.ax
32.1. 1I.Ba SJIeKTpo.IJ.a onycTlfnH B cocyA co CJIa6b1M pacTBo-
pOM nOBapeHHOH conu. K 3JIeKTpOJ\aM nOJl,BenH nOCTOS1I1HoC
HanpJl)l{eHHe. KaK 6YJl,eT MeHS1TbCJI CHna TOKa, npoxoAS1111ero
'lepe3 paCTBOp, eenH B COCYA nOCTenellllO no.aCblnaTb COJlh?
126

32.2. KaK H3MeHHTCH CHJla TOKa. npOXO.l1Sllll.ero llepe3 Ha-
Cblw.eHHbln pacTBop COJIH. eCJIH YBeJlHqHTCH TeMnepaTypa?
32.3. KaK H3MeHHTCH KOJlHqeCTBO Bew.eCTBa, BblAeJlHeMOrO
Ha 3JIeKTpoJJ.ax npH 3.,eKTpOJIH3e. eCJIH: a) YBeJlHqHTb HanpH-
>KeHHe; 6) C6.nH3HTb 3.'1eKTDOlIbl; B) YBeJIH1lHTb norpY>KeHH}'IO
qaCTb 3J1eKTpoJJ.oB?
32.4. OnpeJJ.MHTb XH\fH'leCKHe H meKTpOXHMHqeCKHe 3KBH-
BaJleHTbI Bew.eCTB: BOJJ.opo.n.a. HaTpHH, KHCJIOpo.n.a. .!tByxBaJleHT-
HOH MeAH.
32.5. Ha QTO 3a1pa'lUBaerCH 60JIbllIe 3JIeKTpHqeCTBa: Ha
BblJJ.eJIeHHe 1 MOJISI HHKeJlSI H3 pacTBopa NiS0 4 H.1111 Ha BbI.lI.eJIe
HHe 1 MOJISI >KeJle3a H3 paCTBopa FeCls?
32.6. MeJJ.b Bbl.n.eJlSleTCSI 83 paCTBopa CuS0 4 npH HanpSl>Ke-
HHII U = 8,0 B. HaiiTli pacxo.n. 3HeprHH Ha Bbl.ll.eJIeHHe m =
= 1,0 Kr MeJJ.U. .
32.7. CKOJIbKO BpeMeHH nOTpe6yercSI .n.JISI nOKpbITliSi H3.l1e-
JIHSI CJIoeM 30JIOTa 1'OJIInlfHOH h = 5 MKM. eCJIH nJIOTHOCTb TOKa
B paCTBope XJIOpHCTOro SOJIOTa AuCI s paBHa i = 20 A/M 2 ?
32.8. KaKoH TOJIU.J.HHbI CJIoA cepe6pa 06pa30BaJICSI Ha H3-
AMHH 3a Bpeul t = 3 MHII. eCJIH nJIOTHOCTb TOKa B pacTBope
a3OTHOKHCJlOrO cepe6pa AgNO s paBHa i = 2.6 KAlM'!l.?
32.9. CKOJIbKO OKIICH aJIlOMHHHSI AI 2 0 a pa3JIaraeT TOK
CUJIOH I = 3,0 A B re'leHHe BpeMeHH t = 1,0 q?
32.10. KaKoH CH.I1b1 TOK .l10JI1KeH npoXo.ll.HTb qepe3 3JIeKTpOJIHT.
rrro6b1 XJIOpHCTYIO MeJJ.b CuCI 2 Maccon m = 100 r pa3JIO>KHTb
3a BpeMSI t = 10 q?
32.11. npH 3JIeKTpOJIH3e cepHHcToro LlHHKa ZnSO" B Te-
qeHlle BpeMeHH t = 4,0 q BblJJ.eJlHJIOCb m = 24 r l1.HHKa. On-
ne.l1MHTb cOnpOTHBJIeHHe 3JIeKTpOJIHTa. eCJIH Ha 3JIeKTpO
nOJJ.aHO HanpSl1KeHHe U = 10 B.
32.12. npH 3JIeKTpOJIH3e BOJJ.bI Teqer TO¥- CHJIOH I = 59 A.
KaKoH OO1,eM rpeMyqerO ra3a (npH HOpMaJIbHblX YCJlOBHSlX)
nOJIyqHJICil 3a BpeMSI t = 1 MHH?
32.13. napbl pTY'fH B PTYTHOH na!tme HOHU3HPYlOTCSI peHT-
i'eHOBCKHMH nY'laMH. npu YBeJlH'leHHU HanpSl>KeHHSI Me>KJJ.Y
JIeKTpoJJ.aMH naMnbl .lI.OCTHraercSi CHna TOKa HaCblw.eHHSI I =
::::: 0,80 HA. KaKDe KOnHqeCTBO nap HOHOB c03AalOT peHTre-
HOBCKHe nYtiH 3a BpeMSI t = 1,0 c?
32.14. KaKoH H3HMeHbllIeH CKOpOCTblO JJ.OJI>KeH 06naJJ.aTb
s"1JeKTpoH. IJTOOO HOHH3HpOBaTb aTOM reJHfSl? 3HeprHSI HOHH-
.taLl"H aTOMa rMHSI W = 24,5 sB.
32.15. 3JIeKTpHtfeCKHH npo6oH B03Ayxa HacTynaeT npH
Ilanp.IDKeHHOCTH nMII E = 3,0 MB/M. Onpe.l1eJ1HTb noreHUHaJl
OHH33LlHH B03.l1yxa H CKOpOCTb 3JIeKTpOHOB nepe.l1 y.n.apOM 0
127

....
MOJIeKYJIbl. er.nH ,!lJIHHa CBOOOJl,HOrO npo6era 3JIeKTpOHOB ). "'"
= 5,0 MKM.
32.16. ]1.0 KaKoro nOTeHQ.HaJIa MO:mHO 3apSJJ\HTb yeJl,HHeH.
HblH MeTaJIJIUqeCKHH rnapHK paJ\HycoM r = 5,0 MM? K1iKoij
3apHJI, OH npH 3TOM 6YJ\eT HeCTU? HanpH:meliHocTb nOJIH, nprt
KOTOpOM HacTynaeT npoGo" B03J1,yxa, E = 3,0 MB/M.
32.17. DOIIeMY HCKpOBOH pa3pSJJI, D03HHKaer npH DblCOKnx
HanpH>lteHHHx. a Jl,yroDoH pa3pHJI, HJI,eT npH ,llOCTaTOqHO Ma.'lbIX
HanpH:meIUlHx?
32.18. KaKYIO MHHHMaJIbHYIO CKOpOCTb Jl.OJI>Ken HMeTb
3J1eKTpOH, 'lT06bI BblJIeTeTb H3 BOJIb<ppal'lfa?
32.19. DOIICMY B MOlllHbiX 3JIeKTpOHlibiX JIaMnaX 3HO,ll Jl,e-
JIalOT OXJIa:m.llaeMbiM H nepe.ll BKJIICIIepHeM HaKaJIa KaTo.:J,a BKJIIO-
qalOT aHOJ\Hoe HanpH:meHue?
32.20. MOlllHOCTb TOKa B 3JIeKTpOHHO-JIyqeBOH Tpy6-
Ke P = 0,50 BT. 3HeprHH 3JIeKTpoHoB B JIyqe Ui =
= 8.0 . 10- 111 ]1.:m. Onpe,lleJIUTb CHJIY anO;J.Horo TOKa.
3a.ll.aQH K rJlaBe IX
IX.I. ]1.ecHTb TOqeK Coe,llHHHJIH Jl,pyr C Jl,PYI."0M npo-
BOJl,HHKaMIi conpOTHBJleHHeM R = 40 OM Ka:mJl.blH. K Jl,BYM TO'!'
KaM nOJl,KJIlO'lHJlH HCTOqHHK C 31I.C 8 = 10 B C BHy-rpeHHIIM
COnpOTHBJleHHeM r = 2,0 OM. OnpeJl,eJIHTb CHJlY TOKa B Ka:m-
Jl,OM H3 npOBO,llHHKOB.
IX.2. ll.enb COCTaBJIeHa H3 pC3HCTOpOB COnpOTHBJleHlun.UI
R1 = 0,25 MOM, R'J. = 50 KOM, KOHJI,eHCaTopa nepeMeHhol1
eM KOCTH. Y KOTOpOro eMKOCTb H3MeHHeTCH no 3aKOHY C =
= Co + at. rJl,e a = 1,0 MKcI>/C. H HCTOqHHKa TOKa c 3.D.C
8 = 15 B (pHC. 195). OnpeJl,eJIHTb CHJIY TOKa qepe3 conpOTIfB-
JIeHHe R1' BHYTpeHHHM c:onpOTUBJIeHHeM HCTO'lHHKa npeHe6-
pe'lb.
IX.3. TpH OJl,HHaKOBbiX HCTO'lHHKa TOKa C 3JJ.C 8 = 1,5 B
H TPH 0Jl.UHaKOBbIX KOHJI,eHCaTOpa eMKOCTblO C = 2.0 MK<I>
coeJl,HHeHbl. KaK nOKa3aHO Ha pHC. 196. OnpeJl,eJIHTb 3apH,ll K8)!{'
Jl,oro H3 KOHJI,eHCaTopOB. ECJIH TO'lKH A H 0 3aMKHYTb Hal.O'
pOTKO, TO KaKOH 3apH.ll npOHJ\eT no npOBOJl,HHKY, COe.II.HHJIIO-
llI.eMY 3T1I TOqKH?
IX.4. I1cro'lHIIK TOKa C 31I.C 8 = 100 B C BHYTpeHHII'1
cOnpOTHBJIeHUeM R 0 = 10 OM nOJl,KJIlOqell K 3JIeKTpHqCCKOMY
'18HHHKY. OnpeJl,eJIHTb, C KaKOU CKOpOCTblO BbIpbIB8eTCH 1f3
HOCHKa qaHHHKa nap, KOrJl,a BOJl,a KHnHT, eCJlH MOID.HOCTb, BbI-
Jl,eJIHeMaH B qaHHHKe, MaKCHMaJIbHa? IlnolQ,a,!l.b HOCHKa qaii-
HHKa S = 4,0 CM 2 .
128

IX,5. B CeTb- C nanpHiKCHHeM U = 24 B BKJUOqeH 3.'1eKT-
pO:\IOTOp. HarpY)KelUlblii MOTOp nOTpe6'1HeT MOID.HOCTb B k =
= 10 pa3 6o.1blllYJO, 'leM npH pa60Te BXOJ"'IOCTYIO. Pa3'HOCTb
nOTeHLlIla.'10B Ha KJlC:\!MaX MOTopa npH narp)'3Ke na.ll.aeT Ha
n = 20 0 0 no cpaBHeHHIO C pa3HocTblO nOTeHltH3.'10B npn XOJlOC-
TOM xO;J.e. Onpe;J.e.'lHTb MOIl.lHOCTb TeflJlOBbiX nOTcpb B nO.ll.BO-
.lI.HIl.lHX npOBO.ll.aX npn XOJlOCTO"i XO.ll.e, ec.'m CHJla HarpY30 t UlO-
ro TOKa I = 5,0 A.
IX,6. 3J1eKTpO.ll.BllraTeJlb nO.ll."be\tHoro KpaHa pa60TaeT no,!t
HanpsuKeHHeM U = 380 B H nOTpe6J:1HeT TOK CIIJlOH /1 = 10 A,
hOf;J.a KpaH nO;J.IIHMaeT rpY3 MaCCOH M = 1.4 T o CKOpOCTblO
AAc +'

R &
z
PIIC. 195
PIIC. 196
PIIC. 197
VI = 20 C:\!/C. C KaKOU CKOpOCTblO nO;J.HlIMaCTCH rp)'3, hor.n.a
'lepe3 MOTOp TCqeT TOK CHJloi'! /2 = 15 A? Kru1 MexaHlflleCKHX
nepe;J.aq KpaHa 1') = 900.
IX.7. B paCTBop AgCl nOMeCTIIJlII .Il.Ba O;J.IIHaKOBbiX IlJHpO-
Knx 3.'JeKTpo..1.a II npJf.lJO)KH.'JH K HIIM nocToHHHoe nanpsuKeHHe
U = 100 B. npll 3TOM na OTpHI.taTC.'JbHO:\I 3J1CKTpO.ll.e CTaJlO
Bbl,!te.'JSITbCH m = 1,0 Mr cepc6pa B ceKYHJl.Y. nOCepe.Il.HHe Me)j{-
!J.Y 3J1eKTpo;J.a:>m nOMeCTIIJ1H TpeTHH TaKoii )j{e 3J1eKTpo,!t H IlC-
pe3 pe3HcTop conpOTHBJlenneM r = 50 OM COeJl.HHlI.'JH ero C
nOJlO)j{IITe.'JbHblM 3J1CKTpO.ll.OM (puc. 197). l.lTo II B KaKOM KO.'1H-
qeCTDe 6YAeT Bbl,!teJlHTbCH Ha Cpe.ll.HCM 3eKTpoAe?
r JI A 8 A X. 3J1EKTPOMAfHETH3M
 33. B3aHMO.ll.eiicTBHc MarHHTHoro nOJlH C TOKOM
33.1. KaK B3aH:\IO;J.eHcTBYIOT Me)j{JJ.Y co60ii npoBo..1.HIIKIl C
TOKO\-! J II 2, nOKa3aHHbIe Ha pUC. 19B? KaK 6y.n.YT OHH B3aH-'
....J..1.eikTBoBaTb, eCJlH IIX CKPYTl1Tb B )KrYT?
33.2, nOlle:\!y .n.Ba napanJle.'JbHblX npoBO.ll.HIlKa, no KOTO-
pbIM TeKYT TOKH B O;J.HO!tl nanpaBneHHII, npIlTHrHBaIOTCSl, a .Il.Ba
napanne.lbHblX 3.1!eKTpOHHblX nYIlKa OTTa.'1KIIBaIOTCSI?
5 3aR. 189 7
129

33.3. K:3K 6y.l1Y'" DeCTI! ceGS:! MarllllTH3H cTpcnKa II p3MI\a
c TOK01\!, nOMeellHLle OKono npOBO;J,II1IKa C TOKOM? KaK H3Me-
HItTCH pe3ynbTaT, eCJIIf MarHlITUYIO CTpCnI\.Y If par-my C TOKOI
nOMeCTlfTb OKo.,10 3.'1eKTpOHlIoro nyqKa?
33.4. DpoBonOl<a npoTacKIlDacTcH Me)f\.l1Y ,nByr-UI 3a>KIIMa-
MIt, K KOTOpbIM nO;J.KnlOlleu IICTO'lIllIK 31I.C, co CKOpOCTblO, paD-

)L

5)
:::::----

.

8)
--- ::::
-
)L
aJ


12 J
PIIC. 198
PIIC. 199
Hoii CKOpOCTIl .l1peiicpa 3.1eKTpoHoB II IIanpal3nCHIIOii B npoTII-
BOnOnO>KII}IO cTopony. BYJJ.eT nil 3TOT npOBO.l1.HHK C TOKOM C03-
JJ.aDaTb BOhpyr ee651 ManUITHOe nOJIe?
33.5. OnpeJJ.eJIIITb 1I11JJ.YKLlHIO MafllJlTIIOrO nonn, ecnll MaK-
eliMaJIbllblH BpaalOHii MOMellT ellJ1, .n.clICTBYI01lI.HM Ha paMhY
nnOa.l1.blO 1,0 e12, paBell 5 . IO-t H . M npll cline TOKa B 1,0 A.
Ha pa\IKe naMOTano 100 BIITKOB npoBo,!!,a.
33.6. KaK 6y.aCT DCCTII ee6H paMI<a e TOKOM, nOMe1ll.CHHaSl
B PtlarHIITHoe nO"'Ie, nOKa3anHoe na pile. 199, a-B.
@ @  'J 
II S, , ,
M
I I
I
PIIC 200 PIIC 201
33,7. llBa KpyroBbIX npoBoJJ.HIIKa MorYT CBo60.ll.IIO Bpa-
1lI.aTbCSI BOKpyr BepTIfKanbHbIx oeeiL KaK 6y.n.YT paeno.'1araTb-
CSI npoBo.n.lllfKII, eC.I1H no IIIIM npon) CTHTb TOKIf B HanpaBnellIl-
SIX, YKa3aHHblx Ha pile. 200: a) OCIf COBnaJJ.aIOT; 6) OCH He COB-
na,naIOT?
33.B. Do ;t.BYM O;1.IIHaKOBbl:\1 MeTannUqeeKllM 06pyqaM,
1-I\1elO1lI.ml 06Hii LleHTp, paenOnO>KeHHblM OJJ.IfH ropli30HTanb-
HO, JJ.pyroH BCpTlIKanbHo, IIJJ.YT O.l1I1HaKODble TOKII. KaK 6y,ner
paenonaraTbCH pa1Ka C TOKOM, nOMC1lI.CHHan 13 IIX 061l1.uii LlellTp?
130

33.9. I( Jl.nyp,f .lI.lIarOH3Jlbll0 nponmOnOJIO>l<lILlM TOtl/<aM
hJl3.J.paTa. cJ1.eJlalllloro 113 0)J.HII3KOBb!X KYCKOB npOBo.rIOKII,
nO'1.I{JllOtleH HCTOtlHIiK 311C. Onpe.aC_lI1Tb HH!l.Yl<ltlllO MarHHT'
Horo nOJIH B lteHTpC KBa.ap3Ta.
01 - 6) 8] zl
@If IHt*
PIIC. 202
33.10. Onpe.lI.e.'1HTb HanpaB.leHHC TOKa: a) B COJleIiOIl.lI.e;
6) B npoBO.lI.e. qTO()bl H36JllO;I.3JIOCb YKa3aHHoe Ha pllC, 201 B3all-
MO'1.C;;CTBHe.
33,11. Onpe.lI.eJIHTb HanpaBJleHlle CH.'1bl B3allMo!l.eikTBIfSI
TOKa C larHIlTHbIM nOJleM .lI.JIH Ka>K;I.orO HJ CJlYtlaCB, nOKa3all-
HblX Ha pHC. 202, az.
1
6) _ 81
V z}
i-L r F /¥"/
 / I
0]
PIIC. 203
33. 12.  Onpe;I.c.'lJlTb HanpaB.'lelllle MarHIlTHoro nOJIH !I..'lSi
Ka>I<;I.O.ro 113 CJIYtlaeB, nOKa3a':'HbiX Ha pHC. 203, a-z. Opo-
BO!l.HIIK nOMelll.alOT nepneH.lI.IIKYJlHpHO MarHHTHoMY nOJllO.
33.13. l(aK 6Y.ll.eT .lI.BllraTb-
CSI npoBo;J.HHK B Ka>K.lI.OM 113
c.lIYQaeB, nOKa3aHHblX Ha
pilC. 204, a-e?
33.14. npOBO.ll.lIIIK C TOKOM
nO:.lelll.eH B O,\HOpO.ll.Hoe MarHIIT-
Hoe nOJle C IIH.lI.YKltHeH B- =
= 20 MTJl. Onpe.lI.eJIHTb CHJlY,
.lI.eilCTB}'1OllI.YlO Ha 3TOT npoBo.ll.-
HUK, eCJIH ero .lI.JIHHa l =
= 0,10 M, CHJIa TOKa I = 3,0 A. a yroJl MC>K.lI.Y HanpaDJleHlleM
TOKa H BeKTopoM Ii a = 45".
33.15. B ropH30HTaJlbHOM O.ll.HOpO.lI.HOM MarHIlTHOM nOJle C
HHJJ.YKltHeH B = 10 MTJI nO.ll.BeWeH Ha .lI.BYX JlerKlfX IIHTSIX ro-
5-
OJ r 51 B)
lID }i]-L-
PHC 204
131

.
pU30HTa..'IbHblii" npoao.D.HIII{ .D.JJ1iHoA 1 == 10 CM, nepneH;J.H}{Y.
.iIpHblH MarHUTHOMY JIOJIIO. KaK H3MeHHTCSI CII.lIa Hanm:eHIUI
I<a*.D.OH "3 HHTeii, eCJlu no npOBO,IJ.HHKY nponYCTHTb TOK CH.lIoii
J = 10 A?
33.16. no ropH30HTaJlbHo:\IY npOBO.D.IIHI<Y ;J.JlHHOH l ==-
= 20 CM II Maccofl m = 2,0 r Te':leT TOK CHJlOH J = 5,0 A. On-
pe;t.eJlIITb MarHHTlIYIO HH,il.YM.lHIO B MarHIITHoro nOJISI; B
KOTOpoe HY}I{HO nOMeCTHTb npoBO.D.HHK, ':IT06bl 011 BHCeJI He na-
.D.aSl.
33.17. Ha rop1l30HTa.'1bHbIX peJIbCaX, pacCTosnUle Me.J.Y
KOropblMH l = 60 CM, JIe}f{llT CTepeHb nepneH.D.HKYJlSlpHO HM.
Onpe,IJ.eJIHTb CHJlY TOKa, KOTOpbIH .Ha,no nponYCTHTb no CTeph--
HIO. ':IT06bl OH Ha':laJI .D.BHraTbCSI. PeJIbCbl U CTepeHb Haxo,nRT-
CR B BepTIIKaJlbHo:\l O,il.HOpO.D.Ho:\l MarHHTHOM nOJle C HH.D.YKl.lU-
eH B = 60 MTJI, Macca CTep}\{HSI m = 0,5 Kr, K03<P<PIfl.lUeHT
TpeHHSI CTep}f{HSJ 0 pe.'IbcbI J.t = 0,10.
33.18. CTep}f{eHb Jle}f{HT nepneH.D.HKYJlSJpHO peJlbCaM, pac-
CTOSlHHe Me>K.D.Y K01G}H>lMH l = 50 CM. PeJIbCbI COCTaB.'I9.1OT C ro-
pH30HTOM yroJI' (% = 30 0 . l(aKoH .D.0Jl}f{Ha 6b1Tb IIH,lJ.YKl.lHR Mar-
HIITHoro nOJlR, nepnen.D.HKYJlSJpHoro n..10CKOC111 peJlbCOB, ':ITOGbI
Crep}f{eHb Ha':laJi .D.BllraTbCSI. eCJIH no lIeMY nponYCI<aTb TOK CII-
..10H J = 40 A? 1(03qXpHl.lUenT TpeHJISI CTep}f{HR 0 peJlbCbI  =
= 0,60. Macca CTep}f{PSI M = 1,0 Kr.
33.19. npOBO.D.HH \{ ,D.JIHnOH l H MaccoH m nO.D.BCIllCH Ha Ton-
KHX npoBo.10':lKax. npH npoXO>K,D.eHHH no HeMY TOKa CH.'lOiI J
OH OTK.lIOHHJlCSI B o.D.HOpO;J.HOM BepTUKaJIbHo:\1 ManUlTHOM nO.'Ie
TaK, ':ITO npOBOJIO':lKH 06pa30BaJiH yro.'1 (% C BepTHKaJlblO. I(a-
KOBa HH.lI.YKl.lHH MarHUTHoro nO.'IH?
33.20. npOBO;J.HHK ;J.JIHHOil l = 30 CM C TOKOM CIIJIOH J =
== 20 A pacnOJIO}f{eH no.ll. yrJlOM (% = 30 0 K O.D.HOpO,IJ.HOMY Mar-
HHTHOMY noJUO C HH,lJ.YKl.lHeH B = 0,4 TJI. HaHTH paooTY. KO-
TopaH 6bIJIa cOBeprueHa npH nepeMew.eHHH npoBo,HHKa Ha pac-
CTOHHHe x = 25 CM nepneH.D.HKYJlHpIlO MarHHTHoMY n0.11O.
33.21. 3J1eKTpOH BJIeTaeT B O.D.HOpO.D.Hoe MarHHTHoe nO.'Ie
C HH.D.YKl.lHeii B nepneH.D.HKYJlHpHO CHJlOBblM JlIIHHSlM co CKO-
pOCTblO v. no KaKOH TpaeKropHIf 6Y.D.eT .lI.BHraTbCH 3J1eKTpOH?
qeMY paBlla paOOTa CHJlbl, .D.eHCTB}'IOw.eH Ha 3JIeKTpoH?
33.22. npOTOH onHca.1 OKPY}f{HOCTb pa.D.Hyca R = 5,0 CM
B O.ll.HOpO;J.HOM MarHHTHOM nO.1e C HH.D.YKl.lHeH B = 20 'ITJI. On-
pe.D.eJIHTb CKOpOCTb npoToHa.
33.23. npOTOH H (%-lIaCTHl.la BJIeTalOT B OAHOpO.D.Hoe Mar-
HHTHoe nOJIe nepneH.D.uKYJlSlpHO ..1HHHSlM HH.lI.YKl.lHH. Bo CKOJlb-
KO pa3 OTJlH':IalOTCSI pa;J.uycbl OKpY>KHOCTeii, KOTopbIe omlCbI-
132

B310T lJaCTHU,bl? Bo CKO.1bKO pa3 OT.'IUlJaIOTCH UX yrJIOl3bIe CK
pOCTIi. eCJIH Y lJaCTHLt O;J.llllaKOBbI: a) CKOpOCTJ1; 6) 3lIepnm.
33.24. .D.BIUK}W.11HCH 3JIeKTpll'leCKIiH 3apH,n MOiKHO pac-
cMaTpuBaTb KaK 3JIeKTpH'.lecKuH TOK. Onpe.lI.eJII1Tb MarHHTHblH
MOMeHT KpyroBoro TOKa, 06pa30Bauuoro 3JIeKTpOlIoM, BJIeTeB-
lllllM no;J. npHMblM yrJIQ\1 co CKOpOCTbIO v B O.lI.HOPOJJ.Hoe 1\Iar-
HIiTHoe nOJIe C I1H,1.YKLtHeH B.
33.25. a-qaCnil.l,a, )"cKopelIHaH pa3HocJ"blO nOTeHLtHa.l0B
V = 250 KB. npo.'IeTaeT nOnepelJHOe O!l.HOpO;J.1I0e MarHIITHoe
nOlle C HH.lI.YKLtlieH B = 0,51 T,'I. To.1ll1.HHa o6JIacTu C no.'leM
d = 10 CM (pIlC. 205). Onpe.u.e.'IHTb
yroJi <p OTKJIOHeHIIH a-lIaCTIiLtbl OT
nepBOllallaJIbHOrO HanpaBJIeHHH .u.BII-
}f{eHHSI.
8
@@@
@@
@00
00
@@@
.
o .
@@
@00
@@
@d0 0

-----
PIIC. 205
PIIC. 206
33.26. npOTOH B.leraer B O,nIlOpO.lI.Hoe MarJlJITIiOe nOJIe B
co CKOpOCTblO v no;J. yr.l0M a K .'1HHHnM MarHHTHoH HH.u.)'Ii:LtIlH
TpaeKTopHSI qaCTHIJ,bl npe,ncTaB.1HeT co60ii BHHTOBYIO JIHHUIO.
Onpe;J.eJIIITb pa.u.H)'c Ii- lllar 3TOH BI-IHTOBOH JIIIHm1.
33.27. OG'bHCHHTb, nOlle:llY lIaCTHlJ,a, .lI.BH}f{YW.aHCSI B mar-
HI1TH01\l no.'Ie. oTpaiKaeTcSI OT 06.1acTH. r.u.e IIHYKlJ,HH MarIlijT-"
Horo nOJISI YBCJIlIqHBae:rcSi (puc. 206),
33.28. 3apSl}f{eHHaSi lIaCTHlJ,a BJIeraeT no yr.1oM a K Ha-
npaBJIeHlIblM napa.l.'Ie.'lbHO 3.'IeKTpnllecKo:llY II r.tarHI1TlloMY no-
JIH:\I. KaK 6y.u.eT ,ABHraTbCSI qaCTIIlJ,a?
33,29. OrplllJ,aTeJIbHaH qaCTHlJ,a BJIeTaeT co CKOpOCTblO v
no.u. yr.'lOM a K napaJIJIe.'IbHO HanpaB.'leHHbI:lf 3JICKTpHlIecKoMY
H MarJiHTHoMY nOJIHM. Onpe;J.e.1HTb, CKO.lbhO o60poTOB c;J.e-
JIaeT qaCTHlJ,a .lI.0 MO:\leHTa HaqaJIa .lI.BH>KeHIISI B HanpaB.'leHmf.
06paTHO\I nOJISIM. HanpSl}f{eHIIOCTb 3JIeKTp}lQeCKOrO nOJIH E.
IfH,1VKl:.IIH MarHHTHoro nOJIn B.
33.30. O.lI.lIopO,iJ.Hble MarHlITHoe II 3JIeKTpHqeCKOe nO.'IH pac-
nOJIO}f{eHbl B3allMIIO uepnCH.lI.IIK)'.'1HpHO. HanpSl}f{eUHOCTb 3JIeKT-
pUlIeChoro nOJISI E = 0,50 KB/M, a HH.nYKlJ,HSI MarHIITlioro nOJISI
B = 1,0 MT.IJ. Onpe.u.eJIHTb, C KaKOH CKOpOCTblO 41 B KaKO!>1 Ha-
npaB.leHlfU .u.o.liKeli .1eTeT!> 3.leKTpOH. lITOObl .u.BuraTbCSI npSl-
MO.lJlIHeii 110.
133

 34. 3JJCKTpOManlHTtIaH IIHJJ.YKL(IIH.
CaMOHH..'I.YKLtIIH
34,1. OnpeJJ.enllTb nOTOK BeKTopa MarllliTHol1 HHJI.YhI.:'HH,
npoHII3bIDalOlllJlH nnocKYIO nOBepxHocTb nJlOlllaJI.blO 100 C'>1 2 '
npll JlIIJJ.YKLtIlH 0,2 T.'I, eC.'I1I nOBepx,HocTb: a) nepnell,J.HKYJlHp-
Jl3 BeKTopy MarHiiTlIOM HHJJ.YKUlm; 6) napaJlJleJlbHa; n) pac-
nO.lO)f(CHa no,iJ. yrnoM 45° K Bel\TOpy WUIIHTHOH HHJJ.YKUJlJf;
r) pacno.'10)l{eHa noJJ. yrJlOM 30'0 K BeKTopy MarHHTIIOH JlHJI.YK-
UIlII .
34.2. OKOJlO npOBO,J.HIIKa C TOKOr.! HaXOJI.HTCSI npSlMoyrOJlb-
Han paMKa ABCD (pHC. 207), Jle)l{alllaH B OJJ.HOH nJlOCKOCTIl C
T]pOBOJI.HHKO1 (00' IIAB). nOT0.K BeKTOpa MarHHTHoH HH-
,1yi<UlIII, npOHJl3blBalOlllilii pa:\tKY H c03,nallllbl" MarHHTHblM no-
.1e1\! npoBo,!UIHKa, paBeH <D. Onpe,nCJIIITb H3MeHeHHe MarlllfTHO-
ro nOTOKa, eCJlH: a) OTKJllOl.JHTb TOI< B npoBoJI.IIHKe; 6) H3MC-
IIIfTb HanpaB.leHHe TOKa Ha 06paTHoe; B) nOBepHYTb paIKY
nOKpyr OCH, npoxo;'UIIl.l.eii 'lCpe3 cepe;J.Hllbi CTOpOH AD H BC,
lIa 90°; r) H3 180'0.
34.3. 3a:ltK!iYThIH BHTOK npOBO]la Ha;\OJI.IITCSI Y npOBO)l.1111Ka
C TOKOM (pIlC. 208). Ey.u;eT ml B03HIIKaTb B BHT1\C TOK, eCJlII:
a) BpalllaTb BHTOK BOKP} r OCII, ,T]P0}..O:I.HLllCH l.Jepe3 FlpOBO;l,IIIIJ\;
(Jr
,0
A oJ)
oJ
?
G-
o
Pile. 207
PIIC. 208
PIIC 209
6) npaLllaTb BOKp}r OClI, napaJl.'IeJlbH<:H np9BO)l.HHKY; B) Bpa-
lllaTb BOKpyr OCH, nepneH,nHKYJlSlpHOH npOBo,nHIIKY; r) .u;BII-
raTb nOCTynaTCJIbHO napaJlJleJlbHO npOBOJI.HHKY; ,n) .n.BllraTb
JloCTynaTe.'1bHO nepnell,!l.HKYJlSlpHO npoBo.n.HHKY.
34.4. Onpe.n.eJllfTb HanpaBneHHe HH.n.YKUHOIiHoro TOKa B
npOBO,J.SlllleM KOJlbue (pHC. 209), eCJlH HHJI.YKUHSI MarHHTIIOrO
nonSl: a) YBeJlIII.JHBaeTCH; 6) }'MeHblilaercSi.
34.5. Onpe,nCJIHTb HanpaBJIeHHe CHn, .n.eHCTBYlOlllHX Ha
npoBo,nHlllee KOJlbllO (pHC. 209), eCJlH HHJI.YKllHSI MarmlTlIOrO
IIO.1Sl: a) YMeHblilaeTcSI; 6) YBe.'III'lIlCaerCSI,
134

34.6. KOJIbLlO 113 CBepXnpOBO.ll.lUlKa n'lOLlla;1.bfO S Ha '\:oJtT.
CSI B O,D.HOpO,D.HOM MarHHTIlOM nOJIe C UH,D.YKLlHeH B. JIHHHU Mar-
IIHTHOH UH,D.YKLlIIH nepneH,D.HKYJISIpHbI nJIOCKOCTH hO.1bLla. On-
pe.n.e.'1UTb MarHHTHbIH nOTOK 'lepe3 hOJIbLlO nOCJIe BbIKJIfO'leIlHSI
BHemnero MarHIfTHoro nOJISI.
34.7. npSlMOH MarHHT na,D.aeT CKB03b 3aMKH}'TblH COJIeHOII,D..
BY,D.eT JIH TaKoe na,D.eHHe CDo60,D.HbIM?
34.8. KaKHc SIBJIeHHSI npolfcxo.n.SIT B KOJIbLle, eClm B nero
B1BuralOT MarHHT? PaccMoTpeTb CJIY'laH, Kor,D.a KOJIbLlO c,D.eJIa-
HO H3: a) npoBo;J.HHKa; 6) ,D.H3.'1eKTpHKa.
34.9. KaKHe SlBJIeHHSI npOHCXO,!l.HT B CTep>KHe, eC.'1H OH ne-
pe,J.BIfraeTcSI B nOCTOSIHHOM l\1arHHTHOM nOJIe no,D. yr.'10M K CH-
.'10BblM JIIIHHSlM? PaccMoTpeTb CJIY'laH, Kor,iJ.a CTep>Keub C,D.eJIaH
113: a) npOBo,D.HHKa; 6) ,D.H3JIeKTpHKa.
34.10. MarHHTHbIH nOTOK l:Iepe3 COJIeHOH,D., c011.ep>KaLllHH
n = 500 BUTKOB npOBo.ll.a, paBHoMepllo y6bIBaeT co C1<OpOCTbfO
6.<1J At = 60 MB6/c. Onpe;J;eJIHTb 3LlC Hn,D.YKLlllH B COJIeIlOU-
,D.e.
34.11. CoJIelloH,D., cO,D.ep>Kauulii n = 1,0 . 10 3 BHTKOB npo-
BO;J.a, HaXO,D.HTCSI B O,D.HOpOJJ,nOM MarHHTIlOM nOJIe, HH,D.YKLlHSI
KOTOpOro H3MeHSleTCSI co CKOpOCTbfO t!.BI ilt = 20 MT JI/c. Ocb
co.!JenOH,D.a COCTaBJISIeT C BeKTopoM UH,D.YKLlHH MarHHTHoro nOllSi
yro.!J a = 60°. Pa,D.HYc COJIenOU.lla r = 2,0 CM. Onpe,D.eJIHTb
3LlC HH.n.YKLlHH, B03HHKaf01U.eH B COJIeHOIf,!l.e.
34.12, BHToK Me.llHOrO npOBO,D.a nOMeLlleH B O.llHOpO,D.Hoe
MarHUTHoe nOJIe nepneH,D.HKYJISIpHO JIHHHSIM MarHHTHoH HH-
.llYKLlHH. LlHaMeTp BUTKa D = 20 CM, ,D.HaMeTp npOBO,D.a d =
= 2,0 MM. C KaKOU CKOpOCTbfO H3MeHSleTCSI HH,D.YKLlHSI MarHHT-
1I0ro nOJISI, ecJIH no KOJIbLlY Tel:leT TOK CHJIOH I = 5,0 A?
34.13. nOKa3aTb, l:lro nOJIHblH 3apSl.ll, npOTeKaf01U.HH no
npOBo,D.HHKY, npH B03HHKHOBeHHH B npOBO.llHUKe HH,D.YKLlHOH-
Horo TOKa He 3aBHCHT OT cnoco6a H3MeHeHHSI MarHHTHoro nOTO-
Ka, a 3aBtiCHT TOJIbKO OT H3MeHeHHSI nOTOKa H conpOTHBJIeHHSI
npOBO,D.HHKa.
34.14. OAHOCJIOHHaSi KaTYlliKa nJI01U.a.llblO S = to CM 2 , co-
,D.ep>K8lll.aSl n = 100 BHTKOB npOBO.lla, nOMelll.eHa B O.llHOpO,D.Hoe
MarHHTHoe nOJIe C HH,D.YKLlHeH B = 8,0 MTJI napaJIJIeJIbHO JIU-
HHSlM MarHHTHoH HH.llYKLlHH. ConpOTHBJIeHHe KaTYlliKH R =
= 10 0..1. Onpe,D.eJIHTb, KaKOU 3apSl,D. npOH,D.eT no KaTYlllKe,
eCJIU OTKJIIOtlHTb MarHHTHoe nOJIe.
34.15. CoJIenOH.ll, cO.llep>KaLllIfH n = 1,0 . 1()3 BHTKOB Me,D.-
HOH npOBOJIOKH Cel:leHHeM S = 0.20 MM 2 , HaXO,D.HTCSI B O,D.HO-
PO,!l.HOM MarHHTHOM nOJle napaJI.'1eJIbHO JIHHHSlM MarHHTHoH HH-
nYKLlHH. I1H,D.YKLlHSI MarHHTHoro no.'1S1 paBHoMepHo H3MeHSI-
135

erCH co CKOpOCTblO !J.BIM = 10 MTJlIC, lllfaMeTp COJleHOH;J.a
D = 5,0 CM. OnpeeJIH'Pb Ten..1oB}'IO MOW.HOCTb. BblJI.eJIHIOW.YIO-
CH B COJlCHOH,ne, KOHUbI KOToporo 3aMKHYTbl Me>KJJ.Y co60H.
34,16. BlfTOK npoBo,na nJlow.aJI.blO S = 50 CM 2 3aMKH}T Ha
KOHJI.C'lICaTOp eMKOCTblO C = 20 MK<I>, nJIOCKOCTb BHTKa nep-
neH,:l.HKYJIHpHa OJI.HOpO,nHOMY MarHHTHoMY nOJlIO. Onpe.1lc..ll1Tb
CKOpOCTb H3MeHeHHH MarHIiTHoro nOJlH, eCJIIf 3apHJI. Ha KOII-
JI.eHCaTOpe paBeH q = 1,0 HKn.
34.17. KBaJI.paT CJI.e..'IaH Jl3 Gerupex npOBOJI.HHKOB ..'I..1lf11oii
I = 8,0 CM H conpOTHBJleJUleM R = 4,0 OM Ka>KJJ.bliL Ha pac-
CTOHHHH [/4.0T OJI.HOro H3 npoBoJI.HHKOB KBaJI.-
paT 3aMKHYT nep€MbI':IKOH COnpOTlIBJleHlleM
r = 1,0 Q.f (pHC. 210). nnocKocTb KBa.1lpaTa
nepneuJI.lfKYJlHpHa OJI.HOpOJI.HOMY MarHHTHo:'IY
nonlO, H3'>leHHlOlJ..leMycH co CKOpOCTblO
!J.B! M = 200 MTnlc. Onpe;I.eJlIiTb CIf.JIY Ta-
Ka, TeKyw.ero no nepeMbl':lKe.
34.18. Onpe.D.eJIHTb 3LlC HH.1lYKlll1II B
npODO.1lHHKe .lI.JIHHOH 1= 20 CM, JI.BH*yro.eM-
CH B OJI.HOpOJI.HOM MarHIITHOM none C HH,nYKUHeii B = 10 MT.1
co CKOpOCTblO V = 1,0 M/C no.1l yr.'10M a = 30 0 K BeKTopy Mar-
mfmOH HH..'I.YKllH H.
34.19. PeaKTIIBHblH ca:o.IO.leT JleTHT ropH30HTaJlbHO co CKO-
pOCTblO V = 900 1\:.1:1':1. Onpe;J.eJlHTb pa3HocTb nOTCHl:.Ua.'10n
Me>K.1l.Y KOHllaMII ero KpblnbeB, eCJIH BepTHKa.'IbHaH COCTaDJlHIO-
w.aH JfHJI.YKUIfH !1-IarHHTHoro nO.1H 3eMnH paBHa B 1 = 50 MKTJJ,
pa3Max KpblnbeB I = 24 M. }.\mKHo JJU Ha caMO.1eTe 1!3.lepHTb
3TY pa3HocTb nOTeHUHaoB?
34,20, npOBO.1lHHK JI..1HHOii I = 1,0 M paBHD:.fepHO Bpaw.a-
eTCH B ropli30HTaJJbHOH nJJOCKOCTH C ':IaCTOTOH 'V = 10 c- 1 . OCb
BpaUJ.eHHSI npOXOJI.IIT ':Iepe3 KOHCU CTep*HH. BepTHKanbH3S1 co-
CTaBJJHlOlltaH MarHHTHoro nO.1H 3eMJJU paBHa B 1 = 50 MKTJJ.
Onp e .1le.'IHTb pa3HOCTb nOTeHUlianOB Me*.llY KOHllaMU npoBO..'l.-
HIIKa.
34.21. nJJOCKIIH BHTOK npOBOJI.a pacnoJIo*ell nepHJI.IiKY-
.1Hp1l0 OJJ:HOp01J.HOMY MarHHTHoMY nOJJIO. KorJI.a BnTOK nOBep-
uy.1CH Ha a 1 = 180<>, no HeMY npomen 3apHJI. ql = 7,2 MKJI.
Ha KaKoH yro.'I nOBepHy.'IeH BHTOI{, eeJJH no He:'fY npomc.l
3apHJI. q2 = 1,8 MK.'I?
34.22. Pa'dl{a, Ha KOTOpoii HaMOTallO n = 100 BHTKOB npo-
BOJI.a COnpOTlIB'IeHlleM R = 10 O"'f, paBHoMepHo BpaUJ.aeT('
B o.1lHOpO,1HOM MarHlfTHOM nOJ1e C HH.llYKllHeH B = 50 MTJI.
Ocb Bpal1l,eHlfH .'IC*IIT B nJlOel(OCTIl paMKIl H nepneH.J.ltKy.'IHpHa
JlIIHIfHM mrYKll"lI. n'IOllla;J.b pa:.u<II S -= 100 C\l 2 . Onpe.c.c-
.{]
PIIC. 210
136

JlHTb. K3KOA 3apSl.'1 np0Te1leT Qepe3 P3MKY npH nOBopOTe ee OT
yrJI3 Cl 1 J1.0 Cl z : I) OT 0]1.030 0 ; 2) OT 30° J1.0 600; 3) OT 60 0 J1.0 900;
4) OT 0 ]1.0 18(f (Cl - yroJI Me>KJI.Y BeKTopoM HH,1.YKl.{11II II HOp-
M3JIblO K p3MKe).
34.23. Job npoBoJ1.3 JJ,.'IHHOH 1 = 2,0 Pol CJ1.e.!J3H KB3J1.paT, KO-
TOphiH p3CnOJIOmeH ropH30HT3JIbHO. KaKoe KO.TIHtJeCTBO 3JIeKT-
pUlIeCTBa npOHJ1.eT no npoBoJ1.Y, eCJIH ero nOTslHYTb 3a J1.Be ]1.Ha-
rOHaJIbHO npOTHBOno.!Jo:mHbIe BeplllHHbl TaK, 1IT06bI OH CJIO-
)l{UJICSI? ConpOTHBJIeHHC npoBoJ1.a R = O,IQ 01.1. BepTHKaJIb-
HaSi COCTaBJISlIOw.aSl HHJ1.YKltHH MarHHTHoro nOJISI 3eM.!JH B  =
= 50 MKTJI.
34.24. KOJIbltO p3,n:Hyca r = 6,0 CI 113 npOBOJ1.a conpOTIIB-
JIeHHeM R = 0,20 OM p3CnOJIo:meHO nepneHJ1.HKYJISIpHO OJ1.HO-
pOJ1.HOMY M3rHHTHOMY noJIlO C HHJ1.YKD.iieH B = 20 MT JI. KOJIb-
0.0 CKJIa]1.bIBalOT TaK, 1ITO nOJIyqaJOTcSI J1.Ba O]1.HHaKOBblX KOJIb-
D.a B BHJ1.e BocbMepKH, JIe)HaI.!..leH B Toii :me nJIOCKOCTH, qTO H
KOJIbD.O. noc.'Ie 3Toro MarHHTHoe no.'1e BblKJUOtJalOT. Onpe.:t.e-
JIHTb, KaKoe KOJIHtJeCTBO 3neKTpU1IeCTBa npOTe1leT no npOBO-
J1.Y 3a BpeMSI: I) KOrJ1.a KOJlbD.O CKJl3J1.blBaJOT; 2) Kor]1.a BbIKJIIO-
Q310T MarHHTHoe no.e.
34.25. npOBO;I.II"-K ]1.nHHoii 1 CKOJIb3HT 6e3 TpeHHSI no J1.BYM
peHKaM co CKOpOCTblO v B O;J.HOpO]1.HOM MarHIITHOM no.'1e, BeK-
TOp HHJ1.YKD.HH B KOToporo nepneH]1.HKYJISIpeH nJIOCKOCTlI, B
KOTOpOH JIe)HaT peiiKH (pHC. 211). PeHKH 3aMKH}'TbI Ha pe3HC-
A C
R
--
€> @ u@ @__
@ fl/ (8) (/
(8)  @iiG>
R, l R Rz
°80 0 0
PHC. 211
PHC. 212
TOp COnpOTlIB.'1eHHeM R. OnpeJ1.e.1HTb, C KaKOH CHJIOH MarHHT-
Hoe nOJIe J1.eHCTByeT Ha npOBO.ll.HHK. C KaKoii CHnOH TSlHYT npo-
BO.'1HHK?
34.26. npOBOJ1.HIIK Maccoii m MUHOH 1 JIeJ{{HT Ha J1.Byx ro-
pH30HT8.llbHblX peiiKax, 3aMKH}'TbIx Ha pe3IICTOp cOnpOTHBJle-
HHeM R. BcSI CHCTeMa HaXOJ1.IITCSI B BepTHKaJIbHOM MarHlITHOM
nO:Ie C HHJ1.YKD.Heii B (pHC. 211). Ko3<j$nltHeHT TpellHSI I\Ie>KJI.Y
peHKaMH H npOBO.ll.HHKOM ..... KaK}'IO CHJIY F CJIeJ1.YeT npHJIO)HHTb
I( npOBO.ll.HHKY. tJTO(5b1 Olf .lI.BHraJICSI paBHOMepHQ co CKOpO-
CTblC v?
137

34.27. npHMoyrOJlbHblH KOHTYP HaXO.lI.HTCH B O.lI.HOpOJl.HOM
MarHIiTHOM nOJle, nepneH.lI.HKYJlHpHOM nJlOCKOCTH KOHTypa.
I1nJl.YKL{HH nOJlH B. nepCMblqKa Jl.JlHHOH lliMeeT COnpOTlIB.'Ie-
IlIIe R, CTOpOHbl AB Ii CD - conpOTIiBJleHHH R. H Ra
(pHC. 212). OnpeJl.eJlIiTb cHny TOKa, KOropblH TelleT no nepCMblq-
I{e, npH ee .lI.BH>KeHHH C nocToHHIIOH CKOpOCTblO v.
34.28. B OJl.HOpOJl.HOM ropH30HTaJlbHOM MaruHTHoM none C
HH.II.YKL{HeH B = 60 MTn HaXO.ll.HTCH BepTHKaJlbHaR H-06pa3-
HaH KOHCTpYKL{IiH H3 TonCTblX MeTannHqeCKIIX CTep>KHeH, nep-
neH.lI.HKYJlHpHaH MarHHTlIoMY nonlO (pHC, 213). no CTep)KHHM
I
0 8 0
o ...@
u
@
l_...;..
@
@ @B
l
@ @
Pile. 213
PHC. 214
PIIC. 215
CBo6o;J;HO, 6e3 HapYllJeHHS1 KOHTaKTa, CKOJlb3HT npoBo.i1HUK
.ll.JlHHOH 1 = 50 CM, r.!aCCOH m = 1,0 r H conpOTHBnemlcM R =
= 0,80 M. OnpeJl.eJlHTb, C KaKoH CKOpOCTblO .lI.BH>KeTCR npo-
BO.ll.HHK, H HanpaBneHue TOKa B nepeMblqKe.
34.29. H-06pa3HYIO KOHCTPYKL{HIO (CM. 3a.lI.aqy 34.28) Ha-
KJlOHHJIH noJl. yrJIOM a = 30 0 K ropH30HTY raK, tt!'o yroJI Me>K-
.ll.y BeKTopoM MarHHTlloro nOJIH H npOBO.D.HHKOM OCTanCR npR-
MbiM. Onpe.D.eJlHTb, C KaKoH CKOpOCTblO .D.BH>KeTCH npOBO,il.HHK,
34.30. no .D.BYM r JIa.lI.KHM, 3aMKHYTblM Me*.ll.Y co60u Me-
TaJInHqeCKHM IlJHHaM, YCTaHOBJIeHHbIM no.D. yrnoM a = 30 0 K
rop1l30HTY, CKOJIb3HT MeJl.Hblit npOBOJl.HHK (pHC. 214). CIlCTeMa
HaXOJl.HTCH B O.D.HOpO.D.HOM MarHHTHOM nOJIe C HHJl.YKLUieH B =
= 40 MTJI, nepneH.D.HKynRpHoM nJIOCKOCTH, B KOTOpOH nepe-
'>felLI.aeTCH npOBo.lI.HHK. KaKou MaKCHMaJIbHOii CKOpOCTH Jl.OCTHr-
HeT npOBOJl.HHK? Con pOTHBJIe II HeM KOHCTPYKL{HH no cpaBHeHHIO
C conpOTHBJIeHHCM npOBO.D.HHKa npeHe6peqb.
34.31. npOBO.D.HHK JI..rIHHOH 1 = 1,0 M H conpoTHBneHlleM
R = 2,0 OM JIeJKHT Ha .D.BYX ropH30HTaJIbHblX IlJHHaX, 3aMK-
HYTblX Ha HCTOqHHK TOKa, 3D,C KOTOporo <1 = 1,0 B. BCH
KOHCTp)"KL{HH Haxo;x,IITCR B BepTHKaJIbHOM MarllHTHOM nOJIe C
HH.D.YKL{HeU B = 0,10 Tn (pHC. 215). Onpe.n.enHTb cHny TOKa
B npoBO.D.HHKe, eCJIII: 1) npOBOJl.HHK nOKOHTCR; 2) npoBOJl.HHK
Jl.BH>KeTCH BnpaBo co CKOpOCTbI<> v = 4,0 M/c; B) Jl.BH>KerCfI
138

BlJeBO C TOH :me CKOpOCTblO. B KaKO1 Hanpan-
JIeHIUI U C KaKOIi CKOpOCTblO Ha,!l.O nepeMew.aTb
npOBOJl.HHK, qT06bl TOK Qepe3 Hero He llleJl?
BHYTpeHHHM COnpOTHI3J1eHHelll HCTOQHUKa H
. conpOTHI3.'leHHeM lllHH npeHe6peLlb.
34.32. npOBOJl.HHK AJIlmOH l = 1,0 M ne-
)KHT Ha J1.BYX rJlaJl.KHX ropIl30HTa.'1bllbiX lllH-
Hax, pacno.'10:H<eHHblX B BepTHKa,'!bHoM Mar-
HUTHOM none C HHJl.YKUHeH B = 0,10 Tn.
C KaKOH YCTaHoBIIBllleHcSI CKOpOCTblO H B Ka-
KOM HanpaBneHHH 6YJl.eT .JJ.BHraTbCSI npoDok
HUK, KOrJl.a K lllUHaM nOJl.KJllOqUTb JlCro'lllHK TOKa c 3.lJ.C
8 = 0,50 B (pHC. 215)?
34.33. B OJl.HOpOJl.Hoe MarHHTHoe nOJle C HHJl.YKllHeH B =
= 2,0 Tn nOMew.eHO ropH30HTa.1bIloe MeTaJlnHLlecKoe Konb-
uo pa.n.Hyca R = 5,0 CM, npfllJeM ero OCb COBna.JJ.aeT C HanpaB-
.1eHHeM non SI , no KonbUY 1II0iKeT CBo60Jl.HO .JJ.BHraTbCSI cTep-
*eHb (pHC. 216). OnpeJl.eJlHTb ycraHoBHBlllYIOCSI yrnoaylO CKO-
pOCTb Bpaw.eHHSI cTep*HSI, KOrJl.a Me>KJl.Y ueHTpoM CTep>KHSI H
KOJIbUOM nOJl.KJllOlIHJlII HCTOlIHIIK TOKa C 3.lJ.C <1 = 1,0 B.
34.34. Ha .JJ.BYx ropH30HTaJlbHblX peJlbCaX, paccToSlHHe
Me*.n.y KOropblllUi l = 1,0 M, ne*HT npOBoJl.HHK MaCCOH m =
= 0,50 Kr, conpoTHBneHHeM R = 2,0 OM, 1(03<j)(jmUHeHT
TpHHSI Mf)KJl.Y npoBOJl.HIIKOM H peJIbCaMH f.L = 0,10, BcSI CHC-
TeMa HaXO.D,HTCSI B BepTHKaJlbHOM MarHHTHOM nO.'1e C HHJl.YKUHeH
B = 0,10 TJI (CM. pHC. 215). PeJIbCbI no.zU,JIlOlIaIOT K HcrOLlHH-
KY TOKa C 3.lJ.C <1 = 10 B. npeHe6peraSi conpOTHBJleHlleM pe.'Ib-
COB, onpe.D,eJIHTb: I) cHny TOKa, npOXOJl.Slw.ero no npOBO,J.HU-
J<Y B Ha'laJIbHblH MOMeHT; 2) C KaKOH YCTaHoBHBllleHcSI CKOpO-
CTblO 6Y.D,eT .D,BHraTbCSI npOBO.JJ.I1HK; 3) MOW.HOCTb, nOTpe6JISle-
MYIO OT HCTOQHHKa; 4) KOJlHQeCTBO renJlOTbl, BbIAeJlSlIOw.eHcSI
B npOBO.D,HHKe 3a ceKYHJl.Y; 5) KaKYIO MexaHHlIecKYIO MOW.HOCTb
pa3BHB8eT TaKOH «.n.BHraTeJIb».
34.35. B KaKOM CJlYLlae MOTOp HarpeeTCSI 6blcTpee: Kor.a.a
cOBeplllaeT MexalUillecKYIO pa60TY HJIH KorJl.a Bpaw.aeTcSJ BXO-
JIOCT}'lO?
34.36. LITO nOKa3bIBalOT raJibBaHOMeTpbl
B cxeMe, H306pa*eHHou Ha pHC. 217? Ra-
TYlllKa C.D,enaHa H3 TOJICTOH npOBOJlOKH. LITO
nOKa*yr raJibBaHOMeTpbl, ecJJH pa30MKHYTb
KJllOq K? ecnH 3aMKHYTb KJllOq K?
34.37. HauTH HH.JJ.YKTHBHOCTb npOBO.D,HU-
Ka, B KOTOpOM paBHOMepHoe H3MeHeHHe cunbl
..
B
!
PHC. 216

t.,.
PHC 217
139

1'OKa na 2,0 A B Te'leHife 0,50 C B036Y*.lI.aeT 3D.C CaMOHU.lI.YI<_
LlHH 20 MB.
34.38. 1.J:epe3 .n.'1UHUblH COJIeIlOH.a, JlH.lI.YKTHBHOCTb KOTO-
poro L = 0,40 Mfu H nJIow.a.ll.b nOnepe'lHOrO Ce'leHIISi S =
= 10 CM 2 , npOXO.ll.HT TOK CHJIOH 1= 0,50 A, KaKoBa HIUYK-
LlHSI-nO.'1H BUYTPH co.IJeHOIl;I.a, eCJIU OH COJ].ep*IfT n = 100 BUT-
ROO? _
34.39. B OJ].HOpOJ].HOM MarHIfTHOM nOJIe naXO;J.HTCH KaTYWKa
H3 cncpXnpOBOJI.HHKa. nOTOK BeKTOpa MaruHTHoH HH.lI.YKLlUU
'lepe3 KaTywKY <I> = 0,20 MB6, nOCJIe BblKJIIO'leHHH MarHHT-
HOro nO.'1H B J<aTYWKe B03HHK TOK CH.'10H I = 20 A, 1.J:eMY paBHa
IIHJ].YKTHBHOCTb KaTYlllKH?
34.40. B KaTywKe ifHJ.{YKTHBHOCTblO L = 0,20 fH CUJIa
TOKa I = 10 A. KaKoBa 3HeprJfH MarHUTHoro no.'1S1 3TOH Ka-
TYWKU? KaK H3MeHHTCH 3HepruH no.1Sl, ec.'1u CUJIa TOKa YBe-
JIJf'lHTCH BJ].noe?
34,41. Onpe;J.eJIUTb 3Hepnflo MarHHTHoro nOJIH COJIeHOH,!I.a,
B KOTOpO\f npH CHJIe TOKa I = 5 A B03HJfKaeT MarHHTHbIH no-
TOK (j) = 0,5 B6.
34.42. KaTywKa HHD.YKTHBHOCTblO L = 0,30 fH, HatO.
TaJUlafi TOJICTblf MeJ].UblM npOBOJ].OM, coeJ].HJleHa napaJIJIeJlbHO
C pe3ucTopOM conpOTUBJIellHeM R H nOJI.I<.llO'leHa K IfCTO'lHHKY
TOKa C 3D.C <1 = 4,0 B H BHYTpeuHHM conpOTIIBJIeHHeM r =
= 2,0 OM. KaKoe KOJIH'leCTBO renJIOTbI BbI;J.eJIHTCfI B KaTYlliKe
" pe311CTope nOCJIe OTK.IJIO'leHUfi HCTO'lHUKa TOKa?
 35. nepeMeHHblH TOK. 3JIeKTpOMarHHTubie
Ko.ne6aHHSI H BO.nHbI
35.1. npOBOJIO'lHaH paMKa n.IJow.a.u.blO S paBumfepHo Bpa-
w.ae-rCH B OJI.HOpO,!l.nOM MarHUTHOM nOJIe C HH.1lYKllHeii B BOKpyr
OCII, nepneH.1lHKy.lJflpHOH HanpaBJIeHUIO nOJIH. 1.J:acToTa Bpa-
w.eUHH 'V. KaK co BpeMeneM H3MeHHIOTCH MarHHTHblH nOTOK <D.
npOXO.1.flw."" 'lepe3 paMKY, U 3LlC HH..'U'Kll"" <1 B paMKe?
35.2. BHTOK npOBOJI.a nJIOUla.u.blO S paBHolepHo Bpaw.aeTcfI
B OJI.HOpOJ].HOM MarHUTHOM nOJIe C HHJI.YKllHeH B BOKpyr OCII.
nepneHJI.uKYJIHpHOH HanpaBJIeHJfIO nMH. LJacTOTa Bpaw.eHHfI
'V. 1.J:eMY paBHO MaKCHMaJIbHoe 3Ha'leHHe 3D.C HH.lI.YKllHH, B03-
HHKalOw.eH B paMKe? nOCTpOHTb rpalJ>HK 3aBHCHMOCTH 3J1C
OT BpeMell". KaK JI3MeHHTCH MaKCHMaJIbHoe 3Ha'leHHe 3n.C II
KaK H3MeHUTCH rpalJ>HK, ecJIU: 1) BMeCTO OJ].Horo BHTKa HaMO-
TaTb N BHTKOB; 2) qaCTOTY Bpaw.eHHH YBeJIU'lUTb B n pa3?
35.3. PaMKa nJIow.a.ll.blO 400 CM 2 HMeeT 100 BHTKOB npoBo-
J].a H Bpaw.aeTcH B OJ].HOpO.ll.HOM MarHUTHOM nOJIe C HIIJI.YKllJfei i
140

10 MTJI BOKpyr OCIf, nepneH.nHKYJIHt>HOH MarHHTHOIY no.'1IO.
nepno;J. BpaJl.leUHH 20 MC. KOlU.lbI npOBOJl.a Qepe3 CKOJIb3HWlle
KOHTaKTbl 3aMKHYTbI H conpOTHBJIeHHe 50 OM, Onpe..1eJIHTb
CJmy TOKa, npOTcKatoll..tero '1epe3 conpOTIIB.'1eUHe. 1..Ie\IY paBHO
MaKCHanbp.oe 3Ha'leHHe CHJIbI TOKa? KaKOBa lJaCTOTa TOKa?
35.4. nO'lCMY npu nOJIyqeHHH nepeMeHHoro TOl<a YA06uee
Bpam.aTb IiHJl.YKTOp. a HKOpb OCTaB.1SiTb HenoJl.BH>KHbL\l?
35.5. reIiepaTOp nepe!\feHHOro TOKa HMeeT Ha pOTOpe llieCTb
nap nOJItoCOB. KaKoH .n.OJI>KHa 6blTb 'IaCTOTa Bpam.eHHH pOTOpa,
'IT06bl reHepaTop BbIpa6aTblBaJI TOK CTaH.lI.apTHOH 'IaCTOTbl?
35.6. no.laraH, 'ITO HanpH>KeHlIe nepcMeHHoro TOKa H3Me-
HHeTCH no 3aKoHY cHHyca H Ha'laJlbHaH cpa3a paBua HY.'Ito, on-
pe..1eJIIiTb lIanp'Sl>KCHHe B MOMeHTbI BpeMelU1 5,0, 10 H 15 MC.
Am.1HTy.n.a HanpmKelllfH 200 B, 'IaCTOTa 50 n.{.
35.7. B CeTb nepeMeHHoro TOKa BKJIto'lIl.'In pe3HcTOp co-
npoTIfBneHHeM R. A\fnJIHTYJl.Hoe 3Ha'leHlfe HanpH>KeHlHI U €I'
KaI{ H3MeIHItoTCH co BpeMeIlcM HanpIDI<eHHe Ha pC3HCTope, TOK,
BblJl.e.l51eMaH MOm.HOCTb?
35,8. BOJIbT!'1feTp nepeMeHiloro TOKa, BKJIto'leHHblil B ceTb,
nOKa3blBaeT HanpH>KeHUe 220 B. HaHTH MaKCUMa.'lbHOe 3Ha-
lI('Hne HanpSl>KeHIfH B CeTH.
35.9. Ha KaKoe HanpSl>KeHlfe Ha;{O paCC\lIlTLIBaTb H30.1HTO-
phi mfHlIH 3.'IeKTponepe.n.a'llf; eCJIH .n.CHcTBytom.ce 3HaqeHlfe
HanpH>KeHlISI 500 I<B?
35.10. 3.'IeKTpOnJIilTKa MOm.IIOCTbto P = 0,50 KBT BKJIto-
lIeua B npOMbIlliJIellHYto CeTb C HanpH>KeHHeM U = 127 B. Ha-
nHcaTb ypaBlieHIIH 3aBHCIIMOCTH CIf.lbI TOKa II H3npH>KeHHH B
u.enlf 3JIeKTpOnJIHTKH OT BpeMeHH. KaKaH MaKCIfMa.'IbHaH !\IOm.-
HOCTb Bbl.ll.e51eTCH B nnHTKe?
35.11. HeoHoBa51 JIaMna HalJJlHaeT CBeTHTbCH 11 racHYTb,
KOr..1a HanpH)KeHHe Ha ee 3JIeKTpO.1.aX .n.OCTurneT cTporo onpe-
Jl.C.'IeHHOrO 3HaQeHlIH. Kato 'IaCTb nepHO.ll.a 6y.n.eT coeTHTbC51
J1aMna, eCJIU ee BK.lto'lllTb B ceTb, .n.eHCTBytom.ee 3Ha'leHHC Ha-
npSl>KelfHH B KOTOpOH paBHO 3TOMY HanpSl>KeHllto?
35,12. nOQeMY CepAe'lHUKIf TpaHc$>pMaTOpoB, reHepaTO-
pOD 11 3JIeKTpO,'l.BlfraTeJIeii HaUllpatoT 113. OT,J.eJlbHbIX TOHKHX
,30nnpOBaHHbIX .lI.p}r OT .n.pyra >KeJIe3HblX nJIacnm?
35.13. nOlieMY npH pa30IKHYTOH BTOpHliHOll o6MoTKe TpaHc-
I>opMaTop nO'lTli He nOTpe6.1HeT 3H€pnm?
35.14. KaK 6Y.'l)'r 1I3MeH51TbCH HanpH>KeHJlH II CIIJIbI TOKOB
B nepBlf'lHOH If BTOpH'IHOH 06MoTKax TpaHcpMaTopa, nOA-
.CJIIO'IeHHOrO K ceTH, npH YBenJlIJemUi nOJle3HOH HarpY3KII
"ICHblllemUl COnpOTlIBJIeHlISI) BO BTOpll'lHOii 06MOTKC?
35.15. KaK lI3"fellHTCH C!!JIa TOKa B nepElf'lHOii H BTOpHIl-
141

"""'II1II
no" 06MOTKax pa60ratoLU.ero Tpallc1x>plaTOpa. e.cJ1Jf )f{eJte3l1blii
cep;te'lHIIK pa30\IKII)'rb?
35.16. nO'leMY TpaHc4>oPMaTOp 1O>Ker Bbll'nu U3 crpol!,
eCJ!1I XOTb O,!l.IIH BHTOK 06MOTKH 3aMKHeTCH HaKopoTKO?
35.17, TpaHc$>p\JaTop nOBblwaeT HanpH>KeHHe C 220 B
ll.0 I, I KB If CO..'l.Cp>KlfT 700 BHTKOB B nepBU'IIiOH 06MoTKe. K.a-
hOB K03(14J11Qlle1lT TpaHc4>oPMaQIUI? CKO.lbKO BUTKOB BO BTO-
pU'Ilioli 06loTKe? B KaKoii 06MoTKe npoBOll. 6oJIbwero Ce'lCIIIHI?
35.18, TpaHcq,opMaTop nOBblwaeT HanpH>KeHUe C VI
= 100 B ll.0 V 2 = 5,6 KB. Ha Oll.HY 113 06MOTOK Hall.CJI1f BUTOK
npOBO,').a, KOHQbI KOToporo nO,1,coell.UIIIIJ!U K BOJ!bTMeTpy. BOJ!bT-
MCTp nOKa3a:I lIanpH>Kelllle V = 0,40 B. CKOJIbKO BIITKOB HMe-
toT OUMOTKU TpaHc$>pMaTOpa?
35.19, notllI>Katolli.IIH TpaHc4>oPMaTop C Ko3<l><PIIQUeHTOM
TpaHc4>opMaQIUI k = 5,0 BKJIto'leH B CeTb C HanpH>KeHHeM VI =
= 220 B. Onpell.e.'1I1Tb Kn.!1. TpaHcq,opMaTOpa, eCJUf nOTepb
:mepruu B nepBH'IHOH 06MoTKe lie npOIlCXOll.UT, a HanpH>KeHHe
lIa DTOpll'lHOii 06MoTKe V 2 = 42 B.
35.20. nepml'lHaH 06:o.IOTKa TpaHcq,opMaTopa IIMeer n =
= 2,4 . 1()3 BIITKOB. CKO.'IbKO BUTKOB ll.OJI>KHa IIMeTb BTOpll'l-
HaH oUMoTKa, '1T06b1 npll lIanpH>KelUIH lIa 3a>KIIMaX V = II B
nepe,1,aDaTb BO DHeWHtolf) Qenb MOLU.HOCTb P = 22 BT? Conpa-
THB.'IClllle BTOpH'IHOf( 06.\IOTKII R = 0,20 OM. HanpH>Kelille B
ceTIi VI = 380 B.
35.21. D.o KaKoro 3I1a'lCHHH lIa,!l.o nOBbiCIITb lIanpHmeHlle B
JllIlfIiH 3JIeKTpOnepe,!l.a'lli COnpOT!IB.'1eHlIeM R = 36 ()p,f, qro6b1
OT 3.'IeKTpOCTaIlQUII MOlli.1I0CTblO P = 5,0 MBT 6b1J!0 nepell.al!o
11 -= 95% 9Hepnm? .
35.22. Or nO,1,CTaHQUIII< nOTpe6I1Te.'I1O nepe,ltaeTCH MOlli.IICCTb
P = 62 KBT. ConpoTHBJ!eHllc J!lIImu R = 5,0 OM. D.JIH CJIY'
'1acn oCYlli.ecTD.'IeHIIH nepe;l,aqu npu HanpH>KeliHIl VI = 620 B
II V 2 = 6200 B onpc,!J.eJIIITb: I) Kat<Yto '1aCTb MOIllHOCTII nOJlY-
qaeT nOTpe6l1TeJIb; 2) HanpH>Kelllle Y nOTpe6HTe.'IH.
35.23, KO.'Ie6aTeJIbHbIH KOHTYP COCTOIlT 113 l<arYWKIf HI!'
,!I.YKTlfBHOCTIl IIll.BYX 0Jl.IIHaKOBbiX KOIIll.eHcaTOpOB, BKJIIO'Iel1llbiX
napaJlJ!eJIbIiO. nepllo;J. co6cTBeHHblX KOJIe6allllH KOHTypa TI =
=-- 20 MKC. 1..IeMY 6YJl.eT paBeH nepllo,1" eCJllf KOH;J.ellcaTopbl
BK,'1to'lIlTb nOCJIe,1,OBaTeJ!bHo?
35.24. KOII..1eIlCaTOp eMKOCTbto C = 50 n CHaqaJ!a no;!.-
K.'Ito'lIl.71l1 K HCTOqHIIKY TOKa C 3D.C 8 = 3,0 B, a 3aTeM K Ka-
rywKc IIHll.YKTIIBIIOCTblO L = 5,1 MKrH. t..IeMY paBHa 'IaCTOT3
KOJle6aHliH, B031BIKWlIX B KOHType? t..IeMY paBHo MaKCIIMaJIb-
lloe 311a'leHlIe CIIJJbI TOI<a B KOHType? ll.eHcTBytoLU.ee 3Ha'ieHue?
35,25. KOJIe6aTeJlbHblH KOHTYP COCTOIiT H3 KaTYlliKH RH"
142

lIYKTIIBHOCTblO L = 80 MhrU, KOH)l.eIlCaTOpa eMKOCTblO C =
- ]00 n II pe311cTopa cOnpOTlIBJleHJle\l R = 0,50 OM. Ka-
I\ JO MOllUIOCTb )l.OJl>Kell nOTpc6J1HTb KOIITYP. '1106b! B IICI no,1,-
,ncp>KIIBaJlHCb HC3aTyxalOIlUfe KO.'le:5aHJHI, npH KOTOpblX MaK-
e' :'13.1bHOC HanpH>KeHlle Ha KOII,1,eHCaTOpe paBHO U = 4,0 B?
35.26. 3apSl>KeHHblil KOII)l.eHCaTOp 3a:\tKHYJlII Ha l<aT}lliKY
\lH..1YKTlfBIlOCTH, l.lepc3 KaKoe BpeMH (B )l.O.lf1X nepllo)l.a) noc.'le
nO..'1.K.llO'IeIlHSI 311eprHSI B KOH)l.CHcaTOpe 6Y,1,e1 paBlla .:mcpnIH
B K3TYlliKe IIH)l.YKTIIBHOCT\I?
35.27. OnpC,1,CJlHTb pe30H311cIIYIO 'IaCTOTY KOIITypa, CCJm
OTHOlliCIUle 1>IaI\CIIMaJlbHOrO 3apH)l.a lIa I<OH,!I.eIlCaTOpe K MaKCH-
M3.'lbIIOH CIIJle roKa B KOIIType paEHO 11.
35,28. B npllcMHIIKe eMKOCTb B KOJIe63TeJlbHOM KOIIType
MO>KHO MeHflTb OT 0,10)1.05,0 He%>, a J!llIt.YKTHBHOCTb - OT 0,50
;10 ] ,0 MrH. KaKou )l.Hana30H '1aCTOT II )l.JlHH BO.ll1 MO>KIIO OXBa-
TIITb HaCTpoHKoii 3TOro npHcMIIIIKa?
35,29: CTaHIlHH pa60TaeT Ha JVlHlle BOJlHbI A = 30 M.
CKOJIbKO KOJlc6allllH IIccyw.eii qaCTOTbl npOHCXO)l.lIT B Te'lelllle
o Horo nepllO,!l.a 3BYKOBbiX KOJlc6a1lllH C lJaCTOTOH 'V = 5,0 KrLI.?
35.30. Il.'IHHa JlIIIIHII 3.1JChTpohepe)l.alJ S = 600 KM. tleMY
paDHa pa3HOCTb «j)a3 lIanpH>KCHIIH lIa 3TOM paccToHIHm?
35.31. Pa)l.II0JlOKarop pa60TaeT lIa BOJllle A = ]5 CM II HC-
nYCKaeT HMnYJlbCbl C lJaCTOTOH '" = 4,0 KrLI.. D.JllfTCJlbHOCTb
Ka>K)l.OrO lImy.lbca 't = 2,0 MKC. Kal<OBa 113\160.::IblliaSl )l.3.1b-
1I0CTb 06HapY>Ke1l1lSl LI.e.ll1? CKO.rlbKO Ko.le6aHIH1 cO)l.ep>KIITCSI B
0;1,110:\1 IIMny.lbce?
3a.ll.a'lH K rJlaBe X
X.t. KBa,JpaTHaH paMK3, C)l.e.'1aHII3S1 1f3 Me)l.HOrO npOBO)l.a
CC'leHIlCM S = 2,0 MM 2 . MO>KeT nOBOpalJHBaTbCH BOKpyr o)l.Hoii
ropll30HTaJlbHOH OCII 00' (pHC. 2]8). OHa HaXO)l.HTCSI B O)l.HOpO)l.-
HOM BcpTHKa.lbHO\1 MarHHTHOM nOJle C IIII,!I.YK-LI.HeH B = 30 "TJI.
Onpe)l.eJlIlTb CIIJlY TOKa, npOTCK3JOw.ero no npoBo,.'tSlW.HM npo-
BO;J.aM, eCJIII yroJI OTKJlOHeHHH CL = 30°,
X.2. ECJlII K TOIJKaM C If D npSlMoyrOJIbHoro npoBo)l.HIIKa.
no KOTOPOMY TClJeT TOK, no:t.K.'1104lfTb QYBCTBIITCJIb1lblH 3J1CKTpO-
MCTP, TO B cJIYlJae 1IaJIlIIIHH Maf,HHTHOro nOJlH, nepneH,JIIKYJISlp-
Horo 06pa3LI.Y (pHC. 2]9), 011 nOK3>KCT B03HHKHOBeHilC pa3Ho-
CTU nOTeHLI.Ha.'10B. Onpe,!l.CJlHTb pa3HocTb nOTellLI.HaJIOB MC>K)l.Y
TOIJKa\1U C H D. eCJIIf 3a.'l.aHbl TOK IIJepe3 06pa3eLI., HH)l.YKLI.HH
B MarHIITHoro nOJIH, TOJIw.lllla 06pa3LI.a a, KOlluellTp3nllH n
3.1eKTpoHoB B npOBo)l.HJIKe.
X.3. 3J1eKTpoH BJleTaeT co CKOpOCTblO V o = ] 00 I<'''./C B 06-
.nacTb, 9 KOTOPO" C03..1.8Hbl O)l.HopO)l.Hble napa.1JIeJlbHble 3J1eKT-
143

plfIJecKoe H MarHHTHOe nOJIH C HanpH}j{eHHOCTbIO E = to KB\I
II HH.!I.YKLtHeH B = 10 MTJI no.n npSlMbIM yrJIo\1 K HHM. Haihl!
3aBHCIiMOCTb pa;J,Iiyca KPHBH3HbI Tpael<TOpHH .nBlDKeHHH 9J1eKT-
pOHa OT BpeMelUl. qeMY paBeH pa.nHYc KPHBH3Hbi TpaeKToplIH,
Kor;J.a 3.1eKTpoH c.ne.'1aJI O.ll.HH o60poT?
. -0'
PIIC. 218 PHC. 219
X.4. Ha KOIII(e HeBeCO'fOro npoBo.J.Slm.ero CTep}j\HH YKpen-
JIeH MeTaJI.11fIJeCKHi't wapHK, KOTOp!>IH KacaeTCH npOBo.ll.SlllI.eH
C<t>ePbl pa,QHyca R = 1,0 M. BTOpOH KOlleLt CTep>KHSI YKpenJICH
B LtellTpe C<t>ePbI TaK, IJTO CTep>KeHb MO>KeT Bpalll.aTbCH 6e3 Tpe-
HIIH B .'IIo60J\l HanpaBlleHHH. BCH CHCTeMa nOMem.eHa B 'O,QHO:
pO,QHoe MarHHTHoe nOJIe C HH,QYJ{[.tlIeH B = 0,50 TJI. KorIla
I
E.
,

I
I
Pile. 220 PRC. 221
Me>K.ny C<t>ePOH II KOHLtOM 3aKpelI.7IemH CTep>K!H1 nO.'l.K.'1IOIJIIJIII
HCTOIJHHK TOKa, yro.'1 Me>KlI.Y CTep>KHeM H BepTlfKaJ1blO CTa.1
paBeH ex = 60° (pHC. 220). Onpe.'l.e.1HTb 3D.C HCTOIJHHKa TOKa.
X.5, CTep>KeHb lI..'1HHOi'I 1 CKOJlb3HT no KOJIbLtY, COnpOTliBJlC-
lIIe .Koroporo HHIJTO>KHO Ma.'10 (CM. pHC. 216). KOfITYP Haxo-
IlliTCS! B O;(1I0pO.nHOM MarHHTIIOM nOJle C HH.nYI<LtHei1 B, nepncH-
,QHKYJ!HpHOH nJIOCKOCTH KOJIbLta. Me}f(.'I.Y KOHUOM CTep>KHSI II
KO.'1bLtOI\l nO.'l.K.1IOIJeH HCTOIJHHK TOKa C 3IlC ($. Onpe.neJUITb,
npH KaKoH yrJloBoH cKopocnI Bpam.cHlIH CTep}f(IIH pa3BIiBaeT-
CH MaKCHMaJlbllaH MOm.HOCTb.
X.6. B ceTb ncpeleHi-fOro TOKa C HanpH}f(eHHeM U BKJlIO-
IJeHa cxeMa, COCTOSllllaH H3 .llByx H.neaJlbHbIX .lI.HOIlOB H Tpe x
OIlHHaKOBbiX pe3HcTopOB conpoTHB.1elfHeM R (pHC. 221). Ka-
KaH MOWHOCTb BbIlI.e.rISIeTCH Ha pe3HcTopax?
X,7. Onpe;J,e.1IITb, BO CKo.lbKO pa3 OTJ!HIJaIOTCH aMnJ!HTY,1bI
KOJ!e6aHliH IJepe3 nepHOll.. KOJle6aTeJIbHblH KOHTYP COCTOtfT 1.3
KaTywKH HH,QYKTHBHOCTbIO L = 40 MrH, KOH.n.eHcaTopa CMKO'
CIblO C = 0,25 MKct>. ConpOTliB.'ICHHe KOHT} pa R = 4,0 O!

11 ACT b lJ E T B E P T A $I.
OnTHKCTPOEHHEATOMA
f JI A B A XI. fEOMETPHlIECKMlonntKA.
Cl>OTOMETPIUI
 36. OTpa>KeHHe H 'npeJJOMJ1eHHe CBna
Ha n1ocKoit rpaHIfLle
36.1. Haihll nocTpoeHHe:\1 TOIlKY Ha ropH30HTa.'1bHoit no-
Bep X HOCTJf , B KOropOH OTpa1KaeTCSI JJYIJ, H)l.ynuu1 113 TOIlKJf A
H noc.'1e OTpa1KeHHH OT nOBepXIIOCTII nona)l.aJOw.JfH B TOIlKY B
(pHC, 222). _
36.2. JIYIl CBeTa COCTaBJISIeT C nOBepxHocTbJO CTOJIa yroJ!
ex = 52". KaK Ha)l.O pacnOJJO>KJfTb nJIOCKOe 3epKaJJO, Ilro6b1 Jf3-
l\fellHTb HanpaBJIeHHe JIYlla Ha ropIl30HTa.IJbHoe?
36.3. Ha KaKoii yroJJ nOBeplleTcH JJYIl, OTpa1KeHHblll: OT
nJIOCKOrO 3epKa.'Ia, npn nOBopoTe nOC.'IeD.Hera Ha yroJl ex?
36,4. n.'IOCKOe 3epKaJIO D.BH1KCTCH co CKOpOCTbJO V =
= 1,5 C:\I:C. C KaKOU no :\10.J.Y.'IJO II HanpaB.'1eHIlJO CKOpOCTbJO
D.OJI1KeH )l.BllraTbCSI TOtIelJHbIlt ItCTOtIlIIlK
CBeTa S, IJT06bI era OTpa>KeHlle B nJIOC-
KOllI 3epKa.'Ie ObI,'IO HenO,!J.BmKHbIM?
 A
"
.
oS
9'// /' "/ "
h
o
*8'-
A
*"

Puc. 222
PRe. 223
36,5. 3epKaJ!0 0/1 Bpam.aeTcH C yrJIOBOH CKOpOCTbJO W
(pHC. 223). C KaKOU CKOpOCTbJO ,lJ.BH>KeTCSI OTpa1KellUe TOtIKIf
S? OS = I.
36.6. nJIOCKOe 3epKaJIO )l.BH>KeTCH co CKOpoCTbK> v =
= 2,0 CMic (pHC. 224), TOIJeIJHblH HCTOtIHHK CBeTa S - co
145

CKopoeTblO U = 3,0 nile. C KaKoil CKopoeTLIO II B KaKOI\f lIa-
npaBJ!elllHf .n.BII>KeTeH OTpa>KellUe TOGKH S?
36.7. npe.n.MeT AB II 3epKa.'I0 00' paenoJ!O>KeHbl, KaK YKa-
3aHO Ha pue. 225. f.n.e cJ!e.n.yeT paenoJ!O>KHTb rJ!a3, GT06bI YBn-
.n.eTb H306pa>KeHile Beero npe.n.MeTa U('J!HKOM?
36.8. KaKoBa .n.onii<Ha 6blTb Hall:l.leHblliaH BblCOT3 Bepnl-
KaJ!blloro 3epKa.la, GTo6bl Ge.IJOBCK Mor B HeM BII.n.eTb CBoe 1130-
6pa>KelUlc BO BeCb pOCT, IIC MellHH no.l0>KemH ro.nOBbI?
fA 0, *S
t
-- .. S '
u
t u B
 .
" . 'I' I . I
" 0
PIIC. 224 Puc. 225 Pile. 226
36.9, .ana 3epKana paenOJlO)hellbl no.n. yrnoM ex = 120 0
.npyr K .n.pyry (pIIC. 226) II nepe.n. HHMH nOMew.ell TOGeGHbIU HC-
TOGHHK CBCTa S. r.n.e CJIe.n.yeT pacnoJ/O>KHTb rna3 lIa6J/IO.naTeJIH,
T06bl o.n.HoBpeMellllo BII.n.eTb Bce H306pa>KeHIIH, Jl.aBae:l.lh/e 3ep-
KanaMH?
36.10. CBcTHlllaHeH TOGKa pacnO.'IO>KeHa 118 paccToHHlIII
12 CM OT JlJIIIHH nepeCeGeHIIH nJ!OCIUlX 3epKan, pacno.'10>KeHHblX
noJi. yr.'IOM 30 0 .n.pyr OT Jl.pyra. Ha KaKOM paccToHHHH HaXOJ/.HT-
CH .n.pyr OT .n.pyra )l.Ba nepBblX 11306pa>KeIlHH CBeTHw.eHcH TOGKII
B 3TJfX 3epKaJ!ax?
36.11. .aBa HCTOGmlKa CBeTa SI it S2 Haxo.n.HTCH lIa pac-
eTOHHIIH 41 CM .npyr OT .n.pyra. .aBa nJ!OCKHX 3epKana paenono-
>KeHbI TaK, GTO H306pa>KeHHH eOBna.n.alOT, npHGe..f paccToHHJUI
OT SI .11.0 O.!l.HOro 3epKaJIa HOT S2.n0 .n.pyroro o.nllHaKOBbi H paB-
Hbl 25 CM. Onpe.n.eJIIITb yron Me>K.ny 3epKaJlaMn.
36.12. npe.n.MeT nOMew.eH Me>K.n.y .n.BYMH B3allMHO nepneH-
.nHKYJlHpHbIMH 3epKaJIaMH. CKo.nbKO nonYGaeTCH H306pa>KeHllfi?
nOeTpOHTb IIX. CKo.'1bKO 11306pa>KeIIHii .n.a.n.YT .nBa napa.'1Jle.1b-
IIb1X 3epKaJIa? Haihn pcrnemfe .n.JIH e.'1YGaH, Kor.n.a yron Me>K-
Jl.Y 3epKaJlaMH ex, npHGeM 360ex eCTb ueJlee qHCJ!O.
36.13. nOGeMY OKlla .n.O:\lOB Jl.lleM Ka>KYTcH TeMllblMH, T. e.
TeMHee HapY>KHblX eTeH, .n.a>Ke eeJlH CTeHbl BblKpallieHbI TeMHoii
KpacKOJ1?
36.14. npH nepexo.n.e H3 B03.nyxa B BO,1,y JIyq CBeTa OTKJIO-
IIHeTCSI lIa yron ex. KaK H3:\femITCH 3TOT yroJI, eCJlII nOBepx BO-
J),bl Ha.'JIITb CJIOH l\f8cJIa?
1-16

36.15. B KaKoH cpe.ne JIY1m CBeTa MOI'YT 6bITb pIlBOJIHHerl-
IIbll\lll ?
36.16. noJl, TaKHM yr.'10M .D,OJI)f{eH na..1aTb CBeT Ha fpaHHU.Y
BO,1,a-CTeKJIO, qTo6b1 OTpa1KeHHblH JIyq OKa3aJICH nepneH.D,H-
KYJIHpHblM npeJIOMJIeHHoMY JIyqy?
36.17. Ha rpallHu.y aJIMa3-CnupT na.n.aeT JIyq CBeTa no.n.
yrJIOM 30°, OnpeAeJIHTb yroJi Me1KJI.Y OTpa)f{ellHblMH If npeJIoI\I-
.'1eHHbL\1 JIyqaMH. npH KaKOM HaHMeHbweM 3HaqellliH yrJIa na-
AeHHH JIyq oTpa3HTcH nOJIHOCTb?
36.18. B3allMHo nepneH.llHKYJIHpHble nyqH II.llYT H3 B03-
.llyxa B )f{HJI,KOCTb, KaKoB nOKa3aTeJIb npeJIOMJICHHH 1KI{JI,KOCTlf,
eCJIH OJl.HH JIyq npe.noMJIHeTCSI non
yrJIOM 36°, a .n.pyroH - no.D, yrJIo\1
20°?
36.19. B .zr.HO Bo.n.oeMa r JIy6mfOH
2,0 f>1 B6HTa CBaSl, Ha 0,75 M BbICTY-
natom.aH H3 BO)].bl, HaHTH .lI.J!HHY TeHH
OT CBaH Ha nOBepXHOCTH II Ha .D,He BO-
Jtoe:\la, ecJIH BblCOTa Co.1Hu.a B .zr.aH-
Hbl" MOMeHT paBHa 45°.
36.20. KaKoB Jl.aJIbHeHWHH nYTb JIyqa (pHC. 227, a, 6), na-
.zr.atom.ero Ha nJIOCKYIO rpaHb non} U.HJIHHJl.pa, H3fOTOBJICHifOrO
H3 KBapu.eBoro cTeKJIa?
36,21. Ha Jl.HO cocYJl,a, Hano.'1HeHlfOrO BOJl.OH Jl.0 BbICOTbI
15 CM, nOMelllell TOqeqHblH HCTOqHIIK CBeTa. KaKoro lIaHMellb-
wero Jl.HaMeTpa Henp03paqHYto nJiaCTHHKY HaJl,O nOMeCTHTb Ha
nOBepxHocTIl BO)].bl, qT06b1 CBeT lIa BbIXO,J.HJI H3 lIce?
36,22. Ha6JIto.n.aTeJIb CMOTpHT Ha CBce u306pa1KeHHe B
nJIOCKOM 3epKaJIe, nOJI01KeHHOM lIa .zr.HO cocy.zr.a C BO,J.OH. Ha
KaKOU rJIy6HHe HaxOJtHTCH 3epKaJIO, eCJIH rna3 Jl3XOJl.HTCH Ha
BblCOTe 20 CM HaJl. ypoBHeM BOJl.bl H aKKoMo.zr.HpoBaH H3 paCCTOH-
Hue 60 CM?
36,23. KaKoBa HCTHHHaSi rny6HHa 6acceiiHa, -eC.1H npH on-
peJteneHHH Ha fJI83- no BepTHKaJIbHoMY HanpaBJIeHHIO fJIY-
6uHa ero Ka1KeTCH paBHoH 2,0 M?
36,24. JIyq CBeTa na.!l.a Ha cTeK.1HHHYto nJiaCTHHKY TOJI-
1lI.HHOH 3,0 CM no.zr. YfJIOM 6ft. Onpe.n.e.1HTb Jl.JIHHY nYTH JIyqa
B nJIaCTHHKe. noJt KaKHM yrJIOM OH BblHJl.eT H3 nJiaCTHHKH?
36.25. JIyq naJtaeT lIa nJIOCKOnapaJIJIe.nbHY nJIaCTHHKY
H3 cpnHHTa no,lJ. yrJIOM 45°. KaKoBa TOmu,HHa nJIaCTHt{KH, eCJIH
nyq npH BblxoAe H3 Hee CMeCTHJICH H8 2,0 CM?
36.26. Y npH3Mb1 C npeJIOMHtom.HM yrJIOM 35° O,lJ.Ha rpaHb
nocepe6peH8. JIYII, na,lJ.atoIU.HH 'H8 Jl.pyr}'lO rpaHb no,IJ. yrJIOM
50°, nOCJle npe.nOMJIeHHH H noc.lJe OTp8>KeHHSI OT nocepe6peH-
al


6) I
M
PHC. 227
147

1t0H rpaltH BepHYJlCH Ha3aA no npe}KHeMY HanpalUleHillo. tteMY
paBeH nOKa3aTe.1Jb npe.noMJ!eHHH MaTepllaJIa npH3MbI?
36,27. Ha rpaHb CTeKJIHHHOH npH3MbI nOpMaJIbHO na.J.ae-r
.1}1l CBeTa. OnpeAeJIlfTb- yro.1 OTKJIOHeHHH JIyqa, eCJIH npe.10M-
JIHIOIU.HH yro..l npll3Mbl paBen a = 30°.
36.28. JIYIl CBeTa BblXOA!lT 113 CTeK.i1HHIIOH npll3MbI noJ1. TeM
n<e yrJ!OM, qTO H BXO.zU1T B Hee. 3HaH, TO npeJIOMJIHIOll1.HH yrOJ1
npll3Mbl a = 45°, naHTIl yroJI OTKJ!OHenIlH JIyqa OT nepBoHa-
qa.'1bHoro HanpaBJIeHIISI,
 37. C4JepHllecKHe aepKana H JIlfH3b1
37.1. nOqe'IY D nacToSlw.ee BpeMH na Tp-aHcnopTe npmle-
IISIIOT lie nJlOCKJle, a BbmYKJ!bIe 3epKana?
37.2. KaK onpe.n.eJlIITh B cOJlHeqlll>lil!leHb pa.l\IIYc KpllBJl3Hbl
BorHYToro 3epKaa?
37.3. Ha BbInYK.'1oe 3epI{aJlO na!laeT .1YIl, KaK nOKa3aHO na
pllC. 228. nOCTpoeHlleM lIalfTH !laJlbHeHllHlH XoJt nytla,
o
lL
:
Pile. 228
PHC. 229
37.4. Ha pilC. 229 !laH XoJt nyqa B c4>epHllecKo1 3epKaJIe.
HaHTH nOCTpoeHlleM nO.'1on<eHl1e $:>Kyca 3epKaJ!a.
37.5. CBeTSlIU.aHcH TOtlKa S HaXOJ,IITCH Ha r.'1aBHOH omu-
qecKOIi OCII BorllYTOro 3epKaJla (pI1C. 230, a, 6), $:>KYCHoe pac-
CTOHHHe KOToporo paBHo f.
c) 1 HaHTH rpa4JllqeCKH1 noCTpoe-
{ F S t- s F HHet 11306pan<euHe. KaKoe OHO:
-1 I.. .-t- !leHCTBIITeJIbHoe 1I.'m MHIIloe?
, . 37.6. . Ha pHC. 231, a6
JlalibI nO.10n<eHlle r.'1aBIIOH on-
Tl1qeCKOH oell e<t>epmlecKoro
3epKa'la, CBeTSlIU.eHcH TOtIKII S
II ee H306pa>KemlSl S'. HauTlI nocTpoeHHeM nOJlO>KeHlle u.eJITpa
KpIlBH311b1 H nOJ!lOea 3epKaJla. KaKoe IICnOJIb'30B3HO 3epKaJlo:
BOrJiYTOe 11.'111 BbmYK.'1oe?
37.7. npe!l'leT nOMell1.alOT Ha DCH BOrIl)TOrO 3epKaJla TaK,
qTO Ha 3KpaHe nOJlYlJaeTCH YBeJ1HqenHOe !leifcTBHTe.'1bHoe 1130-
PIIC. 230
148

6p3>l\eHHe. K3K u3MeHlfTCSI 31"0 u306p3>KeHile, ecJm nOJIODHHY
3epK3JI3 33KpblTD Henp03p3IJHOH llmpMoH?
37.8. .lI.oK333Tb, IJTO J],.'1S1 c<PepHIJeCKoro 3epK3J1a npoH3-
Be.D.eHHe paCCTOJlHHH npe.D.MeTa H H30I5pa>KeHHJI .D.O r J1aBHOro
<l><>Kyca BCer.D.a paBHo KB3.D.paTY rJIaBHOrO <l><>KycHoro paccTOSI-
HHH.
37.9. CBeTHaSlcSI TOIJKa Ha\.O.!l.UTCSI H3 paCCTOHHHH Xl =
= 36 CM OT r.'1aBHOrO 4x>Kyca BbmYKJIoro 3epKaJl3, H306pa-
)KeHHe TOIIKH - H3 paCCTOHHHH X 2 = 9,0 CM OT rJlaBHoro <1><>-
Kyca. HaiiTH rJIaBHoe <l><>KYCHoe paccTOSlHlle 3epKaJla. nocrpo-
lI1'b H306pa>KeHUe rmlKH B 3epKaJle.
a)
*3
5J
8)
*s'
*5
-'ItS
*s'
*5'
PIlC. 231
31.10. f.D.e HY)KHO nocraBHTb npeJI,MeT, IITOC5b1 nOJlYIIHTb
.D.eiiCTBHre.'1bHoe H30C5pa>KeHHe B k = 0,50 HarypaJlbHOH BeJlH-
IJIIHbI B BorHYToM c<PepHlIecKoM 3epKaJle, pa,!l.HYC KpllBII31IbI
KOToporo R = 40 CM?
37.11. Ha BOrHyroe 3epKaJIO, pa.D.HYc KPHBH3HbI KOTOporo
R = 30 CM, n3)!.3JOT CXO.D.HIIJ.HeCH J1YIIH CBeTa TaK, 'ITO HX npo-
.D.OJI>KeHHH nepeceKatoTCH B TOtIKe, Haxo,!l.HIIJ.eikSi 3a 3epKaJIOM
Ha paccTOSlHIIH al = 30 CM. Ha KaKOM paCCTOJlHHH OT 3epKaJIa
coi'i.aYTCSI 3TH J1YIJH nOCJIe OTpa>KeHIIJI? BY.D.eT J1H TOIIKa HX ne-
pecelIeHHSI AeHcTBlireJIbHoH?
37.12. CXo.D.SU1.1.HeCSI J1Y'lH na,!l.atoT Ha BblnYKJIoe 3epKaJIO
TaK, lITO liX npO.D.OJI>KeHHSI nepeceKalOTCJI Ha OCH 3epKaJIa Ha
paCCTOSlHIIH al = 30 CM. nocJ\e OTpa>KeHHSI or 3epKaJI3 J'1YIIH
paCXO;J.SlTCSI raK, lITO HX npO.!l.OJI>KeHHSI nepeCeKaJOTCSI B TO'lKe,
OTCTOHeH OT 3epKaJIa Ha paeCTOSlHHH a 2 = 60 eM. OnpeAe-
J1I1Tb pa)l.Hye KpllBH3Hbl 3epJ<;aJl3.
37.13. npeJI,MeT HaXOAHTCSI Ha paccToSlHlfll a 1 = 30 CM OT
BorHYTOI"O 3epKaJla. Ero H30C5pa>KeHHe B k = 1,5 pa33 OOJIb-
me cat.lOro npe.D.MeTa. OnpeAeJlHTb p3ccroSlHHe 1130C5pa>KeHIISI
no epKaJla H pa;J.Hye KPHBH3Hbl 3epKaJl3,
37.14. BorHyroe 3epKaJIO .D.aer 06paTHoe Ii YBeJlHlIeHHoe
B k = 4 pa33 H30C5pa>KeHHe npeJI,Mer3. OnpeAeJlHTb rJIaBHoe
<PoKYCHoe paCCTOHHHe 3epKan3, eCJIH paccroSlHHe Me>K.D.Y npep'-
eTOM H 11300pa>KeHHeM ero paBHo I = 90 CM.
149

37.15. H306pa>KeHHe, .n.aBaeMoe BorHYTblM 3epKaJIOf, n
k 1 = 3 pa3a MeHbllJe npeJI.MeTa. ECJlH npeJI.MeT -nepeJI.BHHYTb Ha
pacCToslHHe b = 10 CM 6J1H>Ke K 3epl<aJIY, TO H306pa>KeHlie
6y.n.eT MeHbllJe npe.ll.MeTa TOJIbKO B k 2 = 2 pa3a. l.leMY paBHo
rnaBHoe KYCHoe paccToflHHe 3epKana?
37.16. Ha paccToflHHH a = 8,0 CM OT BbmYKJIOrO 3epKa-
JIa nOMem.eHa TOHKaJl nJlOCKaH CTeKJlHHHaSi nJ!aCTIUlKa. 3a
nJiaCTHIiKoH Ha paccTOS1HHH b = 12 CM OT Hee nOMew.aJOT TO-
qelJHblH HCTOqHHK CBeTa. npH
3TOM H306pa>KeHHE', JI.aBaeMoe
J!yqal\fH, OTpa)f(eHHbl!\!H OT ne-
peJI.HeH nOBepxHocTH nJiaCTHH-
KH, COBnaJlO C H306pa)f(eHHeM,
.naBaeMblM nyqaIH, OTpa>KeH-
HblMH OT 3epKaJ!a.Onpe.n.e.'1HTb
pa.n.HYc KPHBH3Hbl 3epKaJ!a.
31.17. Ha rJIaBHOH onnlqe-
CKOH OCH BorHYToro c<t>epuqe-
CKOro 3epl<aJIa paJI.Hyca R =
PIIC. 232 = 50 CM nOMew.eH TOqeqHbll1
HCTOqHHK CBeTa S Ha paCCTOH-
HHH al = 30 CM OT 3epKaJ!a. Ha KaKOM paCCTOHHHH OT HCTOq-
HUKa Ha.n.o nOCTaBIITb nJlOcKoe 3epKaJIO, lfr06bl nY"IH, OTpa-
>KeHHble BorHYTblM, a 3aTeM nJIOCKIIM 3epKaJIOM, BepHYJIHCb
B TOqKY S? ,
37.18. Ha pllC. 232, a-if! .n.aH nyq, npOllJe.n.IlJHH CKB09b
J1I1H3Y C KYCHblM pacCToHHHeM f. nOCTpOHTb Xo.n. nyqa JI.O
.'1HH3bl.
37.19. Ha pHC. 233, a, 6 .n.aH XOJI. nyqa B JIHH3e. Haihn
nocTpoeHHeM nOJlO>KeHHSI rJIaBHblX KYCOB .'1HH3bl.
++
B  _.
-r-rr
+-
PHC. 233
PIIC. 234
37.20. Ha pHC, 234. a. 6.n.aH XO,lJ. JIyqa 1 B nHH3e. HaHTif
nOCTpoeHHeM XO,lJ. nyqa 2.
37.21. Ha pHC. 231, a-e .n.aHbI nOJIO>Kelille rJlaBHOH OnT"-
qeCKOH OCII JIHH3bl. CBeTHw.aflCSI TOqKa S " ee H306pa>KeHHe S'
150

HaHTIi nOCTpoeHHeM nOJIO>KeHlle u.eHTpa JIHH3b1 H ee cf>oKYCOB.
KaKHe 31'0 JIIIH3bl?
31.22. KaK HaJJ.O paCnOJlO>KHTb .ll.Be JIHH3br, IIT06I napaJI-
JIeJIbHble JIYIJH, npoHJJ.B lIepe3 JIHH3bl, OCTaJIHCb napaJIJIeJIbHbI-
r.1H? PaccMOTpeTb JJ.Ba CJIYllaB: I) JIHH3b1 c06HpalOUI,lIe; 2) OJJ.-
lIa JIHH3a paCCeHBalOUI,aB, llPyraB - C06HpalOUI,af!.
31.23. 1\\O>KHO JIH C nOMow.blO llBoHKoBbmYKJIOH CTeKJIHII-
1I0U JIHH3b1 nOJlY'lHTb JJ.eHcTBHTeJIbHoe H306pa>KeHHe?
37.24. lLnH H3rOTOBJIeHHf! 11JI0CKoBbmYKnoH JIHH3b1 C rnaB-
HblM cf>oKYCHbiM paccToHHHeM / = 10 CM 6bIJI HCnOJIb30BaH
$'IHIITrJIac. Onpe.n.eJIHTb paJJ.HYc KpHBII3Hbl BblnYKJIOH nOBepx-
IIOCTH JIHH3b1.
37.25. cI>oKyclIoe paccToflHne JIHH3bl, c.!J.eJIaHHoH H3 $rIHHT-
rJIaca, B k = 1,6 pa3a MeHbllle, lIeM Y TO'lHO TaKoH >Ke no cf>op-
Me JIHH3b1, CJJ.eJIaHHOH H3 nJIeKCHrJIaca. HaHTH nOKa3aTe.'Ib
npeJIOMJIeHHH nJIeKCHrnaca.
37.26. KaKoBbl paJJ.lIycbl KPHBH3Hb! CTeKJISHlHOH BomYTo-
BblnYKJIOH pacCeHBalOUI,eH JIHH3b! C onTHllecKou cHnoH D =
= 2,5 MTP, eCJIH O,AHH H3 HHX OO.1bIIIe !l.pyroro B k = 1,6 pa-
3a?
37.27. KaK H3MeHIITCfI cf>oKycHoe paccTOsHlIIe cOOHpalOUI,eH
JIHII3b1, C.lI.eJIaHHOH H3 KBapQeBoro CTeKJIa, eCJIH ee nOMeCn!Tb
B BO!l.Y?
37.28. 1\\HHMblH HCTO'lHHK HaXOJJ.HTCfI 8 rJIaBHOM <PoKYCC
/ C06HpalOUI,eH JIHH3b1. f!l.e HaXO!l.HTCfI ero H306pa>KeHHe?
37.29. npe.!J.MeT HaXOJJ.HTCfI nepeJJ. pacCeHBalOw.eH JIHII30H
lIa paccToHHHH 4/. Ha KaKOM paccToflHHH OT JIHH3b! nOJIY'lHTCfI
MHHMoe H306pa>KeHHe H BO CKOJIbKO pa3 0110 oYJJ. MeHbllle ca-
!.mro npC)l.MeTa?
37.30. JIHH3a JJ.aeT YBe.'1H'leHlle k = 3,0 npe.ll.Mera, Haxo-
JJ.SIUI,erocfI Ha paccToflHHH a = 10 C\I OT Hee. HaHTIi cf>oKYCHOC
paccTcHHHe JIHH3b1.
37.31. PaccToHHHe OT npe,A.\feTa JJ.O 3KpaHa 1 = 5,0 M.
KaKoH OnTH'leCKOH CHJIbl H3,!{0 83HTb JIHH3Y H rJJ.e ee CJle!l.yer
nOMecTHTb, IlTOObi nOJlY'IHTb H306pa>KeHlle npe..'l.MeTa, YBeJIIf-
lieHHoe 8 k = 4 pa3a.?
31.32. TO'leIlHblH IfCTOIIHIIK CBeTa HaXOJJ.HTCfI Ha rJIaBHOH
OnTH'lecKOH OCH c06HpalOw.eH JIHH3bl. KorJJ.a OH nOMeUI,aJIC'f! B
TO'lKe A (pHC. 235), ero H306pa>KeHHC HaXOJJ.HJIOCb 8 TO'lKe B,
a Kor!l.a HCTO'lHHK nOMecTHJIH 8 TO'lKY B, ero H306pa>KeHHe
OKa3aJIOCb B TOIJKe- C. 3Hafl, liTO AB = 10 CM H BC = 20 CM,
HaHTH <PoKYCHoe pacCToflHHe JlHH3b1.
31.33. npe)I.M H 3KpaH HaXO,AflTCfI Ita pacCToflHHH 1 =
= 1,0 M JJ.Pyr OT JJ.pyra. nepeMew.afl Me>KJJ.Y HHMH c06upalO-
151

ll.I.YIO JIHH3Y, no.'l)'lIaIOT ,ABa nOJIO>KeHHH, pa3,!J.e.neHHblX paCCTOSl-
HHeM a = 60 CM, npJl KOTOpblX OHa ,AaeT lIeTKoe Jl306f'a>KeHlIe
npe,A:\leTa lIa 3KpaHe. HauTiI cf>oKYClloe paCCTOslHHe JIHH3bl.
37.34. JIHH3b1 J H 2 C,AeJIaHbl H3 O,AIIOro copTa CTeK.'la
(pHC. 236). HauTH OnTHlleCKYIO CHJIY JIHII3bl 1, 3HaSl, liTO JIHH-
3a 2 HMeeT OmHlJecKYIO CHJIY Dz = 2,25 .n.mp.
37.35. BorHyroe 3epKaJIO pa.n.Hyca R = 53,2 CM HanOJI-
HeHO Bo.n.oiL Onpe.n.e.nHTb cf>oKYCHoe paccToHHHe 3Toii CHCTeMbi.
37.36. JII11I3a C cf>oKYCHbiM pacCTCHHHeM f = 60 CM DnJIOT-
IIYIO npHJIeraeT K nJIDCKO:\lY 3epKaJIY. Ha OnTHqecKoH DCH .'mH-
"fJ C
,. .

-1
s
'7"
,
PIIC. 235
PIIC. 236
PIIC. 237
3b1 Haxo,).IITCH CBeTHll.I.aSlCSI TOliKa S Ha paCCTOHHHH al = 15 CM
OT JIHII3b1. KaKoe H306pa>KeHlle ,AaeT 3Ta CHCTeMa H r.n.e OHO
HaXO!l.HTcH?
37.37. JIHH3b1 C OnTHlJeCKH:\I1I CHJIaMH 5,0 H 2,5 ,Amp Ha-
XO.n.HTCSI Ha paccToHHIUI 0,90 M ,APyr OT ,Apyra. KaKoe H306pa-
>KellHe ,AaCT 3Ta CHCTe.la. eCJIH npe)I.MeT paCnOJIO>KHTb Ha pac-
CTOHHHH 30 CM nepe.n. nepBoH JIHH30H?
37.38. Ha paCCTOHHHJI 0,50 M nepe.n JIHH30H C cf>oKYCHblM
paccToHHHeM 30 CM nOMell.l.eH npe.D.MCT BbICOTOH 1,5 CM, BTcpaH
JIHH3a C cf>oKYCHbIM pacCToHHlleM 20 CM pa'cnc.'lO>KeHa Ha pac-
CTOHHHH 45 CM OT nepBoH. r.n.e HaXO!l.HTCH H306pa>KeHHe npe.u.-
MeTa? KaKOBa BblCOTa 3TOro H306pa>KeHHH?
37.39. CneBa OT JIHH3bI C CnTHlleCKOH CHJIOH 2,0 .n.mp Ha
paccToHHlfI1 25 CM OT Hee Ha>-,o!l.ll'rCH CBeTHlU,aHCSI TOqKa, Cnpa-
Ba Ha TaKOr.! 1Ke paCCTOHHHH nOCTaBHJIH MDCKoe 3epK8JIO nep-
neH.n.HKYJISlpHO DCH JIHH3bI. Ha KaKOM paCCTOHHHH OT JIHH3bI
c06epeT Jiyqll nOJIyqeHHaSi cHcTeMa?
37.40. K BblnYKJIOMY c<J>epHlJeCKoMY 3epKaJIY npll..'IO>KeHa
CTCKJISIHHaSl JIIfH3a (pHC. 237). nepe.n. 3THM 3epKaJIOM Ha pac-
eTOHHHH Ul = 40 CM OT Hero nOMelU,alOT CBeTHll.I.}'IOCH TOIJKY S.
311aH, liTO H306pa>KeHlle TOIIKH HaXO!l.HTCH Ha paCCTOHHHII a 2
= 15 CM OT 3epKaJIa, onpc;r.e.'lIlTb pa.n.IIYc ero KpHDII3HbI.
152

 38. OnTHqeCKHe npH60pbl
38.1. BbIcoTa 3!1.aHHH Ha 4KrronJIeHKe paBHa h = 36 MM,
cfoK CHoe paCCTOHHHe 06'beKTHBa annapaTa f = 5,0 CM, Onpe.
;J.e.'1HTb BbiCOTY 3.D.aHHH, eCJIH 4>o'rorpacp HaXO;J.HJICH OT 3;IaHHH
Ha paCCTOHHHH a = 50 M.
38.2. MO>KHO JIH c$>TorpacpHpoBaTb MHHMoe H306pa>KeHHe?
38.3. KaKaH 3Kcn03HLlHH .D.OnYCTHMa npn C'beMKe BeJIOCH-
ne.1J.HOH roHKH, eCJIH Ha HeraTHBe pa3MbITHe H306pa>KeHlUI He
.'I.o.,l>KHO npeBblUIaTb I1x = 0,50 MM? CKOpOCTb BeJIOrOHl.I.!.HKa
v = 36 KM/q. cI>oTorpacpJlpOBaHHe npOlI3Bo.D.HTCB C paccTOHHHB
a = 1 ° M annapaToM C OnTHqeCKOH CUJIOH 061>CKTI'lBa D =
, = 20 .D.mp.
38.4. DpH naJl60.1bllle:>'f Y.D.aJIeJIlfll 06'beKTHDa OT nJIeHKH
<fx:>TOannapaT .D.aeT pe3KHe CHHMKH npe)I.MeTOB, HaXO.D.Hl.I.!.HXCH
'13 paccToHHHH a = 3,0 M. C KaKoro HaHMeHblllero pacCToHHHH
'dOJKIIO 6Y.D.eT nOJIYllaTb pe3KHe CHHMKH, eCJIH Ha 06DeKTHB Ha-
ca,nHTb c06HpalOlllYIO JIHH3Y C OnTHQeCKOH CIIJIOH D = 5,O.u.nTp?
38.5. C nOMolllblO <fx:>ToannapaTa C 06'beKTHBOM, OnTHlJeCKaH
CH.rla KOTOpOro D = 10 .D.mp, <fx:>Torpa$HpYJOT npe)I.MeT, Ha-
'(O.D.S1IllHikH Ha .u.He BO.D.oeMa rJIy6HHoH hI = 1,2 M. KaKoBo
paccToHHHe Me>K.!J.Y 06'bCKTIIBOM H nJIeHKoH? 06'beKTHB pacno-
Ion<eH Ha paccToHHHH h 2 = 0,50 P,f OT nOBepxHocTH BO.1J.bI.
38.6. 06'beKTHB npoeKLlHoHHoro annapaTa HMeeT <fx:>KYCHoe
paccTomme f = IS CM. Ha KaKO:>'! paCCTOHHHH HY>KHO no-
..eCTHTb .D.Han03I1THB pa3MepoM 9 X 12 CM OT o6DeKTHBa, IITO-
6bI nOJIYIJHTb Ha 3KpaHe H306pa>KeHHe pa3MepOl\f 45 X 60 CM?
38.7. KaKoe YBe..1HlleHlle MO>KHO nOJIyqHTb C nOMOIlI,blO
:ipoeKLlHOHHOro annapaTa, 06'beKTHB KOTOporo HMeeT rJIaBHOe
t>oKYCHoe paccToHHHe f = 20 CM, eCJIH 3KpaH HaXOJUITCB Ha
paccTOHHIiH a = 6,0 M OT 06'bCKTHBa?
38.8. PHCYIIOK B KHHre JfMeeT BbrcOTY h = 5,0 CM, a Ha
- <paHe h' = 0,95 M. Onpe.D.eJIHTb <fx:>KycHoe paCCTOHHHe 06'bCK-
1 fBa ,mll;J.llaCKona, eCJIH paCCTOHHHe OT 06'bCKTHBa .D.O 3KpaHa
a = 4,0 M.
38.9. KaK Jf3:\-leHIITCH KpHBH3Ha xpycTaJIHKa rJIa3a, eCJIH
JepeBecTH B3rJIfI.D. C 06JIaKOB, nJIbiBYIllHX B He6e, Ha npOe3>KalO-
YIO 6J1H3KO aBToMalllHHY?
38.10. nOlJeMY, OTKpblB r.lJa3a no.1J. BOJJ.OH, MbJ BJI.D.IIM TOJIb-
) HeSiCHbIe OqepTaHHH npe.D.MeTOB, a B MaCKe .u.JlH HbrpHHIIH
rpe.zweTbI BH.!J.HbI COBepIlleHHO OTqeTJIIIBO?
38.11. BbJqHCJIHTb HaHMeHbIllee pacCToHHHe Me>K.!l.Y .u.eJIe-
J HHj\1If UIKaJIbi Jl3Mep1lTeJI!>Horo npJluopa, KOTOpLJe 6bI OTtleT.1H-
153

......
BO pa3nHIJanHCb C paCCTOHHHH I = 5,0 M. HaHMeHbllllfH yro.,
3peHHH npUIISlTb paBHblM ex = I'.
38.12. KaKoH He,AOCTaTOK apeHHH y qenOBeKa. ,AJlH KOTO-
poro paccToSlHHe nauJlyqlllerO apeHHSI 12,5 CM? KaK OT He-
,AOCTaTOK M01KHO HcnpaBuTb?
38,13. J];ml nHKBH;J.aLlHH He,AOCTaTKa 3peHlfH lJeJlOneK nonb-
3yeTcH OIJKaMH OnTHlJecKoH CHJlbI +2.75..nnTp, KaKoB 6J111>1\-
HIf" npe!l.eJl aKKOMO,AallHH rna3a ,AanbH030pKoro qenOBeKa?
38.14, npe,AeJlbf aKKOMO.ll.allHH Y 6nH30PYKOro qeJIOBeKa
nemaT MemJ1Y 10 H 50 CM. Onpe,AenHTb Ha KaKOM HaHMeHbllleM
paCCTOSlHHII 3TOT qeJlOBeK ClofOmeT IJHTaTb KHHry, ecnH Ha,n.eHeT
OIJKH, C nOMOlli.blO KOTOpbIX OH XOpOlllO BH,AHT y,AaneHHLIe npe;J.-
MeTbI.
38.15. npH HeKOTopoM non01KeHHH npe,!U\leTa nyna ,Aa.'Ia
qeThIpeXKpaTHoe YBeJlHlJeHHe. KaK H3MeHHTCR 3TO IJHCnO, ecnu
paccToSlHHe OT npe.ll,MeTa ,AO nynbI YMeHblllHTb B 1,5 pa3a?
38.16. Onpe,AeJIHTb OnTHIJecKYIO cHny nynbI. ,AalOUleil
.D.BYKpaTHoe YBeJIHqeHHe.
38.17. KaKoMY apHTe.7I1O npHXo,AHTCH 60nbllle pa3.!J.BHraTb
Tpy6KY TeaTpanbHoro 6HHOKJlSI - ,AaJlbH030PKOMY HnH 6J1H-
30PYKOMY?
38.18. 3pHTenbHaH Tpy6a Kennepa c <PoKYCHblM pacCToSl-
HHeM 06'beKTHBa f = 24 CM YCTaHoBneHa Ha 6ecKOHeqHOCTb.
Ha KaKoe paccToSlHHe Ha,AO nepe,ABHHYTb oKynHp Tpy6b1, 1ff06bI
HCHO BH,AeTb npe,AMeThI Ha paccTOHHHH U = 10 M?
38.19. Tpy6a ram-lneH (c paCCeHBaIOw.eH nHH30H B KaqecTBc
oKynSlpa) ,AecHTHKpaTHoro YBeJIHqeHHH npH YCTaHOBKe Ha
6ecKOHeIJHOCTb HMeeT ,AnHHY 54 CM. Onpe,AeJIHTb cf>oKYCHbIe
paCCTOSlHHH 06'beKTHBa H oKynHpa. Ha KaKoe paCCTOHHH
HY>KHO CMecTHTb oKynSlp, QT06b1 IJeTKO BH,AeTb npe.zu,feTbI, Ha-
XO,ASllli.HeCH Ha paCCTOHHHH 60 M?
38,20. TenecKon. o6'beKTHB KOToporo HMeeT cf>oK)'cHoe
paccToSlHHe 1,0 M, a oKynHp - 5.0 CM, HaBe,AeH Ha JIYHY, If
ee H306pameHHe C<PoK}CHpOBaHo Ha 3KpaH, pacnOO>KeHbl"
Ha paccTOHHHH 25 CM OT oKynHpa. Onpe,AeJlHTb paccTOHHIC
Me>K.!J.Y 06'beKTHBOM H oK)'nSipoM, a TaIOKe ,AlfalofeTp 11306pa>Kc-
HHH. ecnH yrnoBOH pa3Mep JIYHbl 30'.
38.21. 1'13 acrpoHOMHtlecKoH Tpy6bI. y KOTOpOH <PoKYCHoe
paccToHllue o6'beKTHBa f = 2,5 M. BblHynu oKynSip H npocTo
rna30M paccMaTpuBalOT H306pa1KeHHe y,AaneHHoro npe.zu,feTa.
KaKoBo YBenHlJeHHe TJ>y6bf B 3TOM cnyqae?
38.22. MomHo, nR nOJlYIJHTb Ha 3KpaHe H306pa1KeHHe, ,na-
BaeMoe MHKpOCKOnO}I? Te.,ecKOnOJ\l? liTO HY1KHO ,AJlSI oro c,Ae-
naTb?
154
I

38.23. 4>oJ<ycHoe paccToHHHe o6ceKTHBa MHKpocKona
B.O MM. OJ<YJIHpa - 4.0 C'-t. npe.lMeT HaXO,lUITCH OT o6ceKTHBa
fla paccToHHIIH 8,5 M'\f. Onpe.n.enHTb JIHHeHHoe YBenH'lellHe
tdllKpOCKona ,lI,JIH 1I0pMaJIbHOrO rJIa3a H paCCTOHHHe Me>K.lI.Y o6'b-
eKTUBO\f H oKynHpoM,
38.24, J\\IIKpocKon HMeeT ,nJIHHY 20 CM. cI>oKycHNe pac-
CTOHHIIH 06ceKTHBa H oKynHpa COOTBeTCTBeHHO paBHbI 0,40 CM
H 2,0 CM. Ha KaJ<OM paccroHHHH aT ol5'beKTHBa Ha,no nOMeTHTb
npe.zu,feT, IlT06bl ero OTlleT JIIiBO BH,neTb lleJIOBeKY C HopManbHblM
3peHHeM?
38.25. Y MHJ<pocKona .'I.'JHHa Tyl5yca 18.9 CM. OmHlleCKaB
CH.lJa ol5'beKTliBa 250 ,nmp H oKynHpa 20 ,nmp. PaccToHHlle OT
npe,nMeTa .'1.0 ol5'beKTIlBa .J,1 MM. HaHTH JIHHeHHoe yBeJIllqeHHC
MIIKpOCKona.
 39. cJ>oTO!\leTpHB
39.1. nOHCHHTb pHcYHKaMH, nOlleMY B non,neHb OCBeIll.CH-
nOCTb nOBepxHoCTIf 3eMnli HaH60nbllJaH.
39.2. .rIaMna, CIiJIa CBCTa KOTOpOH I = 25 K.n., YKpenJICna
lIa nCTOJIKe nHqrra. Onpe,neJIHTb CBeTOBOfi nOTOK, na,nalOll.I.Hit
liB non H CTeHbI .'mqrra.
39.3. Ha,n LleuTpoM Kpyr.'lOro CTO.'la pa,nHyca R = 60 CM
lIa BbiCOTe h = 0,80 M BHCHT JIaMna CHJIOH CBeTa I = 100 K,!J..
Onpe,nenHTb OCBelll.eHIIOCTb B LleHTpe H Ha KpalO CTona.
39.4. J1aMny cHnoH CBeTa I = 100 K,n. BHCHUlYIO Ha.n. CTO-
JlOM Ha BblCOTe h = 1,2 M, onYCTHJIH H no"lYQHJIH OCBelll.eHHOCTb
no;}, JlaMnOH E = 100 JlK. Ha KaKYIO BbiCOTY onycTHnH JlaMny?
39.5. Ha CTCJl6e BbiCOTOH h = 6,0 M BHCHT <J>onapb. CHJIa
CBeTa KOTopOro I = 500 K.n.. Ha KaKOM paccToBHHH OT cTo.1J6a
OCBelll.eHHOCTb nOBepxHocTH 3elnH E = 3,'0 JlK?
39.6, Ha KaKOH BbiCOTe cne.n.yeT nO\leCTHTb JlaMny Ha
l.I.enTpOM KpyrJlcro CTO.la, IJT06bl Ha KpaHX cTona nOJlYIlHTb
\ian60JlblllYIO OCBelll.eHHocTb?
39.7. CBeTH.lJbIlHK H3 MaTOBoro CTeK.la HMeeT <PoPMY llJapa
,nHaMeTpoM 20 CM. CH..la CBeTa HCTOIlHHKa 60 K.n.. Onpe.n.enHTb
IJWlHbIH CBeTOBOH nOTOI< H CBeTHMOCTb CBeTHnbHHKa.
39.8. CBeTHnbHHK, HleIOUlHH <J>oPMY lllapa pa.lI;Hyca 10 CM,
Haxo.lI;HTcB Ha pacCToHHHH 0,5 M or CTOJIa. CBeTHMOCTb CBe-
TH.'lbHHKa 4,0 . 10' nK. KaKoBa OCBC1lleHHOCTb cTona Hcnocpe.n.-
CTBeHHO no.lI; CBeTHnbHHKoM?
39.9. OcBC1lleHHocTb nosepxHocTH, nOKphIToii llepHblM CYK-
110\', paBHa E = 120 JIlL CBeTHIOCTb OJ1HHaKOBa BO Bcex Ha-
]55

npaBJIeHHSlX H paBHa R = 6,0 JlK. OnpeJJ.eJlIITb K03qxlJlfl.llleHl'
nOrJlO1l\.eHHB cYKHa.
39.10. lI.Be JlaMnbl CHJlOH CBeTa 25 H 40 KJJ. HaXOJJ.BTCB AP}-r
OT Apyra Ha pacCTOHHHH 1,2 M. rAe HaAo nOMecTHTb f}x>TOMeTPI1-
qeCKHA 3KpSH Me>KJJ.Y mu.m, QTo6b1 OCBell.leHHOCTb 6bIJIa 0JJ.11-
HaKoBoA C TOA H ApyroA CTOpOHbl?
39.11. Ha paccTOBHHH I = 4,0 M JJ.pyr OT Apyra H Ha BbICO-
Te h = 3,0 M HaA 3eMJIeH BHCsrr JJ.Ba f}x>HapB CHJlOH CBeTa I =
= 200 K;!1 Ka}f{.lJ.blA. OnpeJJ.eJIHTb OCBeIlleHHOCTb noJJ. f}x>Hap'eM.
39.12. npH neqaTaHHH f}x>rorpaiPHlJeCKoro CHIIMKa Heranm
OCBe1l\.aJlCH JlaMnoA, nOMeIlleHHoH Ha pacCToHHHH r = 0,60 M,
B TeIJ:eHHe 1"1 = 9 c. KaK HaJJ.O H3MeHHTb BpeMB 3KCn03HI.{IUI,
eCJIH JlaMny npHMH3HTb Ha I = 20 CM?
39.13. Ha JIHH3Y cp0r006'beKTIIBa CeJIa Myxa. KaK 3ro QT-
pa3HTcB Ha KaqeCTBe cHHMKa?
39.14. J],HaMeTp OODeKTHBa TeJIeCKOna d 1 = 75 MM, a Alla-
MeTp 3pa'lKa rJla3a d z = 3,0 MM, Bo CKO.'IbKO pa3 3TOT TeJIeC}\OIl
YBeJIHqHBaeT BHJJ.HMYIO HpKOCTb 3Be3,!{?
39.15. Ha KHHo3KpaH pa3MepoM 5 X 3,6 M H3 OODeKTIIBa
KHHoannapaTa na)l8eT CBeTOBOH nOTOK 1,8 . 10' JIM. OnpeJJ.e-
J1HTb OCBell.leHHOCTb H CBeTHMOCTb KHH03KpaHa, ecnH K03<M>il-
I.{HeHT OTpa)KeHHJI 0,80,
39.16. npoeKI.{HOHHbIH annapaT HMeeT 06'beKTHB C <PoKYc,
HblM paccroBHHeM f = 20 CM. J],Han03IITHB pa3MepOM 3x4 CM,
Haxo.a.H.Il\HHCSI Ha paccToHHIIH a = 20,6 CM ox JlHH3b1, npcayc-
KaeT CBeTOBOH nOTOK <D = 12 JIM. OnpeJJ.eJIHTb OCBell.leHHOCTJ
H CBeTHMOCTb H306pa)KeHHSI AUan03IfTHBa, Ha 3Kpane, ecaa
Ko3<M>Hl.{lfeHT OTpa)KeHIfJl paBeH p = 0,75.
39.17. CHaqaJla clx>TorpaiPHpYIOT Aa.'lbHIIH 06'beKT, nOl.)".1
6JIIf3KHH. KyJJ.3 HaJJ.O nepeMecTHTb 06beKTHB? KaK Jla..'.lO 113'-
HliTb 3KCn03HI.{HIO?
39.18. Ha HeKoTopoM paccToHHHlf OT TOqelJHOro HCTOqHIfKa
CBeTa nOMell.leH 3KpaH. KaK H3MeHHTCH ocBew.eHHOCTb B l.{eHT-
pe 3KpaHa, ecnH no JJ.pyrylO CTOPOHY OT HCTOqHHKa Ha TaKO\1
)Ke paccToHHHH nOCTaBHTb nJlOcKoe 3epKaJIo?
39.19. B rJIaBHOM f}x>Kyce BorHYToro c<J>ePUqeCKoro 3epK'"
.'1a C paJJ.HycoM KPHBH3HbI R = 1,0 M HaXO,!{IfTCH TOqe"iHblH II"
TOIJHHK CBeTa. OnpeJJ.eJIHTb oCBew.eHHOCTb B l.{eHTpe 3Kpa1l3.
pacnOJIO)KeHHcro Ha paCCTOSlHHH I = 2,0 M OT 3epKaJla, ec..1Jl
OCBe1l\.eHHOCTb B 3TOM MeCTe B OTcYTCTBHe 3epKaJIa Fo = 40 Jlh.
39,20. JIaMnO'lKa CHJIOH CBeTa 10 = 40 KJJ. HaXOJJ.lfTCH U3
paccTOHHHI:I al = 30 CM OT JIJ!}{3b1 C clx>KYCIV>IM paccToHHIl.?',1
f = 50 CM, KaKaSi 6Y.!.leT CHJIa CBeTa 3TOH .'IaMnbl B pe3YJIbT8 Ie
JJ.eHcTBHSI J1HH3L1?
156

1+-1
fDt
PRC. 238
Pile. 239
39.21. TotJeqHblii HCTOtJHHK S oeBeIIJ.aeT 3KpaH C nOMOIIJ.blO
JUlH3b1 (pHC, 238). OnpeJI;eJIHTb OCBeIIJ.eHHOCTb 3KpaHa B TOIJKe
M, eCJIH CHJla CBeTa HCTOqHHKa J = 25 1<)1, OnTHqeeKaH CHJla
J1HH3bI D = 1// = 2,0 JI;nTp, paccToHHlle OT HCTOIJHHKa )10
.1HH3bI Ul = 0,80 p.r, paccToHHHe OT J1HH3H JI;O 3KpaHa I = 1,0 M.
3a.ll.aIJu K rJlaBe'XI
XJ.I. lJeJIOBeK paceMaTpHBaeT 3paqOK CBoero rJla3a B nJIOC-
KOM 3epKaJIe TOJIIIJ.HROii d = 1,5 CM Ha p3ceToHHHH H3HJIY'llllero
3peHHH. Ha KaKOM paccToHHIUJ OT 3epK3J1a paenOJlo:meH rJIa3
'IeJIOBeKa?
XJ.2. Ha ropHblX )l.oporax H B ropollax C Y3KHMII ymlltaMIl
y nOBopoTOB IIHOr,D.a yeTaHaBJUmalDT BbrnYKJIbIe 3epKaJIa, On-
pe.ne..lIlTb, Ha CKOJIbKO YBeJIHqllBaeT yroll 3penHB 3epKaJlO, .nlla-
MeTp- KOToporo paBeH paJI;HYcy ero KPHBH3HbI, no cpaBHeHHID
C nnOCKHM 3epKaJIOM Toro :me .nHaMeTpa.
XJ.3. Ha B03JI;yxe y aKBaJlaHrnCTa B MaCKe yrOJl o63opa
= 110°. Onpe.neJIHTb yrOJl o63cpa Y aKBaJl311rlICTa B Bo.ne.
XIA. OI>epllqecKoe 3epKaJIO H JIIIH3a 3aKpblTbI nC.1OCKa-
t.fH 6YMarH. JIyqH, na.nalOIIJ.lle II OTpa)l{eHHble OT 3epKaJIa, no-
K33aHbI Ha pHC, 239, u; npe.ZlMeT H ero H30opa:meHHe B JIIIH3e
nOKa3aH Ha pHC. 239, 6. Onpe.neJIHTb nOCTpoeHHeM nOJIo:me-
HUB H Bce xapaKTepHCTIIKH 3epha.'1a H J1H, H3bl
X1.5. .lI.BoHKOBblnYKJIaH J1HH3a C <J>oKYCHbIM paCCTOHHHeM
F = 10 CM C03.naeT H300pa)l{eHHe TOqe 1 tHoro HCTOQHHK3, pac-
nc.'10:meHHoro Ha paCCTOHHHII b = 2,0 CM OT r.1aBHoit OnTli1:leC-
ROU OCH H d = 28 CM OT J1HH3b1. 3a JIHH30ii nOMelll.alOT nJIOCKOe
3epKaJIO TaK, 'ITO arpa:meHHl>le OT 3epKaJIa JIyqH nocne npo-
X.on<.neHJlB nHH3bl C03,u.alOT H30opa:meHlle, COBna}1alOllI.ee C HC-
rOqHHKOM. Ha KaKOH yrOJI HY)l{HO nOBepHYTb 3epKano BCKpyr
OCII, npoxoJI;HllI.eii Qepe3 rotJKY nepecetJeHHB 3epKaJla C rnaBHoii
nTHQeCKOit OCblO JIHH3bl H nepneHJI;IIKy.'1HpHOii nJlOCKOCTH. B
KOTOpoii JIe)l{aT HCTO'lHHK H rJI3BHaH OnTllqeCKaB oeb, 'IT06hI
306pa:meHHe, paHee COBna)1aBlllee C IICTOtJHHKOM, CMeCTHJIOCb
lJa U = 2 CM JI;a'lbllle OT J111113b1?
157 .

X1.6. ECJIJI CJ1C>KJlTb BMeCTe .rnm3br 113 TeJIeCKOna, .nalo-
w.ero YBenli'leHHe 1'T = 4,0, TO nonY'lHTCSI nyna C <PoKYC II bl '.1
paCCTOSlHIIC'\f F = 1,6 CM. KaKoH ,lI.JIHHbr Ha.no B3S1Tb Ty6yc,
1lT06b1 no.'1}"IJHTb MIiKpOCKon C YBeJIIIlJeHHeM 1')1 = 25?
f nAB A XII. Bon HOBbiE H KBAHTOBbIE CBOACTBA
CBETA
 40. BonHoBaR np"po.ll.a CBeTa
40.1. Bo.na oCBew.eHa 3eJ1eHblM CBeTOM, .zr.JISI KOTopOro .n..'ulHa
BOJIHbI B B03.nyxe 0,50 MKM. KaKou 6y.neT .nJ!llHa BO.rIHL!
B Bo.ne? KaKoH LlBeT BH.nHT 'lenOBeK, OTKpblBllllfii rna3a no 1.
Bo.noil?
40,2. KaKHe JIYIJH CHnbHee pacceliBalOTcSI 3CMHOii aTMO-
ciPepoil?
40.3. 06"bSlCHHTe npoHc)'O>K.neHlle LlBeTa KpacHoro CTCK:
na II KYMalJa.
40.4. Ha 6C.1JOM iPoHe HanlfC3H TeKCT CHHHMII 6YKB3MII.
4epe3 CTeKno KaKoro LlBeTa Henb3S1 YBH.neTb Ha.nm-rcb? Ka-
KHMH 6y.nYT Ka33TbCH 6YKBbI, eCJIH HX paccMaTpHBaTb lJepe3
KpacHoe CTeKno?
40.5. JIYIJ: 6enoro CBeTa na.naeT H3 nOBepxHocTb BO.nbI no,]:
TnOl\l fjJo. 4eMY paBeH yron Me>K.ZI.Y HanpaBneHHSlMH KpaHHlfx
KpacHbIx H KpaHHHx iPHOneTOBbIX nY'leH B Bo.ne, ecnH nOKa3a-
TeJlli npenOMneHJlH IIX paBHbI COOTBeTCTBeHHO 1,329 II 1,344
40,6. H3 npll3MY C npenoMnHIOw.HM yrnoM fjJo na.naeT nyq
6enoro CBeTa no.n yrnoM 45°. Onpe.ne.nHTb yron Me>K.l1Y Kpaf1-
HIIMH nY'laMH BH.nHl\fOro cneKTp3 npH Bblxo.ne H3 npH3MbI, ec 111
nOK33aTenH npenOMneHHSI HX paBHbl 1,624 H 1,671.
40.7. Onpe.nenHTb BenHQHHY npo.no.rIbHOH XPOM3T1iQeCKOi!
a6eppaLlHH ABoHKoBbmYKJIOH J!liH3bl C pa.nHycaMH KpHBH31.>1
R = 50 CM. JIHH3a c.neJIaHa H3 CTeKna, nOKa3aTeJlH npenOMJ1e-
HHH KOTOpOro ,lI.JIH KpaHHHX nYQeH BH.nHMOro cneKTpa paBllbl
III = 1,575 H n" = 1,597.
40.8. D.Ba KorepeHTHbix HCTOIJHJlKa (pHC, 240) JlcnycKal(,f
6enblH CBeT. 4TO npe.ncTaBnHeT co60H KapTHHa HHTepctJepeHLlHII
Ha 3KpaHe, pacnonO>KeHHOM Ha paccTOHHHH 0,50 M OT HCTO'lHlI-
KOB? KaK H3MeHHTCSI KapTliH3 HHrepctJepeHLlHII, ecJIH 3KpaH
OTO.nBHHYTb ew.e Ha 0,50 M?
40.9. Pa3HocTb xo.na JJ.BYx HIlTepctJePHpYIOW.HX nYlJeH MO-
HoxpOMaTHlJeCKOro CBeTa paBHa ),,/4. Onpe.ne.nIiTb pa3HocTb
iP33 KOJIeG3HHH.
J58

40.10, .lIBa KorepcHTllbIX HCTOqHHKa (pHC. 240) HcnycKalOT
71''JilOXP07lfaTHqeCKlIii CBeT C .n.ruIHoii BOJIHbI 0.60 MKM. Onpe.ne-
.11ITb, Ha KaKOM paccToSIIUfH OT TOqKH, pacno.rrO>KeHHOH Ha 3K-
paHC Ha paEHO\! paCCTOSIHI1H OT HCTOIJHHKOB, 6y.neT nepBbIH
MaKCH"IYM OCBeUleHHOCTH. 3Kpan y.naJIeH OT HCTOIJHHKOB Ha
3,0 M, paccToSIHlfe MC>KJlY IICTOqHHKaMIf 0,50 MM.
40.11. I1cToqHIfK CBeTa S H nJlOCKOe 3epKaJIO pacnOJlO>KeHbI,
h3K nOKa3aHO Ha pHC. 241. By.nYT JIH HHTep4>ePHpcB3Tb JIYIJH.
npHllle,!J.IlJHe B TO'lKY P?
40.12. Ha MblJIbHYIO nJIeHKY na.naeT IIOpMaJIbHO nYQOK
.'1YIJeH 6eJIoro CBeTa. KaKoBa HaHMellbwaSi TO.'1111Htla nJIetl-
h.i, eCJlH B oTpan<ellHoM CBeTe OHa l\a>KeTCH 3eJIeHOU
) = 532 HM}?
--{----+---
Sz
PIIC. 240
s
*
p
PHe. 241
40.13, JIYIJII 6eJIoro CBeTa na.nalOT HOpMaJIbtlO Ha TOHKYIO
nJIOCKOnapaJIJIeJIbllYIO np03paQHYIO nJiaCTHHKY. KaK 6Y.l1eT
',CHSlTbCH OKpaCKa nJiaCTHIIKH, eCJIH YBeJIH'lHBaTb yrOJI na.ne-
IfH?
40.14. Ha TOHKHH CTeKJISIIIHblH KJlHH na.naeT HOpMt!JIbJlO
YIJOK MOHoxpOMaTHIJeCKoro CBeTa C .l1JIHHOH BOJIHbI A =
-= 0,60 MKM. HauTIf yro.1 KJIHHa, eCJIH paCCTOSIHHe Me>K.ny HH-
rep4>epeHl.lHOHHblMH nOJIOCaMH S = 4,0 MM.
40,15. KaK 113MeHHTH KapTHHa .l1lfiPpaKUHoHHoro cneKTpa,
CCJIII peIlleTKY C neplIo.nOM 0.020 MM 3aMeHHTb peWeTJ<01f C ne-
pllO;J.OM 0.010 MM?
40.16. Onpe;J.eJIHTb nocTOHlmylO !l.HiPpaKUHoHHOH peweT-
1m, ec.rm lIa perneTKe .l1J11IHOH 2,5 CM HallecellO 12500 WTPH-
XOB.
40.17. HaHn! lIalI6o.rtbIllIIH nopSI;J.oK cneKTpa .nJlH 6eJIoro
BeTa (40-70 HM), eC.'I1i nCCTOSIIIHaH )J.HiPpaKUHOlltiOH perneTKH
paBlIa 2,0 MKM.
 41. KBaHToBaH npHpO.ll.a CBen
41.1. Onpe.neJIHTb 3HeprHIO H Maccy clx>TOHOB, COOTBeTCTBYIO-
IJ..J.IiX KpacHoH (A] = 0,76 MKM) H iPlfOJIeTOBOH (A2 = 0,38 MKM)
rp31IHUaM BH,!I.IfMoro cneKTpa,
159

41.2. OnpeJJ.eJlUTb Maccy U m.my.lbc 4'oTona, cooTBeTcTBYIO.
mero peHTreHOBCKO\'Y H3.'IY'leHillo C lJaCTOTOH 3. 10 17 rl(
41.3. KaKoH Hr.my.lJbc- cf>oToHa, 3HeprnS! KOToporo paDlia
3 3B?
41.4. OnpeJJ.eJlHTb JJ.J1Hny BO.'JHb!, cooTBeTcTBYlOlAYIO 4>0-
TOHY, Macca KOToporo paBHa p,mcce nCKOSl1.l.lerOCH 3.'IeKTpolla.
41.5. OnpeJJ.eJlIITb JJ.JlIIHY BOJI, JlbI cooTBeTcTBYlOm)'1O cf>oTo-
HY, 3HeprHH KOToporo paBHa 3Hepnm nOKOH npOTona.
41.6. Onpe.!l.eJlHTb JJ..1UHY BOJlHbl <PaToHa, ur.mYJlbC KOTo-
poro paBeH HmYJlbcy 3.'IeKTpOHa, npOJleTCBllJero pa3Hocn
nOTeHl.lHa.'IOB U = 4,9 B.
41.7. MOUlHOCTb cBeToBoro nOTOKa (t. = 500 HM), na,!J.a-
IOIlI.ero HopMaJlbHO Ha nOBepxHocTb nJlOmaJJ.blO Sl = 1,0 JJ.M:!,
paBHa \V = 100 BT, CKO.'IbKO <PaTOIlOB
l/, L£ 2 naJJ.aeT e>KeCeKYH;J.Ho na S2 = 1,0 C:I!!
J u....
3TOH nOBepxHocTH:"
41.8, COJlHelJHble JlY'lH B Te'leHHe ro-
JJ.a npHHoCS!T Ha 3eM.'11O 5,4 . 10 2 ( n.>i,
II 3HeprlfH. Ha CKOJlbKO 113MeHH.'IaCb 6u
Macca 3e:lf.'1l1 3a 100 .'IeT, eCJlH 6bI Of.a
3TY 3HeprlilO He 113.rlyiJa.'Ia B npOCTpaIl-
CTBO?
41. 9. 113MeHuTcS! Jill «>KeCTKOCTb» H3J1Y'leHIIS! peHueHoD-
cKcH TPy6KH, eCJlU, He MCHHS! aHOJJ.1I0ro HanpSl>KeHIIS!, 113!11ellHTb
HaKa HUTH KaTo,!J.a?
41. 10. no;J. KaKHM nanpSl>KeHHe\f pa60TaeT peHueHoBCKaH
Tpy6Ka, eCJlII MIIHUM3.-lbHaS! .!I.JlHUa BO.rIHbI B cneKTpe peHTrc,
HOBCKOro 113J1Y'leHHH paBna 60 H:'d?
41. I I. OnpeJJ.cJ1HTb KpacHYIO rpallHllY cf>oTo3<JxPehTa .!I..1H
Ka.'IHH H nJ1, aTJlHbI
41. 12, npOll30if,!J.eT Jill cf>oT03<IxPeKT, ecml MC.lI.b 06.'IYlJaTb
CBeTO:\f C MIIHOH BO.'IHbI 400 H:\f?
41. 13. C KaKOH MaKcH:\faJlbHOH CKOpOCTblO BblJleTalOT 3.!leKT-
pOHbI H3 llHHKa, eC.'I1I ero c6.'I)''laTb y.'JbTpa4JlloJleTOBbIM CBCro'!
(t. = 320 HM)?
41. 14. KaKoH 'laCTOTbI CBeT cJleJJ.yeT uanpaBH'tb Ha nOBcp.'
HOCTb .'IHTHH, 'lT06bl MaKCIIMa.rlbHaH CKOpOCTb <J>oTo3.'IeKTpCHoB
6bl'la paBHa 2500 K.\f'C?
41.15. KaKHM CBeTOM 06,rrY'laJ111 lle3HH, eCJlH .lI..1S! npchp'
UleHIIH 3MHCCHII 3J1eKtpoHoB nOTpe60BaJlOCb npIlJlO>KIITb 3J-
JJ.ep>KIIBaIOIlI.YIO pa3HoCTb nOTeHI,J:lla.'IOB 1,75 B?
41.16. aKYIO .3aJJ.ep:mHBalOlllYIO pa3HocTb nOTeHllJlaJlC-!J
Hao npH.'Jo:mUTb K <J>oTo3.'Ier.teHTY, IJT06bI «OCTaHOBIITb» 3.1Ch-
PIIC. 242
160

TpOHbI, HCnYCKae\ILle Bonb1>paMoM nO..1 .lI.eHCTBlle;\, ynbTpacimo.
lCTOBbiX nYtleii .lI.JIlfHOit BonHbl 130 HM?
41.17. Ha pHC. 242 npe!l.CTaBneHbI 3aBHCHMOCTH 3a.ll.ep>KH-
BalOw.eH pa3110cTH nOTeIlUUanOB OT qaCTOTbI oOJIYtlalOlllero
CBeTa .lI.ml .lI.BYX pa3nHtlHbiX MaTepH-anOB KaTO.ll.a cpor03JIeMeH-
Ta. KaKoH H3 lIfaTepHanoB HMeeT MeHblI1YIO pa60TY BbIXO.ll.a?
nOtleMY 3aBHCHMOCTb nlmeiiHaR? lIeMY paBeH TaHreHC yrna
HaKJIOHa nHHHH rpa<}mKa?
41. 18. Ye.nHHeHHblii ruapHK pa.nHyca 0,50 CM OCBeTHnH
CBeTOM C }J,JIHHOii aonHbI 250 HM. CKonbKo 3J1eKTpOHOB nOKHlleT
ruapHK, eCJ1H ero .lI.onOJIIIHTenbHO OCBeTHJlH CBerO'1 C .nJHlHoii
BonHbI 200 HM?
f J1 A B A XIII. A TO,"ASI ctJlBHKA
 42, CTpoeHHe arOMa
42.1. lIe;\,y paBeH nOJIHbIH 3ap R!I. 3JIeKTpOHoB B aTOMe xpo-
Ma?
42.2. nO.TIHblii 3apH.n H!lpa aTOMa paBeH 2,08 . 10- 18 KJI.
lITO 31"0 3a 3JIeMelu?
42.3. nOJIb3YHCb Teopueil Bopa, onpelle.nHTb .lI.JIH aTOMa
BO'1.0pO.ll.a pa.nHYC nepaOli OPOUTbl 3J1eKTpOlla Hero CKOpOCTb
Ha HeA.
42,4, OnpellenHTb HanpH>KeHHOCTb H nOTeHllHaJl nOJlR Mpa
aTOMa Bo.nopolla lIa nepBoii 6opoBcKOH op6HTe,
42.5. Bbltllle.rJIfTb cHny npHTR>KeIlHH lIfe>K.D.Y 9neKTpoHoM
H .lI.pm' aTOMa BO.ll.Opo.na B OCHOBHO!\l COCTORHHU. Bo CKOJlbKO
pa3 31"a CHJla 60nbrue cunbl BceMHpHoro TRfOTeHHR Me>K.ny 9J1eKT-
pOHO!\-1 H npoTOHoM Ha TaKOM >Ke paeCTORIllfH?
42.6. Onpe.neJlHTb nOTeHLlHanbHYIO, KllHeTHtlecKYJO H non-
IIYIO :meprnH 3neKTpoHa, HaXO!l.RllI.erOCH Ha nepBoH op6uTe B
aTOMe Bo.nopo.ll.a.
42.7. Onpe.neJJuTb nOTeHUHan HOHlf3aUIIH aTOllfa BO.nO-
pO.ll.a.
42,8. Onpe.ne.nHTb nepBblH nOTeHUHaJl B030ym.ll.eHHH aTOM a
Bo.nopO..1.a.
42.9. <I>OTOH C 9HeprHeii 15,5 3B Bbl6Hn 3neKTpOH li3 He-
B036Y>K.lI.eHHOrO aroMa Bo.nopO!la. KaKYIO CKOpOCTb oY.lI.eT HMeTb
9.1)tKTpO" B.nanll OT H.npa aToMa?
42.10. KaKue cneKTpanblfbie JIIfHliH nOHBRTeH np" n03-
6 ;1st. 1891
161

6Y)f{,neHHII aTOMapHOrO BO.ll.OpO!la 3.1eKTpOHalllll C 3ueprneA
14 9B?
42.11. KaKHe cneKTpaJIbHbIe JIHHHH nOflBflTCfI npll B03.
6Y>K.lI.eHHH aTolIIapHoro Bo.aopo.ll.a 3.1eKTpoHallU! C 9HeprHeli
12,5 9B?
42,12. Onpe.ll.e.nHTb MIIHH:\f8JIbHYIO .lI.JIHHY BO.1HbI B YJIbTpa-
HOJIeTOBO" cepllH BO.ll.Opo.aa,
42,13. BbIIlHCJIHTb 9HeprliIO 4>oToHa, COOTBeTCTB}lOllI.ero
nepBoii JIHHHH B BH.lI.HlIIOH cepml BO.ll.opo.ll.a.
42,14. HaHTH rpaHHUbI HH<ppaKpacHoii cepHII BO.ao-
pO.ll.a.
 43. CTpoeHHe R.II.pa
43.1. KaKoB COCTaB H..lep aTO'-IOB 6ePIlJI"lHH, yrJIepo.n.a,
HaTpHfI, onOBa, <PePMllfI?
43,2. KaKoB COCTaB H30TonOB Kllcnopo.aa Aua, fa,
'O?
43.3. lJelll OTnHllaeTCfI no cocTaBY fI.lI.pO nerKoro H30TOna
re.nHH OT fI!lpa cBepXTfI>Ke.noro BO.ll.OpO.ll.a?
43.4. Onpe.ll.e.nHTb 9HeprHIO CBfl3H fI.npa re.1HfI He,
43,5. BbllllICJJHTb 3HeprliIO CBfl3H fI.npa anlOlIfHHHfI HAL
43.6. BblllHCJJHTb 9HeprHIO, Heo6xo.nIlMYIO .lI.JUi pa3.n.e.neHllfi
R.npa nHTHH 1Li Ha HeihpoHbI H npoToHbI.
43.7. HaHTH y.ne.nbHYIO 9HeprHIO CBfl3H HYKnoHoB B fI.npe
.neihepHfI fH, fI.lI.pe KHCnOpO.1la 6a II SI.lI.pe nonOHHfI UOpo.
43.8, HaHTH 3HeprHIO CBSl311 a-llaCTlIUbi B SI.npe 60pa nB.
43.9. HaHTH 3HeprHIO CBR3H HeiiTpoHa B H.lI.pe reJIIISI
He.
43.10. Onpe.ne.nIlTb HaH\ieHblUYIO 3HeprHIO, Heo6xo.ll.H:\IYIO
.nnR pa3.l1.e.neHIISI SI..lpa yr.lep0..la 2C Ha Tpll o.:tHHaKOBble llaCTH-
UbI.
43.11. HanHcaTb SI.nepH}'JO peaKUHIO, npOHCXO..!lSlI.llYIO npH
6oM6ap.nHpoBKe 6epHnnHSI Be a-llaCTHualllH H cOnpOBO>K.aalO-
I.llYIOCR Bbl6HBaHHe:\1 HeihpoHoB.
43.12. HanHcaTb SI.lI.epHYIO peaKuHlO, npOlICXO.ll.flI.llylO npH
6o",5ap..!lllpoBKe JIllTllfi 1Li npoToHa:\1H II cOnpOBO>KJJ.alOI.llYIOCfI
BbI6HBaHHe\1 HeihpoHoB.
43.13. HanHcaTb He.nOCTalOI.llHe o603HalleHIIH B cne11YIOllI.HX
fI.nepHbIx peaKlJ,Hflx: HK + ..' -+ Ca + IH; Mn + tH -
162

 !Fe + ....; ... + He -+ AB + n; fH + l' 
-+ ... + An.
43.14. Bbl.ll.eJISleTCSI JlJIH norJIOlIlaeTCSI :meprHSI np" CJJe.
.nYJOllI.HX SlJl.epHblX pea KlU1 SIX: 1) U + iH -+ 4Be + n;
2) gu + tH -+ He + He; 3) AU + He -+ !OB + n;
4) 4N + !He -+ 70 + IH.
43.15. KaKaSi :meprHSI Bbl.D,eJISleTCSI npJl SI.1epHoA peaKD,HH
U + 'H -+ 2 He?
43.16. KaKaSi :meprHSI Bbl.ll.e.IJSleTCSI npH TepMoSl,!l.epHOH
peaKUHH IH + fH -+ He + bn?
6*

nPHJ10)f(EH liSl
JI.ecRTH'IlIble npHUSBKH K H33BaHHRM e.llHHRIl
r - rllra (10")
M - Mera (10 6 )
K - KH.10 (10 3 )
r - l'eKTO (IO!)
ll- .IleUH (10- 1 )
c-caHTH (10- 2 )
M - MHJ\JlH (10- 3 )
MK - MHKpO (l0-1)
H - RSHO (/0-91
n - nHKO (10- 12 )
2. TafiJiHUS SHa'leHHA CHHYCOB H TSHreHCOB
:II I JI JI I JI JI
JI JI u U t.I JI u
u c: u JI z z
?i t.I .,  t.I GI  t.I ..
 to  ;: .. "" to
., :c .. z Z
0- ;; .. 0- j ;;; 0- Z ..
L. U f-o L. f-o L. U f-o
0 0,0000 o .0000 31 0.5150 0.6009 61 0,8746 I 804
I 0.0175 0.0175 32 0.5299 0,6249 62 0.8829 1.881
2 0,0349 0.0349 33 0,5446 0.6494 63 0.8910 1.963
3 0.0523 0,0524 34 0.5592 0,6745 64 0,8988 2,050
4 0,0698 0,0699 35 0.5736 0,7002 65 0.9063 2.145
5 0.0872 0.0875 36 0.5878 0.7263 66 0.9135 2,246
6 0.1045 0,1051 37 0.6018 0.7536 67 0.920:5 2.356
7 0,1219 0.1228 38 0,6157 0,7813 68 0.9272 2,475
8 0.1392 0,1405 39 0,6293 0,8098 69 0,9336 2,605
9 0,1564 0,1584 40 0,6428 0,8391 70 0.9397 2,747
10 0,1736 0,1763 41 0,6561 0,8693 71 0.9455 2.90t
II 0,1908 0,1944 42 0.6691 0.9004 72 '),9511 ;,078
12 0,2079 0.2126 43 0.6820 0,9325, 73 0,9563 3.271
13 0.2250 0.2309 44 0.6947 0.9657 74 0.9613 3,487
14 ,2419 0.2493 45 o 7071 1,0000 i 75 0,9659 3,732
15 0,2588 0,2679 46 0,7193 1,039 76 0,9703 ...011
16 0,2756 0,2867 47 0,7314 1.072 ' 77 0,9744 4,331
17 0,2924 0,3057 48 0-,7431 1,111 ! 78 0,9781. 4,705
18 0,3090 0,3249 49 0.7547 1,150 79 0,9816 5.145
19 0,3256 0,3443 50 0,7660 1,162 , 80 0,9848 5,671
20 0.3420 0,3610 51 0,777L 1,235 ! 81 0.9877 6,314
21 0.3584 0,3839 52 0,7880 1,280 82 0.9903 7,115
22 o 3746 0,4040 53, 0,7986 1.327 83 0.9925 8,114
23 0.3907 0,4245 54 0,8090 1,376 84 0,9945 9,514
24 0.4067 0.4452 55 0,8192 1,428 85 0.9962 11.43
25 0,4226 0,4663 56 0,8290 1.483 ' 86 0.9976 14.30
26 0.4384 0.4877 57 0,8387 1,540 87 o 9986 19,08
27 0.4540 0.50% 58 0,8480 1,600 I 88 0.9994 28,64
28 0.4695 0.5317 59 0,8572 1,664 89 0,9998 57.29
29 0,4848 0,5643 60 0,8660 1,732 I 90 l,onO:J 00
30 0,5000 r),3774
1
16-l

3. nJlOTHOCTb Bew:eCTBa
TBcp:loe
BCUleCTBO
11.10'
Ia/W'
JKHJlKOCn I
11.10'
1<1"/ w'
rB3 (np.. I
Bcpwa.u,Hbu p, Kr/y'
ycnol\llRxl
AnMa3 3,5 AueToB 0,79 AsOT 1,25
An/O!dIlBHn 2,7 BO.lla 1,00 BO.llOPOll 0,09
}l(eneso 7.8 fnHuepHB J ,26 B03AYX 1,29
30noTo 19,3 Macno 0,90 KHcnOPO./l 1,43
JIell 0,9 KepocHIl 0,80 rneKHcnblii
Mellb 8,9 PTYTb 13,6 ru 1,98
HHKenb 8,9 .
OnoBo 7,4
CBHHel{ 11,3
Cepe6po 10,5
CTanb 7,8
CTeKno 2,5
UHHK 7,0
LJyrYH 7,8
4. K09cJ1cJ1HUHE'HT renJlOBOrO pacwHpeHHR BemeCTBa
K09c1>4>IiIl\ReHT li-'9'
TBepADe nHHellHoro JKHJ1KOCTb oC;"eMHoro
BeUleCTBO paCWHpeHHR BCWHpellRJI
a.IO--5. K-I P_IO- I , K-"
A 1/OMHHHil 2,4 r.'1HuepUH 0,5
}l(ene30 1,2 K.epocHH 1,0
KBapu 0,04 PTYTb 0,18
Me.!l.b 1,7 CnHpT 1,1
CTanb 1,1
CTeKno 0,9
UHHK 2,9
5. MOp,yJlb ynpyrocTH
M8TepRBn E,rnll
An/O!dHHHA 10
}l(eneso 200
Mellb 130
CBuRen 16
CUJlb 210
t.tUJ10 60
l{):j

6 nall,'IeHHe RaCblw.eHHIIIX nap08 BO.3.111
1 0,653 II 1,31 21 2,49
2 0,706 12 1,39 22 2,64
3 0.759 13 1.49 23 2,81
4 0,813 14 1,59 2-1 2,98
5 0,880 13 1.71 25 3,17
6 0,933 16 1,81 26 3,36
7 0,999 17 1,93 27 3,56
8 1,07 18 2,07 28 3,78
9 1,15 19 2.19 29 3,99
10 1,23 20 2,33 30 4,2-1
TeM!ICPO"
TYpo. 00
BelI1ec:T11O
Ll8anlI1I .
Kna
I reMn. poo l
TYpa, 0(3
I relmCP4. \
Typa, 00
lloanelllle
..rr.
J.4aneHH..
Kna
7. YAeJlloHali TennOe'llKOCTio BelllecTBa
c.IOI. nJII:/(KI'.K) I
c.IOI. n>Kf(Kr K)
BelI1eeTBo
AnIOMHBuA
BO.lla
)l(eJJe30
KepocB8
n eJI. .
MeAb
0.90
4,19
0,46
2,14
2.1
0,38
0,13
0,23
1,59
2,43
0,46
0.83
CBHHelt
Cepe6po
CepHas KHc.10Ta
CnHpT
CTanb
CTeKJlO
8, YAeJlloHaS TennOTa n reMnE'paTypa nnaSJleHHR BelllecTB8
Bem.eeTBo A.\OI, nJII:/KI' t, "C
nell 333 0
Mellb 175 1083
CBHHCl1. 25 327
165

9. ¥enbHaR TennOT8 napoopa30BaHRR R TeMnepaTyp8
KHneHHSI aew.eCTB8
BeUlCCTBO
'.!OI, D..w./Kr
I, .C (II pH HOP" an..
HO» J18aneHHH)
Balla
PTYTb
CnHpT
2,3
0,28
0,85
100
357
78
10. Yenb"aR TenoT8 cropaHHR TonnHsa
B«ilLleCTBO
q- II)", D.."N./Kr BClLlecTBo
q-IOI,ll.w./Kr
:  2:
46 
3,8
29
oeH3HH
fa3
He4>Tb
t 1_ D.H3.1eKTpH1JeCK8R npoHllU8eMocTb BellleCTB8
BeUlec:TBO
II

BeUleCTBO
B
Bon
BOCK
feYHH8KO
K.BspU
KepocHH
MaCJ10
81
3.0
5.0
4,5
2,0
2,0
naps4>HB
f1JJeKcHr JldC
C.'1lOll8
CTeKJ10
cJ>aplj)op
360MHT
2.0
3,5
7.0
7,0
6,0
3.0
167

12 YAenLRoe conpOTRSnE'HHe BeIUCCTS.
Bew.ecTBo
)'./IeJlbHoe conpCTHB.
nellHe p.lo-'. 0.. ..
Te....ep8TYPllhili
K09e!>Hl\HeHT
a 10-'. K-I
Bo.lh4>pau
)l(eneJo
KOHcT811TaB
Me.ab
HHXPOM
CBRHe
CTanb
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6.3
8.7
50
1.7
110
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4.6
6,2
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13. nOK83aTeJlH npeJlOMneHMR
Bew.e<:Tllo
II
BewecTBo
II
Anua3
Bo.aa
KBapll
Macno
2.42
1.33
1,54
1.52
CnRpT
CTeKno
cJ>nHHTrnaC
1.36
1.5
1.8
14. Pa(joTa BLlXOA8 9neI<TpOHa H3 MeT8JlAOB
MeTBU
A. sB I MeTB.II.II
4,50 HnpHA
2.16 nJlaTBHa
2,39 UeJHA
4,47 UHi1K
A. sB
BOJlbcIJp...
K8JIJIA
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168

15. Macea HeKOTOpl.lJ! HYIIJlR.!lOIl"
H80Ton I MacCia HellTplIJIblIoro I H30TOD I Macoa lIellTp8JIb
8TOMa a. e. M. HO ro aTOllS,
a, e. II.
I H Bo.nopo,IJ. 1,00783 iBe EepH.MHH 8,00531
iH neiiTepHH 2,01410 lOB Bop 10,01294
rot TpHTHii 3,01605 lic YrJIepoJl, 12,00000
He feJlHl{ 3,01602 17N A30r 14,00307
He feJlllii 4,00269 180 KHcnopoll 15,99491
iiLi JIHTHii 6,01313 I iO KHC.l0pOll. 16,99913
Li JIHTHA 7,01601 HAl AJlJOMHHHH 26,98116
UPo nOnOHHii 209.98297
. Anti BB:IIOIK.lI.eIlHII ldilCCH IIllpa lIeOOXO.llHIdO IlloIqeCTb C}MllapHYIO Macey !J,/Ielt.
TPOUOB.
16. ACTPOHOMHqeCIlHe Be.1HQJfHW
K OCIIHQeCKOf CpcnHHI! I ('peABAA I rlepHO,ll o(\pa.
..e.no PIIABYC, .. Macca. IU' nnOTHOCTb. Ll<eIlUH BOKPY'
10' Krl M ' OCH, CYT.
Co.'1Hue 6,95.10 8 1,97,10 80 1,41 25,4
3eMJI SI 6,37.10' 5,£6.102 1 5,52 1,00
JIYHa 1,74.10' 7.30,1022 3,30 27,3
n.TalleThi
CO,'BeqHOA
CHCTeNhi
CpC;!.Hee paCCTOtillHe
oT Conllll.a. 10" KM
nepHOJl. o6paIQ.ellHil
BOKp}'r Conllll.a
B rona"
MepKYPHR
BeHepa
3eYJlH
Mapc
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57,87
108,14
149,50
227,79
777,8
1426,1
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4494
9508
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1,000
1,881
11,862
29,458
84.013
164,79
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169

17. OCHOBHble c1JHJH'IeCKHe nOCTORHHble
4>1I3H'ICCK811 DOCTOJlHH&JI
CHOpOCTb CBeT8 B B8KYY'
ue
fpaBHT8UHOHB8H nOCTO'
HHH8H
nOCTOIIHH811 ABora.apo
'HHBepC8JlbH8H (MO.'ISlp'
Hall) ra!lOBaH DOCTOIIH-
B8H
nOCTOSlIIH811 BOJIbUMaH8
nOCTOIIHH811 cJ>apa,Aell
SJleMeHTapHA !lapHA
aCC8 neKTpOH8
aCC8 npOTOlia
b\acc8 HeiiTpOHa
y .aenbHA S8pll.a 3neKTpo-
H8
ATOMHaH eAHHHua YIICCbI
(1112 MaCCbI 8TOM8 HYK-
nH.ll8 12C)
SJleKTpH'IecKaH nOCTORII-
HaH
MarHHTII8H nOCTOHHHaH
nOCTOHHHaH nJlaHK8
U603B8'1eHHL
,
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2,9£8.10 8 M/c
6,67.10- 11 uS/(Kr,c')
6.02.10 23 MOJIb- 1
8,31 Jl>K/(K.Monb)
I ,28.10- 13 Jl>K/1(
9,65,1{}4 Kn/MOJlb
I ,60.IO- li KJI
9,11.10- 81 Kr
1,672.10- 27 Kr
1,675.10- 27 Kr
I .76.10 11 KJI Kr
I ,66. 10- 27 Kr=931 MB=
= 1,49.10- 10 Jl>K
8,85.10- 12 cJ>/M
1,26.10- 8 fH/y
6,62,10- 84 Jl>K.c=4 ,I4X
X IO-l B.c,
1,054.10- 81 Jl>K.c=6,59X
XIO-18 9B.c

lB. OCHoBHLle TpHroHOMeTpH'IecKHe 4K>PMYJlLl
sin 2 a.+cos ll a= I
sec a-tg 2 a = 1
csc' a-ctg ll a= 1
sin a csc a = I
cos':tsec a=1
tg a ctg a = I
I
sln(;t=
VI +ct J.
I
cos a =
VI +t5 a
sin 2a=2 sin a cos a
cos 2a..=cos 2 a-sin 2 a
2t ':t
tg2a.=
ctg 2a :::0
I - tg a
ctg 2 a- I
2ctga.
. a "1/
5'"2"= V
I-cos a.
2
cos 2.. I /
:2 V
1 + Cas fJ.
:2
stn (a :l: IJ) =sln acos  :l: COs a sin'
cas (a :l: IS) =C05 ':t cos IJ T sin (1. sfn 
t" a -L. tg 
t (a. :l: ) = '" -
1 =t= tg a tg IJ
R ctg a ctg  T I
ctg (a :l: ...) :::0
etg  :I: ctg a.
a+ a-j3
slna.+sin=2sin -cos-
2 2
.. a+1J . a-
sma.-sm=2cos-sm -
2 2
a+ a-
cos (1.+eos  =2eos  cos 
a+ a.-
cos a.-cos  = -2 sin - sin -
2 2
sin ( -L. f\)
tga:l:tg= -
eos a. cas ,1
- sin (a. :I:: 6)
ct a :I:: ct   = :I:: . ,{
sm asm...
2 sin  sin  =cos (a-) -cos (a+)
2 os a. cos  =-eos (a.-) +';05 «(1. + Ii)
2 sin a.eos  =sin (a.-) +sln (a+)

19. HekoTopwe BHeCHCTeMHble eAHHHUW
J roll_3.1I.10 7 c
{ 101.3 Kna
1 ITM= 760 101M pI CT.
...14 pT. C1.-133.3 Ds
. Ka.l1""'!4.18 Ail!.
I A-IO-I CM
I :/B= 1.6.10- 11 1l>K
{ 1,66.IO-t4 r
I a. e. M,ca 931.4 /lb8
20 O03HaqeHIIR II H83B3HRR OCHOBHblJI I!JH3RQeCKIIJI BeJll'IJHH
A - aunep
a. e. M. - nOYllaR
- e.nHHHua
Maccw
B - Bo.lbT
BO - BelSep
BT - BaTT
fH - reHpD
r - rpaMM
fit - cePit
1l)K - A>KOy.1b
.nnTp - ....HompHH
K - KeJlbBHH
K,A - KaH.llena
KJI - KYJlOH
.II - JlHTp
nK - ./1IOKC
nM - J1IOMeH
101 - MeTp
MHH - MHUYTa
OM - OM
H - HblOTOH
na - naCKaJlb
paA - pSADaH
C - ceKYHD,8
rp - CTepa.llHaH
TJI - TeeJia
cJ> - 41a pa,A
Q - qac
:/B - :/.leKTpOH-BO.lbT

AJlcII8BHT JlaTHHCKHA
AncllasRT fpeqCCKHD
Ao-a
Bb - 6
Cc - n
Dd-,J.3
Ee-9
FI - 941
Gg - r3
Hh- 8W
1.-0
Ij - AOT
Kk - K8
Ll - 9,1b
111m - 9M
Nn. - 9H
00-0
Pp - n
Qq - KY
R, - 9))
SJ - 9C
TI - T9
Uu-y
Vo - 8
Wm -Jly6nb-B3
Xx - RRC
Yy - HrpeK
Zz - 3et
Aa - 8J1bclls
BI3 - 6eT8
rV-raMMa
6. - lIenbTa
Ee - 9nCHJlOB
z - veTS
H1]- 9Ta
as - TeTa
h - Aora
Kx - Kanna
AA - naM6,Aa
'IJl- MIO
!\:\' - RIO
S; - RCR
00 - OMRKpOB
nn - nR
Pp - po
ra - CMfMa
Tt - TaY
Yo - MnCRJlOS
1D<p - 4>H
x)! - XH
W'I' - nCR
Qw - oyera
J73

r p 3 J1 e H e H .T 0 B
Y n n
nEPlIO;(b1 I I VI I
I II III I IV V VII VIII
1 2
1 1,00797 H 4,0026 He
BO.aOpO.D TenHH
3 4 5 . II 8 9"
6 0 10
2 6,939 Li 9,0122 Be 10.811 B 12,O1ll5 C 14,0067 , ,9994 18,9984 F 20,183 Ne
:nITHH 6CPHJ1J1HH 60p ) r J1epo..'1 ICHcnopo.a e!>TOP )feoH
.-
11 12 13 - 16 17
3 14 J S Cl 18
22,9898 Na 24,312 Mg 26.9815 AI 28,086 Si "64 35,453 39,948 Ar
30,9738 . cepa
!lUrHH MSfHHH 8"JIOMHHHH KPCMHHH 1jJ0c1> Jm!>p aprOH
19 20 21 22 23 25 26 27 28
39,102 K 40,08 Ca Sc 44,956 Ti 47,90 V Cr .51,996 Mn 54,938 Fe 5,84 7 Co 58,933. Ni 58,71
C;P('"
4 lCa")HH ICaJ1bl.(HH ClCaH.1HH O MapraHell »;eJ1e3O 1C06aThT HHKeTh
THraH B8HanHH
29 30 31 32 I 34 35 36
. Se Br
Cu 63,54 Zn 65,37 69,72 Ga 72,59 Ge 74,922 ,96 79,909 83,80 Kr
ceneH 6POM
MeAL l\HHIC ra,]'H" repMaHHH MbHI}, J:pHhTOH
37 38 19 40 41 43 44 4$ 46
85,47 Rb Sr y Mo 95,94 Tc (98) Ru Rh Pd .
87,62 88.905 Zr 91.22 Nb 92 ''Ii: ]01,07 102,905 106,4
p)15H..'1HH CTPOHl\HH HTTPHH l\HPKOHHH HH06HH nH6.aeH TcxHellHH pyrcHHH POJllIH naJ1J1a"-HH
5
47 48 49 50 52 53 54
Ag 107,870 Cd 112,40 114,82 In 118,69 Sn 121,75 I S ,60 Te 126,904 I m,30 Xe
..
ccpc6po lCa'MHH JiHJ1HH on080 TCJ1nyp !lOA ICCCIIOH
C)b
S5 56 57 72 73 75 76 77 78
132,905 Cs 137,34 Ba La ;::: Hf Ta 183,85 Re 1862 Os 190,2 Ir Pt 195,09
138,91  178,49 18C,' 192,2
'1bljJpaM peHHH )
6 lIe]HH 6apHH TallraH ra$HHH raHnn OCMHH HPH"-HH n'18THHa
79 80 81 82 84 85 86
Au 196,967 Hg 200,59 204,37 .Tl 201,19 Pb 208,980 ] . 0) Po (210) At [2221 Rn
10.10ro pryn nnnHH  honoHHH aeraT P8JlOH
CBHHCU BH.::'.f
87 1!8 89 8 104 106
7 [223] Fr[ 226] Ra Ac [227J r Ku /2611 .
,z,paHIIHH pa1 H H anSRHH '" .
. ICYP'lUOSHH
. n a H f i 0 If IJ;hI
58 59 60 61 62 63 5 66 67 68 69 70 7l
64 tb
Ce Pr Nd Pm Sm Eu Gd Dy Ho Er Tm Yb Lu
uepIIH np33eO.DHM IIC01MM npOMerHH C3MapHH esponHH r8JlOJ1HH-t1 6HH ilHCnpO]Hit rO")bHH 3p6HH T)'.THH MTTCp6MH 110TellHH
140,12 14(' 907 144,24 [1471 . R,924 162,50 164,930 167,26 168,934 173,04
150.35 151,96 157.25 174.97
"a K T 11 )J1 .J: hI
90 91 92 93 94 95 90 98 99 ]00 101 102 103
Th Pa U Np Pu Am Cm k Cf Es Fm Md (No) Lt
TOpHH npOTalCTMHHH ypaH HCJ11)'HHK nllyTOHHH a..epHUH H ICIOPHK kJlHJ{ JCLTHOPHHK 3iiHUITeHHHJ{ $ep/dHK MeHp;e TeSH" (R06"C/lHH) noypcHcHK
232,038 231] 238,03 mJ [4] [2431 (247] r49] (2541 [253] f2561 154] [271
I
 .
nEPIIO,lXJI1IECKAR CJlCTEl\1 4 9JIEMEJITOB ,lX.II. MEH!(EJIEEBA

01B ETbl
5. I = 4,4;  = 23". 6. lei = 8,7;  = 3"(0. 7. lei = 8,7;
j} = 21"(0, 8. idl = 6. 9, i7t = 7,1; a = 4SO. 10, T-X = 5,2; 'y = 3,0.
 - -+- 
II. Ibl = 4; j} = 60°, 12, let! = 1,7; l = 240°; l e 2 1 = 3,5; 2 =
= 300°. 13, IMIM: I = 5. 14. I = 10; a = 58°. 15. II = 5,8;
..,.. -+- -+- -+-
le 2 1 = 7,1. 17. lei = 2,6; Idl =- 1,7, 21. x = 2 eM. 22. lei = 6;
x = 4 CM or I5oJlbwcro BCKTopa.
1.4, x = Xo - 00 cos a.t, y = Yo - Vo sin a't; y = Yo + Xo X
X tg a - "tg a. 1,5. y = 0,2 + 4x, 1.6. 5..0 = 2 M; 5,,0.= 4 M;
58.n = 4 M. 1.7. 't = 6 c. 1,10. V n = 0,5 Mlc; [len = 3 Mlc; 5 = 55 M;
[lcp = - 0,07 Mle. 1.11, [I = 2!1].v.j(t't + v 2 ) = 48 KW'l. 1.12. v =
= (Vj + ( 2 )/2 = 50 KW'l. 1,13, t'l = (n + 1) vcr/2 = 6 KMlq; 02 =
= (n + 1) vcpl(2n) = 3 KWq, 1.14. [If = (n + I) [lc,/2 = 6. KW'l;
v 2 = (n + 1) vcpl(2n) = 2 KWq. 1.15. vcp = 25 wc,  = 83 K sa.
llaHRoMY HanpaBnCHHIO' 5 = 140 M. 1.16. t = I 'I; 5 = 70 KM; 50TH =
= 120 KM. 1.17. t = .iI(VI - ( 2 ) = 18 MI'R; 51 = 4,5 KM;  = 1,5 KM.
1.18. '( = (/ + Vj'tl + v 2 't 2 )/(Vf + vJ = 10'130 MHII; S:t =  = 60 KM
1,19, t = (/- v,.lO)/(Vf - ( 2 ). 1,20, Ha pacCToSlHIIH 8,7 KM 01 nYHlc.
Ta A. 1.21, t = 0,5 MHR. 1,22. VOTS = 15 KMI'l. 1.23. t = t)t/(tl +
+ tv = 45 c. 1.24. t = 2t,ti(/ 2 - If) = 12 'I; up =1 (tn-t l )/(2i l t 2 )=
= 5 KMlq; VT = 1 (it ;- t2)/(2tlt?J = 15 KMlq; 1,25, 15 MHII.
1,26. up = (/- 5)/(21) = 4 K\f/q) un = (I + 5)/(21) = 16 KWq. 1.27.
b = 35 M. 1.28. a = arctg (v/u). 1.29. Vn = 1 wc; up = 0,25 Idle.
1.30, v = 50 KWq. 1.31. v 2 = 600 Mle. 1.32. 5 = I tg arcsin (Ul/['2) =
= 1,2 M. 1.33.  = 135°. 1.34. U = 5 Mle; llyeT C 3analla. 1.35. t <=::
 30 KW'IJ Ha IOrO-BOCTOK. 1.37, u = 30 KMI'I, llYeT e ceBcpo-3analia.
1.38. vQ = U sin (a + )/sin ::::; 3,9 Mle; vp = U sin alsin j} <=::
=2,8M1c. 1,39. v=vr/2, 1.40, u=v/sin a, 1,42. u=v/cos a=3,2 Mlc.
1.43. vn = vA tg a.
2.6. 02 = 0,5 M/c; ['5 = - 0,9 Mle. 2.9. 1= 10 e; 5 = 25 M.
2.10. i 1 = 0,5 e; /2 = I e. 2.12. a = 4 1 0 Mlc 2 ; V = 20 MlCj YI =
= 25 M; XI = 42 M. 2,13. t'ct! = 2 Mle. 2.14. [I = 6,0 we; vcp =
=3,0 WC. 2.16. a=- 1,0 M/e 2 ; v=7,5 Mle. 2.17. a=4r?/b=
= 2,5 wc 2 ; vCP /VCP2 = 1/2; 1= b/v = 4,0 c. 2.18. 5 = ['6/0+ I ;
['cp = la/(vo + VvB + 2al); vacp = (v3 + al)/(v o + V vB + 2al).
2 19 = t' + a (i J - vn /o ) 2 = 2 6 . =  + a (i 2 - vJa) 2
. .  20 2 . M, 58 20 2
= 34 M. 2.20. a = I,D wc 2 ; 5J = 50 M; S:! = 9,5 M. 2.21.
a=2s.'(2t - I) = 4,0 AI/c 2 ; 512- IY(2t 1 - I) =58 M, r.1e t 1 =
J76

. S T
= 8 C, ' 2 = 15 c.2.22, 65 = cn-. 2.23. HCT. 2.24. t = en + "2 =
= 40 c. 2.25. sIllsB = 2. 2.26. Va = 2v = 2,5 lAIc. 2.27. vMal<C =
2v cp 5
25 _ t'cp (II + ' 3 ) = 20 we. 2.28. 6h = 9,8 M. 2.29. h 1 = 30 td;
t<t 2
h 2 = 90 III; h3 = 150 M. 2,30, 6h = gt/- T; 6h z = 34 M, 611 1 =
= 15 M. 2.31. ' 1 = V 2h!g = 7,0 c; ' 2 = (- Vo + Vvi + 2gh)/g =
h or
= 6,5 c; t 3 = (vo + Vt' + 2gh)/g = 7,5 c. 2.32. t = gt +"2 =
h 2 h gtz
= 7,0 c; H = 2g o t 2 + 2" +""8 = 240 M. 2.33. h Haxo;r.IITCSI H3 ypaB-
... f 2h h l 't'
HeHHSI r g + ;; =1; h = 150 M. 2.34, t = - 2' 2.35. In-
-In-I? gln't' - g (ntf/2; 13 - 1 2 = 0,73 M; I. - I, = 0.64 M.
3 ' 3 g f ---sii ... f----sh
2.38, h = 4" 2g = "4 h M8KC ' 2.39. vo=2" 1 I+ g; 1= r I: + -;
240. 1= «('ij + 2ut'o)/g; I M8Kc = (u + t'o)2/(2g); or = 2 (';0 + u)1 g .
2.4. I = slv = 0,5 c.
3.3. Ct.!. pHC. 243. :>.4.:-' = gx2/(2v3); v = V v + g 2 / 1 ; a =
= arctg (gl/vo)' 3.5, y = gx 2 /(2vij); V o = s V gT(2H) = 9, 8 we. 3.6,
;;,"= 49 wc; a = 37° K ropH30HTY. 3.7. v = Vvij + 2gH = 12 IIVC;
PHC: 243
D'L_ O:b=--t
. ,
t 
I
Xg
t t
PHC 244
OI L a1
!i-
I
t t
: 
''LL
t t
a: - arctg (V 2gH/v o) = 55. 3.8. t = t'Jg = 2 c. 3.8. 1= vr/(2g) =
= 0,5 e; x = t'/(2g) = 4,9 III; !I = v/(8g) = 1.2 N. 3.10. x = vij X
)-. V3'g = 71 III; Y = 3t'ij/(2g) = 61 M. 3.11. h = 2vij/g = 4,9 M;
VI tg 2 a
= arctg 2 = 64°. 3.12. h = 11- °2g = 93 M, 3.13. 6H =
Rs! (_.2 - .,2)
= '2 'I = 2 CIII. 3.14, t' o = V g scosa/(2 tga)=IOu/c. 3,15.
2 ,2 u
1 2 e x2
,,-2('ijh!(gb 2 )-3. 3.16. CM. pHC. 244. 3.17, y=tg ax 25 cos 2 (X .
3.18. I) ;: ,,-=t'o CDS a; Vy=;:'o sin a-g I; v= Vt' - 2"0 sin (x. gt _l.. g 2t 2 ;
7 3 .1897
177

( gl ) vi sin 2 a
2) 1=2vo sin alg; 3) cp=arctg Ig a - - ; 4) H =
V o CDS a 211
v sin 2a' ,
5) s=. 2g . 3,19. H/H2= tg-a; 51/s2= I. 3.20. (=
= Vo sin a :f: Vo cos a tg  ; 11 = 0,37 c; 1 2 = 1,39 c. 3.21. H =
g 
(g2-t 1 + vii - v-fl
= 83-):' =3 r.I. 3.22. H=gt 2 /S=4,9 M. 3.23.a=
g  
gl- gl-
= arctg 8 = 83°. 3.24. H = ""2 - 20 M; S = 2 ctg<!rceos D,S =
= 45 M. 3.25. I) R I = L'i co.s alg = 9,8 M; 2) R 2 = t,f(g cos a) =
= 78 M. 3.26. On= g CDS arctg ( Ig a - -.!l!...- ) = 6,2 Mlc 2 ; aT =
v, cos a
( gl ) Vo sin a
= g sin arctg Iga - = 7,6 tAlc;' 1= = 1,73 c.
v,cosa g
gl'
3.27. h=tI, si n a.l- 2 = 32 II; s = v, CDS a.1 = 30 11.3.28. v =
= -2- 1 / R = 16,2 kW'I. 3.29. v -  X
CD S a ... 2 (h + I Ig a) CDS a
f . C)
xl g =23..1c.3.30.x=2s-v:=211.3,31.1=
J 2 (h+stg a-H) g
2 2 na
- g CDS a = 2,3 c; S = g cos' a = 13 II. 3.32. v, =
= CDS a 1 / gs = 21 Jc; lJ,J = J ,24 c. 3,33. 5.....,.
J 2 sin (-a) cos
= 2v Ig al(g cos a)=57 M; H=vij sin a tg aI(2g)=7,1 td. 3.34. t'OTII=
= VI +v:,-2"OIV02 cos (aI-a'!.). 3.35, Ig a=/JI/, a = aretg (HI£) =
= 58°. 3.36. x 2 + 1/ = A2 - OKPY>KIIOCTb C Ut'HTpOIll B Ila-
lup ., 
'lane Koop;J,IIIIaT. 3.37. an = v M = 13 cvC-. 3.3S. 1=3",5 M.
3.39. VCIVMIIH = 20. 3.40. a = 4n 2 RI72 = 3,4 cMlc'; (J.).jw I =
= Vg72/(4n 2 R) = 17.3.41. v = 2;R cos 6=2,3.10 2 Mlc; 0=4n 2 Rx
X cos 6/72= 1,7 cwc'. 3.42. 1,=  = 2 c. 3.43. t: = 4;r.N11 2 =
= 6,3 paNc?. 3.44. 1= V tg Ie = to c. 3.45.  = arctg 4nN =
= 85° 3.46. v = 2s _ t' o = 90 Kt!'1'  - 1/  + (v - vo) =
I ...:-- t R2 t
= 0,71 wc!. 3,47. oM = : V r 2 + 4s 2 = , WC!; II = arctg s =
= 83° K BepTIIK3.'1H. 3.48. v = 2:rr.nR = 15 Ktf'l. 3.50. VI =
= 2 ..Ic; v 2 = 0; V 3 = 1,4 Mlc; t'. = 1.4 wc; 01 = Oz = 03 = O. =
= 2 Mlc l Y cccx TO'leK OJlIIHaKOno H HanpanJiCIIO K ueHTpy KOJICca.
3.51. v = u etg alecos (rl R) = 36 KW'I, nnpaBo. 3.52. h = 2n 2 n 2 X
X Ltlg = 4,5 M. 3.53. vB = 2w (R + r) = I WC. 3.54. J) Vy =
= (VI + v 2 )/2 = 5 wc; W = (t'l - t'z)/2R = 10 pa;ve; 2) t'y =
= (VI - v 2 V2 = r we; W = (t'l + v,)/2R = 50 pac. 3.55. u =
I7S

.
AB
= V +4ntn20At = 26 We. 3.56 . u =- OA () = - 24-KW'I; T. e.
HanpaBJleHa Ha3aJJ;. 3.57. u = V 4n 2 n z RI + rJ = 317 Wc, BHHTOB1R
JlHHHR e warOM h = vln = 1,34 M,
uti sin a 0' 5
1.1. fll=arctgs_utJcosa I 30 ,fls=fll;tZ=IS-2utlcOS:.1.
= 33 MHH. 1.2. fli = 45 ; flz = Cf'. 1.3. SMHR = vlt Sin (a + arCS1I1
X VI sin a ) = 0,78 KY.
Vv + vi - 2VIVZ cos a .
5 sin a
1.4, 5MIIII =5 sin a = 10 M. 1.5. h
=
1L1
t, t z t
2 sins (al2)
2 VI yf 2h
= 1,7 M. I.G. S = _ - =0,3 M. 1.7. CM.
cos a g
pHC. 245. I.B. 5 = (v sin 2a - g51)/g = 2,3 M,
v sin 2 a
1.9. H = R (I - cos a) + 2g
4.4, F:x = 0; FJI = 5.0 H. 4.5, Fz = 10H; F:x=8,7 H. 4.6. a =
= 2,5 wcz; P = 55 H. 4.7. I) P = 740 H; 2) P = 630 H; a = g.
4.B. I) T = 3,9 KH; 2) T = 3,6 KH; 3) T = 3,3 KH. 4.9. V =
= V 2gh = 6,93 wc. 4.10, a = aretg (alg). 4.11, a = F/(m l + m) =
F 
=3,Owc 2 ; T=m z F/(m 1 +m Z )=O,90H.4,12, a=g+ + =
m l m z
. Tn
= 10,8 r!cz; T = m + m F = 1,0 H. 4.13, I) a = F/ M = 4.9 we!;
I I .
2) a = mg (ml + M) = 3,3M/c t . 4.14. a = (- ml) g/(m z + ml)=
= 1,96 tlct; T = 2m l m-d!/(m l + m z ) = 1,18 H; F = 2T = 2,4 H
mz - m, sin a . '
4.15, f=2Mmg/(m + 2M). 4.16, a = + = 0,98 wc-;
ml m2 g
m,mz (I + sin a)
T = ml+mZ g = 17,6 H; F = 2T cos a = 30 H. 4.17.
ml sin a.-mz sin  mlm z (sin a + sin f\)
a = + g; T = + g. 4.IB, al =
m l m2 ml mt
2 (2m 1 - mz) 2ml - mz 3ml m z
= 4ml+mz g; a l = 4ml+mi g; T = 4ml + m z g. 4.19. a =
= g; T = O. 4.20. al"; 2mg/(M + 5m) = 1,96 wc 2 ; Dz = alJ f 5 =
m,
- 4,4 wc z . 4.21. F = (M + m l + m z ) - g = 7,8 H. 4.24, BJiaro.
m z
,AapS! CHJle TpCIIHSI. 4.25. I) FTPI = 0,50 H; 2) FTPZ = 0,98 H..
4.26. CM. puc. 2.46. 4.27, Ct.!. pHC. 247. 4,28, tg ao = J1; CM. pHC. 248.
;;-r-
fF
Pm:. 245
L
J,9H F
PUC. 246
PUC. 247
7*
179

4.29. C\I . pHC. 24Y. 4.30. F MHII = V (J1mg}l-F2 = 3,9 H. 4,31. F =
= mg V J1 2 COS 2 a:- sin 2 a = 1,7 H. 4.32. KOJleco KaTHTCJI 6e3 npo-
CKaJlb3b1BaHHH - CIIJla TpeHHH HanpaB.'leHa BJl.OJlb HaKJlOHtlOH n.10-
CKOCTII npOTHBOnOJlO>KIIO BHeWHHY CHJla"'. B cnY'Iae CKOJIb3HIl\eA no-
BepxllocTH ,AOCKH CHJla TpellHH HanpaBJleHa B npoTHBono.'10>KHYIO CKO-
pCCTH CTOPOIlY. 4,33. F=2mg+ /=3 H. 4,34. k = J1mgll=150 H/\!.
F""
mg
'pmg
_______-.-(mgstn (/.
_' I
I
I
...vpmg cos«
I

lX
:t
PIIC. 248
PIIC 2.49
4.35. t.o = 20 loVe.. 4.36. a = (sin a - J1 cos a) g = 2,4 wc!.
F
4.37. a = m (CDS a + J1 sin ex) - J1g = 10 we 2 . 4.38. t =
1 V 211 4 F (cos a - J1 sin a)
sin a g (I - tg II ctg af .39. a = ml + m2
(m2 + J1m]) g
ml +m z = 1,4 loVC'!.. 4.40, T = m (g sin a - J!g cos a +
['0
+ y) = 2,6 KH. 4.41. a = (I - m/m2) g; F Tp = mlg. 4.42. a = 0;
T=IO,8 H.4.43. a=gsina(l+M/m}.4.44. t=.1 211m l -
Y (m 2 -m l ) g
= 5,4 c. 4,45. npenHTCTBYCT CHJla conpOTHOJleHHH, J..oTopaH B03pa-
CTaCT co CKOpOCTblO. 4.46. t'yCT = alt'/Cal - D 2 ) = 140 KMI'I.
I k
5.1, F'J1 FI = 2. 5,2. I = k + 4a 2 n 2 m 24 CIII. 5.3, J1 =
= (4 nZ n 2 l)/g = 0,20. 5.4. R = i?/(g sin a). 5.5. Tl = mg/cos ex ;
T'}. = mg cos ex; a l == g tg ex; a z = g sin ex; VI = V g l sin ex tg ex ;
['2 = 0; (,)1 = V g/(I Cos ex); (,)2 = O. 5,6. (,) = V g/(I CDS a) =
v'!.
= 7 pa1J/c; T = mg/c os ex = 2,0 H. 5.7. T = mg (cos ex + g/ )'
5.8, t = 2 n VI cos a./g = 1,4 C. 5.9. a/a,. = tg ex/tg t'tt = 1/3;
viva = V sin "I tg "I / (sin a 2 tg t'tt) = 0,4. 5,10. T = m(,)2l!2. 5.11.
I} FI = mg; 2} Fz = mg (1- tJ/(Rg»; 3) Fa = mg (I + tJ/(Rg».
FR + mrr
5,12. FI/F?, = 1,7. 5.13. ex = arccos R' = 60" C BepTUKaJlblO.
mg
5.14. at = J!g (I - tJ/(Rg» = 2,9 wc 2 . 5.15. R = 4081 M. 5.16.
h = btJ/(Rg} = 8,0 C"', 5.17. rMallc = V J1Rg = 6 8 KWTJ; ex =
=arctg(I=22°. 5,18. v=..l Rgtgc. =22 wc; ['M:mc= 1/ Rg I+tga._
... I-J! tg :J.
180

m (Rg sina - v!)
= 3 3 Jc, 5.19. F = R cos:! a =--= 0,3 H; t, =
= VRg :.in a = 0,70 WC. 5.20. w ,= V g tg all = 10 pa;J/c. 5.21.
J1 = (g sin a + (s):! R cos a)/(g cos a - wR sin a).
6,1. F = 8,4 nH. 6.2, F = G(J2JIDI36 = 2,3 MI-!. 6.4. G =
= 6.7'IO-1I1113/r.r,c 2 . 6,5, F = ..!.G.\1m [  - I ] .6.6. F =
7 d 2 (d - R/2)2
= G V 2 (p2 _ p) = 6,0 nH. 6,7. g = 2,45 wc 2 . 6.8. M =
=dR/G=6,O'102'Kr.6,9.h=2,6MM;6.10. F= 1,7H.6.I1. F=
= mgrlR 3 . 6.12. v = V gR = 7,9 KWC. 6.13. B Hanp3B.1etlllH c
BOCTOK3 lIa 3ana;t co CKOpOCTblO v= 460 uc.. 6.14, I1<:no.lb3yeTcJI CKO-
3;tn 3
pOCTh Bpal11.CHIIH 3eMJlH, 6.15. p = (n _ I) G T2 = 3.0.10 Kr/ M 3 .
6.16. (s)=2n(  + ;3 )=5.0.10-' paNc; v=li/2ngR( + 1)=
= 5,9 KM/e, r.llC T 3 - nepHO,A Bp>'!U{C HIIH 3eM,'1 H BOKpyr cBoeH OCH;
3 / gRj T2
R3 - pa;J.HYC 3eM.111. 6.17. h = J I - - R3 = 3.6'll" K1I,
4n 2
rAC T - nepHO,A Bpaw.ellllH 3CM.'IH oOKpyr cBoeK oeH; R3 - ,;J.HYC
3CMJlH. 6.18. afl = g= 9,8 wc 2 ; a3 = GmlRj = 1,3.10- 23 ,,!,oc t ,
6;20. Tn = 164 3CMHbIX rO.ll3.
7.1. Fcp = 525 H. 7.2. Fcp = mL'n = 15 H. 7.3, I) P = 0;
2) p = 0,16 Kr'M/c; 3) p = 0,08 Kr.}.vc. 7.4. I) t:.p = tn,) no,A rrJlOM
240' K ncpBolla'l3.1bHOIllY lIanpao.1eHHI0; 2) t:.p = mil VI no;!. } 1".'10\1
225' K ncpBolla'la.1bHoMY lIanpaBJIeHIlIO; 3) t:.p = 2mv nOl{ yrJloM 18(j°
K nCpBOIl3Qa.1bIlOMY HanpaB.'IeIlIllO; 4) t:.p =0. 7.5. Fl = m V2g:i t +
t
+ mg = 0,80 H; F 2 = 2m 1{ + mg = r,50 II; F:J =
= m V2a <Vii; + Vii;) + mg = 1,29 H. 7,6. I) v1"5' no yrlioM
t
G3' K lIanpaOJlCHHIO nepBOHaqa.blloro .llBII>KeIlIlSl; 2) v 115 no;!. yrJlOM
27" K Hanp3B.CIIHIO nepBOHa'la.lbHoro BH>KcnIlH. 7.7. P = m.l ==
= 15 Kr'wc. 7,8. p = (m 2 - m l ) gt = 49 Kr'Wc. 7.9, F = pSv l =
= 0,13 KH. 7.10. u = m1v/(m l + ) = I ,/c. 7.11. m/ m. ==
= (v + u)/(v - u) = 3, 7.12. u = ('uVI - mV2)/(m + M) = - 0,3
WC D 06paTHoM HanpaB.1euIlH. 7.13. u = lHr:7(m + M) = 5,4 JUc.
7.14. v = mvr/M = 0,1 we. 7.15. I) v = 2mvr/M = 20 cwc; 2) [I =
= V2 m'r!M = 14 oJc. 7.16. I) u = (1I1Vl- mv 2 )/M = 1,6 MC;
2) u - (Mill + mV2)1 M = 3,4 WC. 7. I 7. v = mt.o cos a/ M = 3, I ""c..
7.18. u -= 1 (mtlo) - - ,\-1 2 RH = 16 Jc; a = arctg M VgH = 31".
m+M m
tnt' + ml (v + u) mv + m! Ct. - II)
7.19. UI = 111+1/1 1 ; u 2 = iI; U3 = m+ml 7.20,
181

Ha paCCTOHIIHH, B.nooe 60.1bllleM p aCCTOHIIHII OT OPYAHH .no TO'lKH , rJ1e
yna, 6b1 CHap!\.ll. 7.21. u = 1 9 8gH / + 2H + gt 2 =
J' siw arctg (2H l) 21
= 707 wc; Ii = arctg 2H +g/2 = I C 37'. 7.22, v =
4t..1 2gH
Y sin:! arctg (2H/l)
= M V2g1 sin a./(m cos a.). 7.23. u = Mv cos wm = 870 WC. 7,24.
x = MII(m + M) = 4 M. 7.25. x = Hml t w(M + m) = 5 CM.
7.26. I = (M + m) H/ M = 12 M.
8.1. a) A = Q; 6) A = 0; B) A = 86 !l>K; r) A = 86 !l>K.
8,2. Arne = AN = 0; A Tp = - Mmgs cos w(cos a. + 1:1 sin a) =
= - 2,9 !l>K; A F = - A TP = 2,9 !l>K.8,3. AT = 29 K!l>K; Arne =
= - 29 K!l>K; 8.4. A = 0; N = 0 OTHOCHTCJ\bIlO 6epera; A =
=50 K11>K; N = 10 KBT OTHOCHTeJlbHO pCKH. 8,5. a) 0,1 !l>K; 0,2 !l>K;
6) 50 M!l>K; 0,2 !l>K; B) 50 Mll>K; 125 M!l>K. 8.6. I) A = l1mgl =
= 2,9 !l>K; 2) A = 112mgl/2 = 1,47 !l>K; 3) A = J.llmgx +
(111 + 112) mgl .
+ 2 = 4,7 !l>K. 8.7. I) A = kxij/2 = 45 M!l>K; 2) A =
k (xo - X)2 F Ii
= Ilmgxo + 2 = 23 1II!l>K, 8.8. A = 2" r:: = 3,8 K!l>K. 8.9.
A = mgRi2 = 31 f,\ !l>K , rJ1C Ra - paJ1HY': 3eMJlH. 8.10. CM.
pHe 250: I - paolioMepHoe J{OH>KCIIRC, 2 - paBHoycKopelilloc J1BII>KC-
N
t
NV
PHC. 250
Pllc.251
II lie. 8,11, CM. pRC. 251. 8.12, A = 594 M11.>K. 8.13, N = 4 Ms2/(J =
= 80 KBT. 8.14. Ni N 2 = 4. 8.15. N = mv/4/. 8.16. F = TjN/v =
= 32 KH, 8.17. T = N/(2nnR). 8,18. A TP =  49 !l>K; A F =
= 100 1l>K. 8.20. S2 = SJ. (VJ)2 = 20 M. 8.21, E R = pr-/(2m) =
= 5,0 !l>K. 8.22, I) A = 75 K!l>K; 2) A = 225 Kll>K. 8.23. A =
= 2mn 2 R 2 (ni - ni) = 7,9 !l>K. 8.24, A = mgRi2 = 15,7 f!l>K,
rj1C R3 - pa.llRYc 3CIIIJlR. 8.25. E R = 970 !l>K. 8.26. E R = mv 2 =
= 50 !l>K. 8.27. EJ(=En = 38 !l>K. 8.28. A = mgh (I + 11 ctg a) =
=-= 54 1l>K. 8.29. h= 1,28 III. 8.30. h"18RC = 25 ,5 M. 8.31. v = V 2gl .
8.32. x = V2mgh/k = 20 WI. 8.33, v = V vij - 2gh. 8.34, h =
= viJ/(2g)= 10 III. 8.35, Ii = arccos (2 cos a. - I). 8.36. E = 0,49 !l>K;
( t'-(2 )
nepeuma BO BHYTpeHHlO1O 3l1eprHIO. 8.37, A =m gh -  =
= 4,6 !l>K. 8.38. N =:- pSv 9(gh + rJl/2), r;r.c p - n;JOTHOCTb BO,i1b1.
( (12 - ., )
8.39. N = TjQr gh + Y , r,Ae p - n.l0THOCTb BO,'llol 8.40. h =
182


N
= TJpQg = 10 M, r,Ae p - nJlOTHOCTb OOl!,bI. 8.41. N = npat8 ) =
= 280 KBT, rAe P - nJlOTIIOCTb D03,Ayxa. 8.42. 11 = tg a ( I - - =
2gh
VI
= 0,082; TJ = 2gh 100% = 92%. 8.43. 11 = h/(b + l) = 0,010; 11 =
= (I - I1T),100% = 95%. 8.44. 11 = tg a = 0,10. 8,45. I) tI =
= ¥ 5gl; 2) tI = 2 Vgl. 8.46. a = g sin aJ2. 8.47. h = 2,5R =
= 50 CM. 8.48. h = R/3. 8.49. h = 23RI27, 8.50. B nepBoM.
9,1. HeT, BO BTOpON cnY1Jae CKOpOCTb CTaJia MeHbUle. 9.2. h.Jh l =
M v3 M - m
= (M + m)/ M = 1,2.9.3. h = M + m 2g = 0,43 M; tI = M + m X
X Vo = 2,6 wc, 9.4. A = m (m + M) vI/(2M) = 105 ,nm. 9.S. v =
= M V2gh = 560 we. 9.6. v = m + M V 2g1 (I - cos a) =
m m
. Mm
=0,41 Kwc.9.7. AU=2(M+m) vi. 9,8. I) u 2 = VJ.+fh=5wc;2) U2=
= VI - UI = I we. 9,9. u = (mivi - InzVa)/(ml + ml) = 5 cwc.
(m1-m2) VI + 2mov2 __, 2mlo,,+(-ml)v2
9.10. UI= + m_ = -1 MlC; u 2 = + m =
ml .. ml I
=5 WC. 9.11. U1 = (ml - tnz) v/(ml + mz); Us = 2mlv/(ml + tnz).
9,12. h = 0 12g1 + 2U)I/(2g). 9.13. I) Ap = 2mv = 0,2 H.c;
II = 50 M,n>K; 2) Ap = 2mv sin a = 0,1 H.c; II = 12,5 M,n>K.
_ v sin a + /!f
9.14. Ii = arctg v cos a 47". 9. IS. 'AEI E = 1- n- I = 75%.
9.16. al = (ml - m 2 ) aJ(ml + tnz); a 2 = 2ml aJ(m + tnz),
mlml (VI - V2)
9.17. Ii = mlaJ(ml + tnz). 9,18. II = 2 (ml + Ins) . 9.19,
.... -+
rI- = ui + u, T. e. Ul J. u 2 ' a SHa1J\!T a = .90 0 .
4mlm2 + m., (ml - m
II. I, a1 = g 4m Ins + 1710 (ml + Ins)' 11.2. F = (111 + III) X
X (m + M) g = 22 A. 11,3. a = 0; F'Ip = F - mg sin a = 2,7 H,
11,4, F = 2 V3' mlfflJ . 11.5, a = g V9111 + 4 = 20 wc l . 11.6. U =
(3m l +m l )
m M+m 0
= M + m Vo eos a = 0,88 we; Ii = arctg M tg a = 53 .
V M + m __, pm l
11,7, v = 2gH = 7 MlC. 11.8, '( =, 2'
M Ins (tnz - mlJ g
2RM -V -
11.9. v = - Gnp = 120 WC, r,Ae G-rpaO\!TaI.tHOHHan nOCTOJIH-
m 3
lIaH.
10.2. FI = F 2 = 9,8 H. 10.3. F = 30 H. 10.4. T = 19,6 H;
P = 29 H. 10.5. T = mzg = 9,8 H; P = mlg cos Clt - ffl?R = 7,2 H;
F Tp = m 1 g sin ex. = 9,8 H. 10,6. m3 = 0,10 n. 10.7.. mx = 5,0 Kr.
10.8. F = 0,15 KH; T = 0,21 KH: 10.9. T = 0,24 KH; a = 37'.
183

10.10. F AB =56 H; F 13C =II3 H. 10.11. P=90 H. 10.12,
F AC = 0,29 KH; F BC = 0,39 KH. 10.13. ml = 0,13 Kr; m z =
= 40 r. 10.14. a = 53 0 . 10.15. F AC = 0,68 KH; F CB = 0,34 xII.
10.16. m = 8,9 Kr. 10.17. F = mglw= 0,49 KH. 10.18. H = h +
+ 1  5,5 M. 10.20. a) k = ; 6) k = k l +
2 V (2TI Mg):- I k 1 + k z
+k z . 10.21. m2=mlsina=I,O Kr; F=2m1gcosasina=
= 17 H. 10.22. ma = (ml - m z ) sin a; P = "(m l - m z ) g eos a.
11.1. Fa = 30 H; xP._F. = 40 CM. 11.2. F:s = 45 H; x P ._ F .=
Fa-FI
= 30 C}I. 11,3, Fp = 200 H; xp!_F p = 2 (F I + F 2 + Fa) 1 =
= 18 C\!. 11.4, Fz = 12 H; Fp = 18 H. 11.5. OT!lOeHTeJlbHO ueHTpa
)lacc. 11.6. C\I. pHe. 252; N 2 = 0,98 KH;
N 1 = 8.8 KH. 11.7. F = N = 5,9 KH; 11,8.
N 1 = Mg (L - l)/(2L) = 2.76 KH Ha ncpe-
IIHC Ko.1eca; N z = Mgll(2L) = 3,86 KH Ha 3ak
4k 1 l1h
IIHe KO.1eca. 11.9. m = ----g-- = 40 Kr;. x =
= 114 = 2,5 CM OT npY>KllllbI C >KeCTKOCTblO.
11.10. x = 0,2 Jd OT cepc.nIlHI>I.
11.11. I) = 80%; F/F2 = 0,6.
2FI 2F - mg
11.12. L = 2F _ mg = 1,8 M; Fc = 2 = 25 H. 11.13. FI =
= 21tIl)Flh = 20 KH. 11,14. F = Mghl(21tnl) = 98 H. 11.15. F =
= Mg (rl - r)/(2l) = 25 H. 11.16. fA.  tg (a/2) = 0,27. 11.18.
. 1 R
Fa = 10 H; GlicceKTpHca. 11.19, T = mg + ; FiJ. =
Vi- + 2lR
mgR 21 V (biZ): + (a/2 - 1)2
- V . 11.20. L = = 20 C'f.
12 + 21 R a - 21
mgsinB mgsjna
11.21. FI = sin (a+lI) = 20 H; F 2 = sin (a + II) = 34 H. 11.22.
F = 2J1gh sin a/(I cos 2 a). 11.23. a  arctg 2Jl = 51 0 . 11.24. a =
= 2 arcsin (mlm) = 600; FA = mlg ctg arcsi n (mlm) = 42 H.
11.25. P.  1/(2 + V3)". 11.26. F MU " = mg Vh (2R - h)/(R - h).
11,27. F"UH = Mg/2; p.;;> 0,5, 11.30. F = Mgh/(4l) = 0,49 KH.
II 31 " 1 - 20 II 32 _ m 1 (I + R 1 + R 2 ) + M (1/2 + Rz) =
. . LJ. - CM. . ,x - ml +ms-t-M
=- 9,7 CIII OT ueHTpa 60.'1bWOrO mapa. 11,33. x = 2pa:JRI(Pan + Pit) =
= O,56R OT ueHTpa ltHilKOBOro mapa, r.ne Pan, Pn - nJlOTIlOCTIl a.110-
MHIIHH H IlIUlKa. 11.34. TOJlCTblH. 11.35. m = ml = 250 r; fJ.l =
t1'1 I
= 2 ( , ) 1 = 3 - M. 11.36. KooPAHHaTbi neHTpa TIU;;eCTH (25; 5)
ml T m z
OTlloeHTe.'1bIlO TC1JKH O. 11.37. KOOr-,\IIHaTbi ueHTpa TfI>KecTH (12,5;
7,5) OTHOCHTe,1bll0 To'mH O. 11.41, 1,5 C!of OT lleHTpa. 11.42, x =
184
h
L l
PHC. 252

R
= 2 (2n _ I) OT reOMeTpH'IeCKOrO lleHTpa. 11.43. a) ,,= alI2 OT
na
reOMeTpH'IeCOro lleHTpa; 6) x. = 4 (16 _ n) OT reO\!eTpn'lCCKOrO
lleHTpa. 11.44, x = a V3i28 OT reO\!CTpH'IecKoro ueHTpa. 11.45, h =
= I sin arctg (1/3)= 19 CM. 11.46, Ct= arctg p.= 17°. 11.48. Ha Y3KOI.
mga , /n
11,49. A = MgL/2 = 5 K.l(:w:. 11.50. A = T (v 2-1) = 400 .l(>K.
11.51, A = pga l (41/2 - 3)/24 = 1,1 K.D.>K. r,/te p - nJlOTHOCTb BO-
JlbI. 11.52. v = V aglV3 = 0.98 Wc.
12.1, I) P = 0,49 KTIa; 2) P = 2,9 Kna; 3) P =' 5,5 KTIa;
PUOPUIH = PIRR!IK; He H3NeHHTCSI. 12.2. F = 5,0 xH. 12.3. CM. pilC. 253:
PI = F cos aJS = FI2S; P2 = FIS. 12.4, CM. pHC. 254: J - JlaBJlC-
HHe aTMoccJlepbl B03pOCJ\O; 2 - l1aB.'leHHC anlOccJlepbl YMeHbwH.'10Cb.
12.5. F1J,BB:! > mg, KOr,Aa cocYl1 cY>KaeTCH KBepxy; F1J,BB:!! < mg, Kor-
,/ta COCY,/t paCWHpHeTCSI xBepxy; F 1I8Rn = mg, KOrl1a cocY.1t npHIOA,
12.7. F = pga' - ua ,/tHO; F = pg(il/2 - ua 6oKooble rJlaHH. 12.8.
F=7,8 KH. 12.9, F=39 H. 12.10. F = fltS.jSl = 8,0 KH. 12.11.
F = TltlvB = 9.5 KH. 12.12. SiS2 = nhmg/(flA) = 55. 12.13. h =
= m/(pPTS) = 2,5 CM. r,/te PPT - nJlOTHOCTb PTYTH. 12.14. fJ.h =
P,hl - P K h 2
= P = 2,0 CM. r,/te PM - nJlOTHOCTb Mac.'!a; PH - nJlOT-
1I0CTb KC;:CHHa; Ppr- nJlOTHOCTb PTYTH. 12.15, M = - S m ( .2.. - .!. ) =
PM PB
= 4,0 CM, 12.16, H:::;: 8 XM. 12.17. M:::;: 5,3.1()I8 Kr. 12.18. h B . CT =
= 10.3 M.. 12.19. BO,Aa nO,/tHHMaeTCJI He 6o.nbwe 'Ie\! Ha 10,3 M. 12.20.
FI = 0; F 2 = 11,3 H. 12.21. H3111eHHTcH, TaK xax nOBblCHTCH YpoBell&
BO,/tbl B cocy,/te. 12.22. ECJlH cocy,/t cy:w:aeTCH Koepxy . TO rHpH II PTYT&
He OTOPBYT ;{IIO, a MaCJlO OTOpBeT. ECJ\H COCYJl cYH<aeTCSI KHH3Y, TO lIa-
060pOT. 12.23. A = pS (h - ha/2) = 6,2 .l(H<. rJle ha = 0.76 M.
: ' "
;Pc+ P f.'1 2
1
h
11 h
Pac. 253 Puc. 254 PIIC. 255
12,24. BblTaJlKHBalOm.an CIIJla B03UHKaeT 113-32 pa3HOCTH ,/taBJleHHii lIa
pasHoA rJIy6HHe. 12.25. He Bcn.'1b1BCT, Tax !tax BO.lla no,/t Ky6HK He npo-
HIlKaeT. 12.26. h = H - m/(pS) = 4,0 CM. 12.27. P = 314PB =
= 7,5.10 2 !trIMs. 12.28. p = PIP.l(P1 - P.J = 2,2.1Q3 Kr/M s .
12,29. Pa = PB - 4l1PI(nD2hg) = O,80.lO s Kr/MS. 12.30. S = .
= mIlh (PB-P:\)) = 2,3 M 2 , 12.31. V = m (  - .2... ) = 9,6.10- 3 MS.
PB PCB
12.32. P = PI - (PI - P2) (RiR2)3. 12.33. T ==0 mg (n :: - I) =
= I H. 12.34. P = s/.PB = 0,75. lOa Kr/M 9 . 12.35. Bblwe no;J.-
185

IIH"feTCH wap 113 3J1aCTH1JHOH pe3HRbI, 12.36. HapywHTcH. 12.37. CM.
( PO 0 cos IX )
pHC. 255: I-d2dl; 2-d t >d l . 12.38. F= 2 + PBH X
X ghlo ctg IX = I, I H, 12.39. F = pr£S (H + 5h). 12.40. P = PH +
hI
+ (PB - PH) a = 0,84,103 Kr/y8; F Bepx = PR!Iha'l = O,4!} H:
FIIR)I(R = grr (PR (0 + hI - h 2 ) + P B h 2 ) = 1,5 H. 12.42. h =
= a (pP'l' - pC'I')/(pp'l' - PB) = 4,6 CM; P = PCTga = 7,6 Kna.
12.43, A = (PB - Pn)2 gSH2/(2pB) = 2,5 D.>K. 12.44. A = mg (H +
+ h) - polJ'l/h = 0,15 K!l)l(, rAe mg (H + h) - H3MeHeRHe nOTeH-
IlHa.lbHOH 3HeprHH TCJla; PB g'l/h - H3MeHeHHe nOTeHUHaJlbllOii 3Rep-
rUH SOAbI,
111,1. m./ml = eos wcos (a./2) = 0.58, 111.2, cp = aretg X
X (m2 - ml) V3" = 11°. 111.3. Lllianc = I V I + ,...2 = 2.2 M.
(m 2 +ml) 3
p.mg tg IX p.mg tg IX
111.4, B.'1e80 F = 2 (11+ tg IX); BnpaBo F = 2 (tg IX-II)" 111.5. T =
= Mg cos a./2; ,. = 45° - a./2. 111.6. IX = arcsin (1/6) = 10°. 111.8,
TI = mg eos a./2 = 4.2 H: T 2 = mg V I - 3/. cos 2 IX = 6,5 H.
mg + F (I + l.jll)
111.9. p = s + pgh = 3,0 Kna. (11,10. P = 5po.
111.11. FI!. = a 2 g [PB(h- ; sin IX) + Pa:i0 cos IX] = 69 H; F TP =
= (Pan -.PB) dig sin IX = 8,3 H, (11,12. H = h (32 :B n - 33) =
= 27 CM.
13.1. :x = A sin (2ntlT) = 0,05 sin 4nl. 13.2, x = A sin 2nvl =
= 0,04 sin 100nl. 13.3. CM. pllC. 256, a-8 13,4, T14; T/12; TIG.
v v v 2 v
13,5, T16. 13.6, x = R sin R I; Vx = v cos R I; OX = - R sin R I;
v v  V
CM. pHe, 257, 13.7. x = R eos N'; Vx = - v sin IF ax = R cos R I,
j(
x
t
t
PHe 256
PIIC 257
186

CM. pHC, 258; .1q:'l = n/2; ACP2 == :"I; ACP3 = :"1/2, 13,8, CM. pHC. 259.
2n 2n 4n 3 2n
13.9. v = A T cos T t = 4,4 cwc; a = - A 1"3 sin T t =
= - 14 cM/c 2 . 13,10, vel' = 4AIT = 4 cwc. 13.11, I} t'cp = 0,5 IIIfc;
arctg (Jewlv:.:>
2) t'cp = I ..tic. 13,12. t = w = 0,2 c.
JI
J
I I
t
I I
t
I
PIIC. 258
PHC. 259
14.4. nepHO)1 J<o.e6aHHn MaTeMaTII'leCJ<oro MaSlTHIlKa YBe.UI'IHBa-
eTCH, a ri'pynUIHHoro He HJMeHHeTCR. 14,5. T = 20 c. 14.6. a =
= 4n 2 n 2 (I + d/2) = 9,82 II..tC 2 . 14.7. fJ.III = [I + R:!(2h)l-1 = .
= 3,1.10- 3 . 14.8, M = tclr/ R3 = 68 c, rAe t c - CFKI!. 14.9. a =
= g (I - TiIT) = 1,7 IIIIc 2 ; Hanpao.1eHHe Jl.BH)KeIIHR He nrpaCT POJIH.
[
EnDnH=con$t
r . llff
"Stn Tt
t
14.10. T = 211: V l/V gZ + a. 14.11. T = 2:1 V Rii:" 14.12. T =
= n V Ilg (1 + Vi72) = 1,7 c. 14.13. a} T=2n V m (k 1 +k 2 )/(k 1 k 2 );
6) T= 2:1 V m/(kd- k 2 ). 14.14. T= V 4nml(pgr) = 3,6 c. 14.15. E =
= mgl (I - cos ex). 14.16. E = mgA 2 /(2/). 14.17. CM. pllC. 260.
14,18, !J.Je = 2Jeo: t'M 3tcC = V gxo: nepHO,A J<OJle6aHHH T= 211: V xol g .
ma y' 2hk ( mg ) ?
14.19. A = - I + -; E = mg h + _ 2 . 14.O, T =
k nzg k
L y -
= 2nA (M + m)/(nzv) = 1,26 c. 14.23. v = - [= 68 Kill 'I.
2:"1 1
187

15.1. v = ld(l + n) = 330 Mlc,
rAe c - CKOpOCTb CBeTa, 15,2.1 =
= t.etf(c - v) = 4 KII, rAe c - CKO-
pOCTb CBeTa; v - CKOpOCTb 3BYKa.
15,3. v = Id(l- n) = 1400 wc. rAe
c - CKOpOCTb CBeTa. 15,4. A = v/v =
= 21... 15.5. A = v/v = 7,25 M.
15.6. "-1/'J..s = viv2 = 4,35. 15,7.
viv s = "-1/'A1 = 2, 15.8. I, 2) npo-
AOJlbHl>le; 3) npOAOJlbHble B nonepe'l-
IIble. 15.9. CwI>l1JKOM B cTpYHe - no-
nepe'lHble, CTPYHOA B B03Ayxe - npo-
AOJIbHble. 15.10. Y (x, t) = A sin CD X
X (I - Wt') = 1,7 10-' sin 4n. I ()I X
X (/- .J340). 15.11. Y (x, t) =
- A .
= n sin 2n (vi - xOJ/A) = 7.5'1O-'X
Xsin 2n (1500/-.JO, 15) B CI1. 15.12, Cw. pBC. 261. 15.13. AIA=5' 10- 6 .
15,14. Ax = t'/(2v) = 1 M. 15.15. Aq> = 2nvA.Jv = n/2.
g
A
o
PIIC. 261
11
IV.I.I)T=2nWa=I,4c;A= x _ 4CM;2)q>=
cos arct g MY xa)
=arctg(vI YxQ) ::=ttlI2. IV.2. T=2 n "l; mM . IV.3, T=
,., k (m+ M)
=nY 211(....g) = I,5c.IV.4. I) x=Rcos Yg/RI ;2) l=nV Rlg =
= 42MH8:3) v = Y Rg = 7,9KMf..c.IV.5. t% = arctg (a/g).IV.6, A =
= mglk = 0,6 MM. IV.7. T18; 3T/8; 5T18; 7T18. IV.8. Aq> =
= Ax.2tt1A = 2/3n. IV,9. vI = nlvinl = 356 ru.
16.1, mlmH = 1.20. I()!e. 16,2. m = MH.dNA = 3,0 X
X 10- 2 & Kr. 16.3. nB > npT' 16.4. n = mN 1 v1(.... Sh) = I()I. 16.5,
I) n = pVNA/.... = 8,4.1()22; 2) T::= V pJ(pN A ) = 2,3.10- 18 III.
16.6. I) n= 2,7.10 11 ; 2) T3,3,10'" M. 16.7. n= 2.69.1()26 AI- 3 .
16.8. P = 1,97 K.r/1l. 3 . 16.9. N = 55,6, 16.10. V = Me N/(pN A) =
= O,57.1O-! 1I.3 16.11. d = 3,3.10- 18 M. 16,12. N = 34Q.
16,13, 'I = pVN A 100%/M H10 = 37%. 16,14. L = mNAdlM OI =
= 5,6.1(}I II; LI R3 = 15.
17.1. 113-38 CTOJIKHOBellHH nepeMew.eHHe 1I.000eKYJI 3aTpYAHeHo.
17.2. 't = P VI(zkT) = 8,4. I ()I JleT. 17.3. LJeM lI.ellbWe nOBepxHocTb
'1aCTHUbl, TeM 60J\bwe Mepa HecKoMneHcBpoB8HHOCTH Y,AapoB, 17.4. no-
CKO.bKY CKOpOCTL TenJlOBOrO ABB1KeHBJI 1I.0JleKYJI nponopnHOHaJlbHa
Vr. CKOpOCTb AHcM>Y3HB YBeJlH1JHBaeTCH C pOCTOM TeMnepaTypbl
mN .
(- T3/2). 17,5. n =  = 4.10 18 C-l. 17.6, B aToMapHblx ra3aX
J!I
aTOMI>I ,ABH1KYTCR nocTynaTeJlbHO OT CTOJlKHOBeHHJI AO CTOJIKHOBeHllH,
B KpHCTaJlJle aTOMbi cOBepwalOT KOJle6aHHR OKOJlO onpe,AeneH8b1X P3B-
HOBCCllbiX nOJlO>KeHHA, o6pa3YIOlUllx cIlMMeTpH'IHYIO npoCTpaHcTBen-
HYIO CTpYKTYPY, Ha3b1BaeMYIO KpIICTaJlJlH1JecKoH-peweTKoH, 17.10. 'Be-
JlH'lH.1OCb 6b1.
188

18.2. M 1 = fJ.lz = la!J..T = 36 )!KM. 18.3, 1/11 = 0./0.2' 18.5.
JI.Ha\!eTp YBe.'1H'IIITCH. YroJi q> He HJ\!eHHTCSI. 18.7. a = Ea.l:J.T =
= 46 Mna. 18.8. F = Ea.ATS = 69 H; n = ESla 2 fJ.T2/2 = 34 M.1J.i!(.
At
18.10. fJ.S=So2afJ.T= 59. 10-& MS. 18.11, 1 1 = 1 (aaJI-all<)-aat fil =
t
= 83° C; t 2 = J = 28° C. 18.12. A V = VoAT = 15.10-:\ M 3 . 18.13,
06"beM BLI.'1HOWerOCH KepocHHa 6Y.lleT \!CnbWe Ha fJ. V = 30.11< VofiT =
= 5,4.10- 6 M 3 . 18.14. P = pJ(1 + fiT) = 13,36. 10 3 Kr/M 3 .
18,15. = (Pl- P2)/(P2fiT) = 1,0.10- 3 K-I. IS.18. p= (h'!,-
d(l+ac fiT ) .
- h I )/(h 1 fiT). 18,17. 06"beMYMeHbwHTcR.18.19, R = ( ) fiT =
a.It - ac
PK mgfiT (- 30.)
= 56 C\!. 18.20. fJ.T = (I . fi!1T) 6,4 MH.
PM T
19.1. vN/vo. = VOlJ!N. = 1,07, a30Ta. 19,2, VII =
V  - u;-ui °
= 3Rl/J! = 13/0 lit/C. 19.3. AT 2 = ATr v 2 _ t,a = 183 . 19.4. n =
:I t
= p/( k.7) = 2,9. 102:i pc 3 ; N = pV/(kT) = 5,8.10 21 . 19,5. v =
= V(vl + vW2 = 453 wc. 19.6. YBCJ\H'IHTCR lIa 44%. 19.7, p =
= 2 U/(3 V) = 10 5 na. 19.8. T=v 2 p./(3f?)=71 K. 19.10. N=
= p'l//(kT) ::::;2.10 13 .19.11. z =  V 3RT,= 7,1.10 9 . 19.12: Ha til,
,. fA.
BCH JUllleTlI'IeCKaH 511eprllSl ncpew.a BO BHYTpeHHlO1O 5HeprHIO ra3a.
3 In
19.13. AU= 2"  RAT = 12,4 K.lI.>K.
20.1, v= I,O.IO- 2 M 3 .20.2. m= 22r.20.3. A30T.20.4, fJ.mlin=
113. 20.5. Cr.!. pilC. 262: 1 - 1130Tep\la; 2...... 11306apa: 3 - H30KO-
pa. 20.6. EC.'1H "I = "2 H ml = m 2 > TO TI < T 2 ; CC.H fll = J!2 H
P tt1 7
--,' · 2
-- J
5 I
, I I
, I I
p

T
r,
Il r
PHC. 262
PIIC. 263
Tt = T2' TO m l < m 2 ; eC.1H mI = m 2 II TI = T 2 , TO 'II > 1 1 2'
20.8. t..s. = tg altg 0. 2 ' 20.9. a) YDeJlH'IHBaeTC!\; 6) YMcllbwacTcSI.
20.10. '1"Be.1H'IHJlaCb Macca. 20.11. .lI.allJleHHe YBe.1H'IH.'10Cb. 20.12.
YlleHbWHJlaCb Macca. 20.13. PHc.263: I) 1-3-2,1-6-2; 2) 1-4-2;
1-7-2; 3) 1-5-2, 1-8-2," 20.19. P = pgH (hI - h 2 sin a)/(h l -
_ h 2 ) = 1,0'10 6 na. 20.20. h _(L + Hf- V(;+H)3- 4/3HL =
...f>
IRq
,

"= ,I CM. 20.21. M == hi (I + h,jH) = 5,0 CM. 20.22, m = pV X
X ( I - P ) =0,17 Kr. 20.23. t = 4,0 MRH. 20.24. n =
Pa + pgh
= log (Palp)/Iog (I + 'I//V 2 ) = 80. 20.25. f1plp = (T I - T!) X
X 100%/T I = 30°11, 20.26. Tz = (P,£.+ pa) rl/f + Pa) = 258 1(,
SIT 2 ( pa ) Pa . I
20.27, S - = - I + - - - = 1,2. 20.28. V 2 VI = 1,07. 20.29,
2 Tl PI PI
T = f11'/n = 3331(. 20.30. TI = I1I1T/Jt a = 312 K. 20,31. f1m =
pVI1 ( I I )
= - -- - = 2,5 Kr. 20.32. 'l/oIVa=mBl1a/(l1oma + l1amD) =
R TI T 2
pVI1 I ( mal1oTI )
= 0,65. 20.33, m = - = 0,41 Kr. 20.34. m B = - - =
R1' 10 l1a Ts
= 17 r. 20.35. On ycTHTcH B npaBoM KOJlClle Ha b =
(2l + II + h) - V (2l + H + h) 81 (H + Ii) (I - 7'-/1'1)
4
= 9,1 MM. 20.36, M = 2Vf1TI(mf2T) = 5,5 CM. 20.37. P =
RT ( m ll ma\
= 2PIPz!CPI+P2)=O,15 Mna. 20.38. P- 'I/ - + - ) = 0,46 Mna,
1111 l1a
( p'I/ m ) I1l<l1y.r ( PV m )
20.39. my.r = --- = 5,5 r; mil = -- - X
RT ""11 11/1-y.r RT l1y.r
11" l1y.r mRT
X 11 t = 34,5 r. 20,40. P = Po + _ '1/ = 13,8 Kna. 20.41.
,,-J y.r JL
liB = Itaf1j(an/l + Itllna) = 0,029 Kr/Mo.lb.
21.2. npu C>KaTIIH Mo.1eKy.'Ibi H.lleaJlLIIOrO raJa 'Iaw.e CTa.1KHBaIOT-
CH H ,Aao.1CIIIIC ra3a YOCJlH'IHOaCTCR; '1aCTb Mo.'IeItYJI Hacblw.eHHoro napa
nepeU,AeT 0 >K\I;{KOCTb, npH !lTOM p,aBJleHHe OCTaeTCSI npe>KHHM. 21.3.
V < 100 JI. 21.4. OXJla,AHTb ,AO 3°C. 21.5. YpoBeHb BO;J.bI B Tpy6Ke
6Y.1.eT nOHH>KaTbCH. npH 100 °C BO.lla B CTaKaHe H B TfY6Ke 6Y.ACT IIa
O,AHO'>l ypOBIIC. 21.6. P = f!PH/(RT) = 0,581 KrIll, 21.7. n =
=P B 2TI(f!p/I)=5,8.IQI. 21.8, V=(ml +m 2 ) RTICPHIt)=2,3 JI. 21.9. P2=
= npi = 10 6 na 6YAeT npOHCKOAHTb KOH,AeHCaUHR napa. 21.10. HaAo
BBeCTH CTQ.'IbKO napa, 'IT061>1 OH, CKoll,AeHCHpOBaBwllcb, SanOJlHH.'1 BeCb
PH
cocYJJ.. 21.11. Ah = Pi! = 18,7 MM. 21.12. H8.Ao llaK.'IOIlIITb Tpy6KY.
ECJlH ypOOHH BO,AbI B ee KOJlCHaX 6Y,AYT O,AHHaKOBI>IMH. TO Hall. BOAOA
HaXO..'l.lITCH naCblw.CHllbiA nap, a ec.1H paSJlH'IHbI, TO B03,AYX. 21.13, P2 =
PIT'/. mRT PIT!
= -r;- + ItV = 171 Kna. 21.14. PI = T;' + Pl! = 230 Kna;
PHf! V
Macca HeHcnapHoweiicH OO,AbI f1m = m - R1'z = 4,2 r, 21.15.
Vjv B = ltom'/(ltllm B )= I, nopweHb YCTaHoBHTcSI noCepe.1l.lIHe UII.1HH-
,Apa. 21.16. P = PHp./(RT 2 ) = 9,4 rIMs, Bblna,AeT poca. 21.17. f =
mRT
= 1- RTm/(f!VPH) = 59%. 21.18. 1 2 = II + I1 V Pa :z: 61%. 21,19.
n . I n
pH nOBblweHHH TeMnepaTypbl. 21.20, na. 21.21. 2 = 11- = 24%.
PIa
190

21.22. m = J1-; el1 - p;:) = 2,4 r. 21.23. f = (hSl +
+ f 2 S 2 )/(Sl + S2) = 56%.
VI.I. Ah = O. VI.2. t..m/m=0.2; pzlPl=I.2. VI.3, CM. pRC. 264.
VIA. l' = 9P o VJ(4R) = 405 K. VI.5. h = (I - f) l + (I - f) x
X Pa /(/pg) = 31 CM.
22.1, Y >KeJle3a. 22.2. HaH60JlbwylO Ten.10e'iKOCTb HIIICCT >KCJlCSO,
lIaHMeHbwylO - eBHlleu. 22.3. Y ToepAoro Te.1a. 22.4. I) c 2 > Cl; -
2) m 2 > mi' 22.6. C,IC nc = 1/2. 22.7. V = 0,80 JI. 22.8. VI = V X
X (1'2 - 1'3)/(1'2 - 1'1) = 60 .'1; '1/ 2 = V (1'3 - 1'1)/(1'2 - 1'1) =
= 50 JI. 22.9. 1'% = (Cc-rmlT;. + CBm3 1'2)/ (CCTml + COm2 = 364 K.
22,10. t..T = Cc m3 (1'1 - 1'2)' (cc m3 -I- lCT m l + Co m 2 ) - 1,2 K.
22,11. m/m2 = c 2 (1'0- TZ)/[Cl (1'1- To)). 22.12. CJ( = clmM X
X (1'2- TN) (1')1(- T 1 )/[m" (1'1- 1'2) (1'11(- 1'11» =0,90.10 3 !J.:KI(Kr. K);
..
-----/?1' p
-U i
/,, , ,2 I
1 1/' I I
I" I I
,'1 I I
T
t:t 
ljO
20
-20 t
-ljO
-60
- i
I
I. I
- 1 I I
 I' I
1/ I I I
T
PIIC. 264
PIIC. 265
C'K = CM mM (1'2 - TN) (1'1- T K ) /CmH; (1'1- 1'2) (1'111- 1',,)) =
= 42,103 .ll>l</(Kr' K). 22.13. C!oI. pHC. 265. 22.14. 1'% =
CT I + comITo - Ami - Cxmn (To - 1'2) _
C+CB m l = 2i9 K, rAe To - TeM-
nepaTypa nJlaB.1eHHR .1bAa. 22.15. To = 273 K. B COCY,AC KpOMC BO;J,bI
_ C (1'1 - To) - Cnmo (1'1 - To)
6YAeT .'1 ell MaceOH m= mo - }.. = 7,2 r.
cOm! (1'1 - To) + Am2+cJ\m,T2+clmITI + cJ\m 2 T o
22.16. 1'% = Cx m 1 + c a (ma +m 3 )
= 271 K, rAe To - TeMncpaTypa 3aMepsanHH Br);J.bI. 22.17. m =
= [AmI + c B (m 1 + m 2 ) (1'1 - T»)/[r + C B (1'2 - 1'1)) = 3,5 Kr.
22.18. mn/ m =rl(r+1..) = 0,87. 22.19. 'I = cml(7'2- 1'1) X
X 100 0 o/(gm 2 )=32%. 22.20, '11=(CBp'I/+Caml) (1'2-1'1) 1000/(gm2)=
= 38u; '12 = CDPV (1'2 - 1'1) 100%/(gm 2 ) = 36°0.. 22.21. 'I =
= cOml (1'1( - T) 1000/(N() = 89°u; m 2 = ml (1 - c (1'1( - 1') X
X T!(rt",)/ = 0,96 Kr, r,Ae TJ( - TC!.lnCpaT}pa KHneHH!! BO,AbI. 22.22.
cS!:1lp cp '\ V
Q = a- = 3,6 M,.':{>K. 22.23. Q =  = 0,66 M,.':{iK. 22.24. 11=
=- 1,0 CM.
23.1. Q = mt/2 = 50 11.>1<. 23.2. A = i.2m = 3.103 .il>K. 23.3.
I) Me;J.llblii; 2) >l<eJleJHblii. 23.4. AT = 'I (t'i - t.:nf(2c) = I i3 K.
23.5. 111' = nghlc = 0,012 IC 23.8. fJ.T = /(2c); tiT I 23.1O-:r I:.
191

6T = 12.10- 3 K; 6Ts = 21.10- 3 K; 6T. = 31.10- 3 K. 23.7, N =
= (cpV6T + rm)/(n't) = 13KBT. 23.8. V = V 2 (ct1T + 1.) = 3601lllc.
m
23.9. h = (cm!1T + 'Am)/(nMg) = 2,9 M. 23.10. Q = 2" (.11- L'2) X
m .
X [(VI + L'2) - M (VI - (/2» = 4,6 KD,iK. 23.11. 6 T =
= nl\,fv 2 /[2c (m + M)) = 27 K. 23.12. M = m!?/(2qTJ) = 2,2 r.
Ns 11mqv
23.13. m = - = 74 r. 23.14. N = - = 29 KBT. 23.15. 6m =
11 s
MglIs 11mlqV;
= - lq = 21 r. 23.16, n! 2 = mlt..,It' 1 = 100 r; N = - =
11 - 
= 32 KBT.
24.2. Q = 3mR6T/(2) = 2,5 K11iK; C = 3R/(2) = 3,1 KD,>KI
/(Kr. K). 24.3. 6U = Q = 3pV6T/(2T) = 1,0 K11>K. 24.4. Q-=
- 3/2'1/ (pJ - PI) = 3.0 KLJ:iK. 24.5. P2=PI + 2Q/(3V) = 0,57 Mna;
T 2 = Tl II + 2Q/(3pV)) = 329 K. 24.6. Q = 3 (n - I)RTI2 =
= 7.0 Mll>K. 24.8, Q = A. 24.9. TiTI = VJV I ; A = Po X
" (V 2 - '1/1)' 24.10. A  P2 ('1/2- VI)' 24.11. a) A =pz (V 2 - '1/1)+
+ PIl'IlS - '1/2); 6) A = (P 2 - PI) (Vi - VI)' 24.12. tlU =
= 12 KD,>K; A = 8,0 KiliK. 24.13.. Q = 5mR 6T/(2) =
(Pa + mK/S) V6T
= 25 D,>K. 24.14. A = T = 80 ,!],>K. 24.15, A =
= mRTI = 0,17 M.J,>K; lJ = (rm- mRT/Jl) = 2,1 Mll>K. 24.16,
II = R6T/[PaS - (M - m) gJ = 1,6 M. 24.17. A = (n - I) X
X mRT/(n!f) = 17 KD,*; U u = UK" 24.20. 11 = AIOO%/(A + Q) =
= 20°0. 24.21. 1) = 2 (nl - I) (n2 - I) 100%/(5nln2 - 2nl - 3) =
= 17'70. 24.22. 11 = (T 1 - T. - T 2 + T 3 ) 100%/(T 1 - T.) = 25°0.
24.23. Qx/Qu = TxlTu = 113. 24.24. Tx = nTn = 301 K. 24.25.
11/1]1 == [(T 2 - T J ) + 6TJ 6Ti[ (T 2 - T I ) (T 2 + 6T)) = 1,96.
24.26.111 = AIOO% (mq) = 24%; 112 = (Tn- T x ).100%/T n = 42°0.
24.27. P = (T l - T 2 ) mq/(TI't) = 44 KBT.
rt1'TI+MT2M;N(2c))
VII.1. m n l m =dTIJ.=O,062. VII.2. Tx M + m -
""'" 340 K. VII.3. Q = (c 6 T + 'A) m + p't = 1,2 KD,iK.
VII.4. QI = SP o Vr/4 = 1.9 K}I>K; Q., = Po'l/r/4 = 0,38 K!l>K. VII,S.
11 = ( f 2 - PI) (V 2 - VI) . 100%lr3 (p.. V 2 - PlV l ) + 2P2 ('1/2-
- VI) = 9,1 °0. VII.6. 11 = (P2 - PI) (V 2 - VI)' 100%/(3 (PI V 2 -
- P2 V I) + 2P2 (V 2 - VI)) = 10°0. VI1.7. A = rm = 6,9 KLlm;
r (m - 'lp'l//(RT1,n
6T-rmlcpV=I,6 K. VII.8. c= m(TIi-T)
= 1,5 KD,>KI(i\r.K).
25.1. 6 13,4 c . 25.2. q = nem N i = 44 /l\KJI. 25.4,
 , /" Gn' m
F.,1 Fr - ke-!(Gmr} -4,2.10. 2 . 25.5. q = V -r =5,68.10 13 1\.1,
8
25.6. R = J 9ke (16:n 2 p2G) = 76 MKM. 25,7. ql 2 = (kq :I:
:I: V kqZ -. 4kFr 2 ) 1(2k); ql = 38 MKK.'I; q.. = 12 IIIKKJI' 25.8. x =
= r V q3'QI = 4,5 CM OT 3ar . q H3 nF""!c1-iKePHII JlIIHH!!, COCJl.HHSlIO'
192

w.eii JapSl;J,bI q1 II qt. 25.9. Ha paccToSlHIIH a/3 OT q lIa.l1O nOMCCTIITb
nOJlO>KII'teJlbHblii JapR.'I. Q = 4/9q.25.10. F = 2ktj cos 30'Ia 2 = 50 MH.
25.11. B lleHTpe Tpcyro.'!bHHKa Ha,AO nOMeCTHTb sapSl.l1 Q = 8q X
X cos 3 30°/9 = 5,8 IIIKI(JI. 25.12. Q1 = O,957q. 25.13. r =
=2q V k/(3mg) =35 CM. 25.14, q=2rV Flk =30 HK.'!. 25.15. llIapHKII co.
y-
npHKocIIYTCSI, a nOTOM paJOii.l1YTCH Ha paccToSlIIHC r1 = rlv 4 = 3 CM.
25.16.8 = rilr = 81. 25.17. P =,PKe1(e- I) = 1,6 r/cM 3 . 25.18.
(a) = Jf ..-!!- _ k2 ; F" = mqlcos a.
I cos a mfJ sms a
4E A Ee
26.4. r1-=q111(q1+q2)=12,3clII. 26.5. Eo
Ee+ 2 V EC E \ +EA
16 B/M. 26.6. E(o:OI = 25 KBlM; E(o: 31 = E(o: -3) = 17,7 KB/M;
napaJl.leJlbHO OCH X. 26.7, .aBe TO'lKH C KOOP.II.H HaTa\l JI (0; 0), (4; 0).
26.8, E = 37 KB/M; nOli yr.1ol11 a = 66° K OCII x. 26.9, E =
= 1,15q/(4:nEoa 2 } = 0,10 f>\B/M. 26.10. E = pl(4:nE o tfl) = 18 KB/M,
26.11. q = 4'i1E o tflEII = 1,6 HKJI. 26.12. CPo = 2CPACPc / (CPA + CPC> =
= 7.5 B. 26.13. CP1 = O,20KB/M; CPO) = 0,10 KB/III. 26,14, E 1 =
= 0, CP1 = q/(4:nEoro) = 10 B; E 2 ';' ql(4:IE o r 2 ) = 1.1 BIll!, CJ'2 =
= ql(4:nE o r) = 1,0 B. 26,15. E = O. cP = RafFo, 0  r  R; E =
= R 2 a!(Eor), cP = R 2 a/(er), r > R, C\!. pHC. 266. 26.17, (J = 2Eoff/d =
E'b
R r R r
Pnc. 266
E
R r
PHC. 267
= 29,5 II K.lIM 2 . 26.18. R = rcr/cp1 = 6,0 CIIJ: 26.19. Eo = 0; E A =
= q/(4:nEori) = 22 KBlM; Ec = (q1 1:- q'!.)/(4:tEori) = - 18 KB/M.
I ( q1 I q2 ) I ( q1 q2 )
26.20. 'Po = 4:nEO RI T R 2 = 60 B; CP1 = 41!Eo r, + R 2 =
= 15 B; CP2 = (q1 + q2)/(4:tE o r 2 ) = O. 26.21. R = (4q1 +
E
E"I' 6, I} *'
".' --
6' -- 0
,- I
0,05 r,M 0, Gz.
PHC. 268 PIIC. 269 PIIC. 270
+3q2)/(24:tEofjl) - 50 CM. 2G.22. E i = pr/(3Eo), 0  r  R; E
= pR3/(3Eor2), r> R, CM. pllC. 267. 26.23. E 1 = pr/(3EEo) --'"
= 3,8 8/:0,,; E 2 = rrJ(32fo) = 6,3 B/M; Es = pR3/(3Eor) = 4,7 B/M,
C\I. pHC. 268. 26.24. E, - 0,23 KBhl; E" = 113 Bhr, C\!. pllC. 269.
26.25. E A = 0, Ee --'" 0,30 MB/M, CPo'. pIIC. 270. 26.25. 6cp = 4;; B.
193

26.27. A = 0,16 Jl>l<. 26.28. A = 40 NK ll>K. 26.29. II=qIQ/(4:nt'or}=
= 9.0 IIIKJl>K. 26.30. V = ely 4nEom.,r = 0,16 KWC. 26.31. r =
= e2/(4nEomeu2) = 0,25 N\!. 26.32. R = qlq/(2:nEom.v'-) = 81 CM.
26,33. II = - 5q 2 /(4:nE o a). 26.34. va = e Jf  = 0,23 K w6
v, = el VnEomrT = 0,32 KWC. 26.35. v = Vv + 2eru 2 - uime =
( :nEompv'- 1 f 2:nE E ) -I
= 3,0 Mwc. 26.36. r = e + JI -f- = 47 11111. 26.37.
v = Vv + rPt 2 1m 2 = 2,3 Mwc; a = arctg [(eEtl(mev») = 45°.
26,38. s = m"u2/(2eE) = 2,4 CM; t = mev/(eE) = 47 HC. 26.39.
q = mgdlV = 9,8.10- 18 K.'1; VI = mgdl(q - eN) = -17,3 KB.
27.1. npOBO.llHHK A BBCCTII BHYTPb npOB0.!111HKa C H KOCHYTbCSI
ero BIIYTpeHHeii CTeHKII. 27.2. 3apSl>KellHblii np06Hbli! wapHK BlleCTH. He
KacaSiCb. BIIYTPb nO.:loro npOOO.llHHKa, npHKOCHYTbCR K npOBoAIIHKY
naJlbueM H JaTeM wapHK YlIa.1I1Tb. TaK >Ke nocTynHTb co OTOpLIM npo-
BO.llHHKOM. 27.3. 3ase\lJleHHblii npOBo,AIIJIK nO.llHeCTlI, lie KacaSlCb, K
SapR>KeHHoMY, saTCIII y6paTb saSCIII.1CIIHe. 27.4. 3J1eKTpOCTaTIIQCCKaH
HH,AYKllHSI npHBoAllT K TaKolIIY nepcpaCnpeACJJClIlIJO JapSiAOB Ha wapax,
npH KOTOpOM O,AHOHMCllllbie sapSl.llLJ OKaJblBaJOTCH Ha 60JlbweM pac-
CTOSlIIHH, 'IeM pa3110llMcHllbie (pHC, 271). 27.5. 9T0 BOJMOiKHO. eCJIH
sapSl,A 0.llHOrO IIJ wapHKoB Mlloro
60.1bwe JapR;J.a APyroro. 27.6. HCT.
(l-Ie3apSl>KeIlHOe TC.l0 B(lC.!I:CTBHe
3.CKTpOCTaTII'IeCKOii IIH.llYKUIIH TaK-
OJ +++
+ +
+ .:
+ ...+
+
EJ +++
+ +
t+ +
+ ...
+ +
0=
G +++
+ +
+ +:
+
+ T+
T
Pile. 271
PIIC. 272
>Ke 6Y,ACT npHTSlrHBaTbcSI.) 27.7, lla. 27.8. CH.la HC 113MeIIllTCSI. Ha-
npSl>l<ellllOCTb nOJISI BII}TPH I>teTa.1J1H'IeCKHX 060.10'leK 6y,ACT paBlla HY-
JlIO, BHe o60Jlo'leK - lIe HJl>tellHTCSI. 27.9. .D.a. 27.10. HanpR>KeH-
HOCTb nOJJH BHYTPII wapHKa paBHa "YJlJO. B cJlY'Iac SapSl>KeH-
Horo wapHKa OTBCT lie 113111ellHTCR. 27.11. CM. pHC. 272. 27.12.
C\I. pHC. 273. Ha DIIYTpCJlHCii J10BepXHocTH nJlOTHOCTb SapSl,AOB HC
OliIIHaKOBa. Ha BlleWIICH iJOBepXHOCTII JapRAbi cB060,1HbI II n03ToMY
pacnpclIe.1eHbI paBHolllcpHO. LJIICJlO CIIJJOBbIX JlHIlHii BIIYTPH II Bile npo-
BOAIIHKa O.J.IIHaKOBO. 27.13. Ip = 2<rlcri(Ih + 1p2) = 21 B. 27,14,
Q' = Q/2.27.15, F = q (£2 - £1)/2.27.16. F = k(f/(2r)% = O,251>tH.
kq kq
27. 17. If> = i; - V (2r 1 )2 -I- r = IO B. 27.18. Q=2 (r - I sin a)x
x V mg tg aJk=20 IIKJI. 27,19. I( = krf/(4r 2 6.r) = 49 HIM. 27.20. lie
H3\1eIlIlTcSI.27.21. EDO,,-Ll> El1ap.<!'lIna. 27.22. CM. rllc. 274. 27.23.
194

PHC. 273
PHC. 274
E 1 = kq/(Er'f) = 5 KB/M; £2 = kq/r = 3,8 KBIM. 27.24. q' =
= - .4:nR'o (e - l)1e = 31 nKJI. 27.25. 0CD = Eo (e - I) 6cp/(Ed)-
= 0,88 tdKKn/M 2 .
28,4. R = 9,0.10. N. 28.5, C = 0,71 McJ>; 6cp = q/(41tE o R 3 ) =
= 1,4 KB. 28.6. q = 4:ne o dcp/2 = 0,10 t.tKKJI. 28.7. cp:l'P1 = N 2 / 3 =
= 1,0, 10'. 28.8. 6q = (qlr2 - q2rl)/(rl + r 2 )-= 1,2 HKJI; cp =
= (ql + q2)/[4:nE o Cr l + rzU = - 72 B. 28.9. R 2 = R 1 (CP/(CP2 -
- I) = 30 CN. 2'8.10. cpi = cP; = (q'1 r l + ff2r,)lrl = 0,48 KB; qi =
=0; qi= 4:neo (r l CPl + r 2 CPz) = 5,3 HKJI. 28.11. «W'P1 = (1- R/R 2 );
C = 4:teoRlRJ(R2 - R 1 ). 28.12. cP = (CI'Pt + C 2 CP2)/(C I + C 2 ).
28.13, cP = 2'Ptff;t(CPl + CP2) = 48 B. 28.14. Q = C l C 2 (CP2-
-ffl)2 /12 (C I + Cz>1 = 12 .l!.>K. 28.15. al = V dC/e o = 10,6 M; Cl<J. =
= 1/ dC/(EE o ) = 4,8 N. 28.16. JIHCTOK CJlIO,AbI. 28.17. S = 1.6 MI.
JlEoa-CPI <r2
28.18. q = qo ([e - II/E) = 12 MKKJI. 28.19. F = R
= - 0,10 IIIKB. 28,20. F = E o SLP/(2cP) = 1,23 r.:H. 28.21. He
IlsMeHHTcH.28.22. YMeHbwHTcR B 9 paJ. 28.23, I) C = 2eCc!(e+I)=
=l,75C o ; 2) C = 2C o ' 28.25. C=2E o Sld.28.26. Vi = (VI + V 2 )/2=
= 150 B; V; = (VI - V I )/2 = 50 B. 28.27. Ve!> = endlVl(end l +
+ ecpd 2 ) = 0,30 KB; Ee!> = 30 KB/N; V n = E.4Id 2 V1(E n d l + ecJ>d2) =
= 1,8 KB; ED = 90 KB/M. 28.28, V = Ed (C 1 +C 2 )/C I =4,8 KB. 28,29.
Q = (VW; - V WJ '/2 = 0,20 M,U>K. 28.30, (D = Eocp/(2r) =
=O,18,U>KIM'.28.32. A=CV2/2=O,1 JoI'u>K. 28.33. A=(E-I) cP/(2C)=
= 5,0 M,U>K. 28,34. nB03)1 = e.IOO%/(1 + E) = 75%; nBOCK =
o 0 C1C, C, + C.
= 100/(1 + e)= 25".28.35. a) C C 1 + C a + C 2 + C. ; 6) C=
_ (C I + C 2 ) (C a + C.) _ -'1 .
- C 1 +C,+C a +C. . 28.36. CoGnt - C. 28.37, a) C o 6nt - :lC,
6) CO(jnt = C. 28.38. q;lq; = ViI Va = (C 1 + C z + C;s)/(C 1 + C 2 ),
(cp A-CPB+ e l- E 2)C 2 C:I
28.39. cpB-CPA=B+qIC=5,O B. 28.40. V I = C C C ' c C
C 1 2+ 2 aT 1 :I
VIC t VIC t
= 1,0 B; V 2 = -= 0,67 B; Va = - =- 0,33 B. 28.41. q2=
C. C a
=C z (@1- @:)+qIC/C1=0. 28.42. ql=q2=C I C 2 (@"I+SZ)/(C I + C 2 ).
195

28,43, CPA -- 'Pn = G (C:C a - CIC.)/[(C I + C 2 ) (C, + C.>J. 28,44.
4I'A - CPB = (tlIC I - S"C 2 )/(C I + C). 28.45. ql = q2 = Ctf/3 =
= 10 HKn: q, = 2Ctf/3 = 20 HK:I. 28.46. q'iff = Ctf/ 30, qAB=C8/5.
VIII. I. Q = L (D + d) V 4Jt£oK (L - 1)/(Dd) = 1,7 MK K.1.
q ( q3 )
VIII.2. F = q2P/(2neorl). VIII.3. V = £oS 1- 2£oSK = 2,7 KB.
V 111.4. W = 7C82/IO, VIII,S. lup = l!.cpr/3 = 40 B. VIII.5. QI =
= (q/2 :i: q.j2); Q2'=' (q/2 :i: fh/2). VIII. 7. q = Q/3. VIII. 8. T =
= 3if/(16n£oP) + V3qE = 7,6 MH.
29.1. 1=0,5 MA. 29,2. 1 = Vl!.CIM = I MKA. 29.3. m =
=- me1tle = 0,2 Mr. 29.4. v/t' 2 = S.jSI = 1,5. 29.5. R = 35 OM.
29.6. i = VI(pl) = 10 AlCN 2 , 29.7. R = I6mp/(n 2 d Z po} = 9 OM, r,Ae
p H PI' - YAMbHoe conpOTHoneHHC nJlOTIlOCTH CTaJlI!. 29.8, 1=
= RS/IP (I + at» = 6 M. 29.9. Rs = RI (I + at 2 )/(1 + at l ) =
= 22 OM, 29,10, t l = [n (I + at l ) - Ij/a = 247" C. 29.11. 35 WT,
V - V o S (V - V o )
29.12. R 10 8 OM; 1 = lop = 32 M. 29,13. IJI/ly=
= - aypy/a;Pm= 6. 29.14. R 1 . 2 =(/ 2 V:J: V J VZ - 4/1/2V2/(211/2)'
Rl = 30 0)1; R j = 10 0'.1. 29.15. B 4 pa3a. 29.16. Rl =
V (S" + S2)
= 8 1 +S 2 +S, = 8 OM; 11 = I A; VI = IIRI = 8 B; R 2 =
= CS I (S2 + S,)/IS. (Sl + S2 + Sa)] = 12 OM; I. = 1/3 A;
VS l (S.+S,)
V= V a = V- V l =4B;R a = S3(5 1 +S 2 +S,) =60M;I,=
2
= 3" A. 29.17. O; 30; 40; GO; 90; 120; 180 OM. 28. IS. HanpH>KeHHe
D03pacTaer. 29.19, R = Ro (n - I). 29.20. CM. pilC. 275; a) R o 6m =
= r; 6) R o 6m = 1 (I - r1R); B) R = R/(I+
. I
+ R/r). 29.21. a) 0  V nLlI  V o ; 6) 3" V o E;;;
2 I
E;;; V BLlI E;;; 3" V o . 29.22, I) V BWI = 8" V o ;
2) Vax = 219V o . 29.23. a) R = r; 6) R = T/3;
3
B) R = 5" r; r) R = r. 29.24, 2) R = r;
4
6) R = r/2; B) R = 5" T; r) R = &6 1;.n) R =
7 3
= 12 r; e) R = 4 r .
JlKCl3lUiue. npH paC'IeTe COnpOTJIBJleHHH Co10>KHblX Y'IaCTKOB Y,A06-
HO COCTaBJlHTb 3KBHBaneHTHbie cxeNbI, Y'iHTblBaH. 'iTO TO'iKH, IIMeJOIUHe
O,AllllaKOBbie nOTeHUHanbl, MO>KHO coeAHHHTb H.1H pa3:le.'IHTb.
3
29.25. R,,= 4 T. 29.26. VI = 1I 0 V I r/[ Vir + 2 (V, - VI) rl =
= 200 B. 29,27. I A = VRJ[(R 2 + R,) (R I + R.) + R2RsI =
= 0,5 A. 29,28. R = (V - 10')/1 0 ; Rl = 90 OM; R 2 = 0,49 KOM:
R. = 2.5 KGM; R. =- 5 KOM. 29.29, 1  I A (I +) = 6,3 A.
PIIC. 2i5
195

Url (R +2,.)
29.30. VI = R (rl + r t ) + 4r 1 r l == 33 B; VI = V'I (R+2rJ/(R (r 1 +
+r.) + 4rlr21 = 27 B. 29.31. Us = UV 1 R/[R. (V- U a )+R 1 U 1 J =
= 0,34 B. 29.32. CxeNY a, Xor;(a conpOTHBJIeHHe JleJIHKO; cxelllY 6,
Xor.l1a conpOTHBJleHHe Ma.rzo.
30.1. 1=0,5 A; V = 4,0 B. 30.2. I. = IM[n3 - Ir (n-
- 1)1 = 0,60 A. 30.3. III. = 8 UI[ (" - U) R) = 0,30 A. 30,4. 8=
= Ill. (R. - R 1 )/(/ 1 - I.) = 10 B; r = (/.R. - hR 1 )/(/ 1 - 1.)=
= 5,0 ON. 30,5. Cr.r. pHC. 276. 30.6. Rlr = 1,0.101. 30.7. Rx = R.lr
 45 0.. ..... S  U(I + ; )  0,33 .B. 1' K-
30,9. IT = I R = 4 (R 1 +R.) = llr U/RJ
· RIR. +(R 1 + R.) (R.+,)
I R UM
r .
= 1,0 A; I R = R + R = 0,67 A; I R = II
I I. .
_ Ir Rz PHC. 276
- R 1 + R. = 0,33 A; V R . = Ir R = 5,0 A;
IrR1Rz
V R, = U R . = Rl+Rz = 4,0 B; VB = 4 - Irr = 9,0 B. 30.10. 4=
= 34d = 30 B. 30.11. r = R (n- I) = 3,0 ON. 30,12. q =
= CBR/(R + 2r\ = 4,0 MKI(JI. 30.13. q = C4 (R. - R.\/(R. +
+ R. + 2r) = 21 MKK.'I. 30.14. q = 4C8R (R + rVI2R+3r\ X
X (2R + r\) = 0,68 NI(JI, 30,15. 'PA - !VB = (C.R. - C 1 R 1 \ 
X8/[(C 1 +C.) (R I 1:. R . + r\). 30.16. 'PB - 'PA = 4/10. 30.17. 'PB-
-IJIA = 1 1 r- 8 = 2,0 B; 'PA - fJ'B = 8 + I.r = 6,0 B. 30,18.
41 = B (It + 1.)/(/1 - I.) = 12 B; R BB = 24/(/1 - 1.\ - r =
= 10 ON. 30.19. 'PA - 'PB = [4 2 (R + '1 1 + 41 r.J/(R+rl+r.\=
= 1,2 B, 30.20, R = (V- 4 )/1- r = 6,5 OM; VI = B + Ir =
= 5,5 B. 30,21. R = 8. '1/<3. - BI) = 6,0 ON, 30.22. B =
= (SI '. + 8.rN(rl + '.\; I = (ell r. + 8. rl)/[rl r . + R (rl +
+,.)1. 30.23. 8 = (Blr.r. + 8. 'tY! + 4. '1 r.)/(rl r . + r.r. + r:l'l)'
30,24. R = r = 6,0 OM. 30.25. V = 0. 30.26. 1= (SI + 8. +
+ 4.}t(rl + r. + 's) = 1,0 A; VI = B 1 - Ir = 0; V. = tI.-
-Ir= 0; V s = 4.-lr= 0; I' = 1,0 A; V;= 1,0 B; V; = 0,
Va = - 1,0 B. 30,27. R = (3.' + 8Iri)/(rl Bl + 8.r&> = 3,0 OM;
1= <e"1 + 4.),(R 1 +rl + r.)=O,50 A. 30.28. a) 50 A.I/; 6} 200 A'I/.
30.29. 65 A'I/. 30.30. Rx = (R2 (SI - 28 2 ) - 3$2 Rrl)/(81R+
+ 8 2 rl + 2 B 2 R) = 3,0 OM. 30.31. 4 2 = 8 1 (R I R. -
- RzRs)/[rl (R I + R. + R3 + R.) + (R 1 + R.) (R. + RC» =
= 2,2 B; nmoc nO.'l.KJlIO'l\?H II: RI' 30.32. qa = C8 (2R + r)/(R + r) =
= 0,50 HKn; q6 = - C8 r I(R + r) = - 0,30 HKJI; qs = CB (3R +
+ 2r)!(R + r) -= 0,90 HK.'I; qz = C 4R/(R + r) = 0,10 HKJI.
31.1. A = 3 ,U>K. 31.2. A = 0,29 x,U>K; P = 29 BT; R = 5 OM.
31.3. P = lPlR, CM. pHC. 277, a, 6. Tax, 'lT06b1 TOK 6b1J1 nOCTORHilblii,
:il,4. P: = P. tualVI)J = 180 BT; Pj = p. (V 1 /U I ). = 20 BT. 31.5.
197

PI = 80 BT; p. = 40 BT; P; = 8,9 BT; P; = 17,8 BT. 31.8. 400 BT.
31.7. YBeJlH'IHBaeTcSI. 31.8. 40 BT; 60 BT; 80 BT; 120 BT; 180 BT;
240 BT; 360 BT. 31.9. Rp. = V (VI - V)IP = 6,230111.31.10, VI =
pg  , %' L : { :/ :1 602.:Br,P:
 = nPIP I = 67%. 31.11. PI =
= lPVfPI(P' + lP)2 = 0,69 KBT;
p. = 2lPVfP 1 (2P, + lP). =
U R = 0,93 KBT. 31.12. I. = (V-
PRc.277 - Ilr)lr = 42 A; ni = I-/IrlV=
=95%; n. = 1- l.rlV = 5%.
31.13. II.. = (8:1: V'S2 - 4rP)/(2r); II = I A; I. = 2A. 31.14. RI..=
= (4. - 2Pr)/(2P) :I: V(4 2 - 2Pr)2/(4p2) - r 2 ; RI = 3 OM; R 2 =
=0,3 OM. 31.15. E = 2,16 M.D.>K. 31.16. CM. pHC. 278; P nonH = 41;
PBII = I" - flr; 'I = I - Irl8. 31.17. CM. pHC. 279; P no : 1Jt =
=4 2 /(R;- r); PBII = [4/(R ;- r)2 R; 'I = R/(R;- r). 31.18. Cw.
p
'_l' 7J
P"..cr
I=L 1=1- I C=f.. I
I 2r I r I r
PHC. 278
pHC. 280; I = 8/(R ;- r); V = 4 B/(R ;- r); 'I = Ri(R ;- ,)
P nonH =- 8 2 /(R + r); P BII = SZR/(R T r 2 ); P BHYT = 4 2 r1(R ;- ,)-
P BII MaKeHM3.1bH3 npH R = r. 31.19. 1= 11 + 1 2 /2 = 1,3 A; 11(3 =
= It + I. = 2,6 A. 31.20. 1 118 = (PI/ - P 2 /n/(P I /.- P 2 II) ==
_ _ (Ii p.-/i PI)2 _ ')
- 8 A. 31.21. Pl'oIa/lc - 1 /1/2 (II-I.) (lIP 2 _ I.P I ) - 32 BT. 31.2.
c;  _____ ft: 
ft+r P. I '
{- l  M I
'-#rIft - I :
'c, C l. {.
PHC. 279
4 = 2P Ma l<c'I -= 12 B; , '"""" PNallcl fl = 3 OM. 31.23. P Nallc =
$2 rj /[4R (I - 'I» = I I BT. 31.24. r = (n - I) R I R 2 /(n!! - n R I ) =
_ (R ;- r.) - V(Rf + r 2 )l - 4Rfr 2 _
= 14 OM. 31.20>. R 2 = 2R I -
= O,620M; 'II = 80%; '12 = 20°6.
198

31.26. P BHYTP =P I (I-'1I)/tJZ =32 Br, YKCJ3aHue. MOIUIIOCTb, BLI-
,AeJJHeMaSi BO BlleWHlO1O uenb, B nepBoM H BropoM cnyqaax O,AHHaKOBa.
370 BRAHO R3 cpaBHeHHR Krl.U.
31.27. , = Y R I R 2 . 31.28. II = c8/{3R) = 0,1 A; Iz =
= c8/(1.5R) = 0,2 A. 31,29. P OOCJI = P Dap = n8/(4,) = I BT.
I
u
t ---------
It
p
11
R
31.30. Q = Nc8 2 /,. 31.31. P TeOJl = {U - c8)2/r = 1,6 BT; P noTp =
= (U - c8) U/, = 4,8 BT. 31,32. n = c8/U=O,8; P = (U- 8)c8/,=
= 2,4 BT. 31.33. CM. pHc.28I; P OOTP = {UZ- Uc8)/'; P nO ;I.3 =
= {@U - @2)/,; P Te0 3. = {U - @)2/,; '1 = c8/u; Pn 0 1I. 3 MaKCR-
11
E
PRC. 28 I
MaJlblla npll c8 = U/2. 31,34. c8 = U/2 = 6 B. 31,35, I = Plc8.... =
= 0,5 A. 31.36. P OOTP = I U = 0,88 KBT; Pyex = UI - 1 2 R =
= 0,75 KBT; 1] = 1- IR/U = 85%. 31.3 7, P = UI- UI2/1o =
= 58 BT. 31.38. Il.2 = (U.:I: V U2 - 4RP)/(2R); II = 25 A; Iz =
= 30 A. 31,39. CM. piIC. 282; P oonR = I U; PYCX = I U - 12,;
Puna =- p,; tJ = 1 - Irl U; P MCX lIIaKCH\la.1bHa npH I = U/(2r).
199

31,40. ''b=P1/ 1 (/%;:/1)/(P1/I-
- PilI) = 83%; '12 =
P 2 / 1 (I. - II) I (PI/ -
- P1Jf)= 67%; 10 = (PilI -
- PZ/f)l(P1/,- Pz/I) = 60 A.
31.41. 10 .I8H. 31.42. 'I =
= cPPol' (T 11:1 - T 0)/ V = I c,
r,Ae P H Po - YJ1CJ1bHOe conpo-
THB.1CHlle H nJlOTHOCTb CBHIIua.
31.43. AT = J"2(Yf/(cp,) = 4 1<.
V
31.4 4. P=CPo-'t'rJ AT = 1,5 KBT,
rAe AT = T H - To. 31.45. r = B V R't/(cmAT) - R = 3 OM.
31,46, a) I = II + Iz = 32 MHII; 6) 1= 111J(/1 + IS> = 6 1011111.
31,47. m = 84 r. 31.48, 1= flmgv/(VTj) = 59 A; VI = vp/(sin a-
- fl cos a) = 2,5 wc, rAe sin a - YKJlOIl. 31,49. I = mgv (J.t cos a-
- sin a)/(V1J) = 0,24 KA, rJ1e sin a - YKJlOH ropbl, 31.50, R=
= (UlI- mgh)/(/Z/) = 9,7 OM.
32.1. CH.'Ja TOKa CHaqaJla YBCJlHqHBaeTCH, a nOTOM OCTaeTCH no-
CTOHHHOii, 32,2. YBeJl\lqHBaeTCH. 32,3. Bo Bcex cJlyqaSlx YBeJlHqHBa-
eTCH. 32.4. xH = 1,0 Kr/KMOJlb, k H = 10,4.10-' Kr/KJI; xNII =
= 23 KrlKMOJlb, k Na = 2,4.10- 7 Kr/KJI; .1'0 = 8,0 Kr/KMOJlb, ko =
= 8,3.1O-JI Kr/KJI; xCu = 32 Kr/KMOJlb, kcu = 3,3,10- 7 Kr/Kn.
32.5. OllHHaKoBo. 32.6. W/m = nFV/A = 24 Mll>KIKr. 32,7. 1=
= hpnF/(A/1 = I q. 58 MHH. 32.8. h = Ajl/(pnF} = 50 MKM. 32.9. m=
= AIt/(nF) = 1,9 r. 32.10. 1= mnF/(At) = 4,0 A. 32.11. R =
ltRT ( As A K )
= VAI/(muF) = 2,0 OM. 32.12, V = - -+ -, = 62 X
FP nBJ.1s n H J.1R
X 10- 5 MS. 32,13. N = It!(2e) = 2,5.10'. 3 2.14. V = V 2 W/me =
= 2,94,IOS we. 32,15, V=E'J.. = i5 B; v = V2eH/m e = 2,3. I ()6M1c.
32,16. cp = Er = 30 KB; q = 411eoErl = 1,7 HKJI: 32,18. v =
= V 2A/m e = 1,26.IQlwc. 32.20. 1= PJW = 0,10 IoIA.
p

JLl .JLI
r r
PIIC. 282
I X.I. TOK II npOBO.llHHKe, saMKHYToM Ha HCTOqHHIt TOKa C 311C,
II = 2$ /(2R + lOr) = 0,20 A; TOK B npOBO.llHHKaX, nO,AKJIIOqCHHblX K
IICTO'lHHKY C 311C 1 2 = $/(2R + lOr) = 0,10 A; B OCTaJlbllblX TOK pa-
Bell HY..IO.
I X.2, I = t! (aRIR. + RI+RJ = 48 IoIKA. I X.S. qA = 2CB/3 =
=2,0 MKJI; qB = - 2CB/3 = - 2,0 IoIKn; qc = 0; Aq = 2BC =
= 6,0 IoIK.II. I X.4. v = B Z RT/(4R,rPSfJ-) = 0,47 wc. I X.5. P =
/Un (l-n):3 vIII VI. (/ 2 - II) 'IJ
= k [k-(I-n)2) = 0,16 BT. IX,6, vII = V - Mg II =
= 26 ewc. IX. 7. Ha JlcBoA cTOpoHe cpeAHero ,IJ1CKTpO.lla 6Y;J.eT IIblJ1C-
JlHTbCH cepe6po: m: g = 2r + AmrU/(2Fnm ) = 0,64 IoIr/c; Ha npa-
m_ 2mA q ( r + g U )
_ '''I nm
BOH CTOpOilC 6YJ1CT E:.J,AeJlSlTbCH XJlOP; ""T = AA g I 2r +AAg V /(2FnmJ)-
= 0,44 Mr/c.
200

:i:t.2. Y 3J1eKTpOHllbiX nYQiWB cpco6J1a;J.aeT KYJlOHOBCII:Oe orran-
KHBaHHC. 33,4. By.zteT. 33.5, B = 50 MTJI. 33.6. a) nOBcpHeTcH; (5,
B) nOBepHCTCSI H BTSIHeTCH B oaCTb 6oee CHbHoro nOJlR.
33.8. PailKa paCnOnO>KCTCH no,lt yrJlOM 45° II: ropllsoHTY. 33,9.
B = O. 33.14, F = 4,2 MH. 33.15. I1T = BlI = 10 MH. 33.16. B =
= mgl(ll) = 19,6 MT.'1. 33.17. 1= p.mg/(B!) = 13,6 A. 33.18. BI =
= Mg (.... cosa-sin a)/(Il) =9.6I11TJI; B..= Mg (p. cos a+sin a)/(Il)=
=0.50 T.'1. 33.19. B = TT'g tg al (II). 33.20:' A = I Blx sin a = 0,30 ,U>K.
33.21. OKPY>KIJOCTb pa;J,Jlyca R= mevl(eB); A =0.33.22. v= ReBlm p =
= 96 Kt!C. 33.23. a) Ra/Rp=2; wa/wp= 1/2; 6) Ra = R p ; wa/w p =
= 1/2. 33.24. PM = m e rJ/(2B). 33.25. Ip = arcsin (dB V e/(moY» =
= 30°. 33.26. R = mpv sin w(eB); h=21tmpv cos al(eB). 33.28. By-
;{CT .llBHraTbCH no cnHpanH C HSMeHHJOw.HMCH warOM. 33.29. n =
= t'B cos a/(21tE), 33.30. v = £1 B = 0,50 Mwc.
34.1. a) <D = 2,0 MB6; 6) <D = 0; B) <D = 1,4 IIIB(5; r) <D =
= 1,0 MB6. 34.2. a) <D = <D; 6) <D = 2<D; B) <D = cII; r) <D = 2<D.
34.5. a) KO.'1bUO pacTHrllBaeTcSI; 6) KO.bIl.O C>KHMaeTCSI. 34.6. CD =
= BS. 34.7. HeT. 34,8. a) B npoBollHHKe BOSHIlKaeT 3.'1eKTpH'IeCKJln
TOK; 6) .Il1l3.'1eKTpHK nonSlpllsycTCH. 34.9. a) B npoBO.ll.HIIKe npollcxo-
J{HT p3311e leHHe 3apSl,AOB; 6) ,ltH!I.1eKTpHK nOJlSlpllsye-rcSi. 34.10. $ =
= nl1<Dll1t = 30 B. 34,11. $ = n:1r 2 cos al1BIl1t = 12,5 IIIB. 34.12.
I1BI!:J.t = 16pl/(zur-D) = 0.54 Tn/c. 34.14. q= nSB/R = 80IllKK.'1.,
rl1lD3S ( I1B ) 2
34.15. P = -;;- = 29 MKBT. 34,16. I1BIl1t = q/(CS) =
16 P ut
2R12 I1B
= 10 'MTldc. 34.17, I = (:1r + 5R) (2r + 3R) "Xi = 33 MKA. 34.18.
C = -Blv sin a = 1,0 MB. 34.19. I1Ip =B llv = 0,30 B. 34.20. I1Ip =
. [ q2 (I - cos a l ) ]
= 1IB ll-v = 1,57 MB. 34.21, a 2 = arccos I - ql =
° BSn
= CO, 34.22. 1) q = R (ccs  - cos ( 2 ) = 0,67 NKJI; 2) q =
= 1,811KJI; 3) q = 2,5 MKJI; 4) q = 10 MKJI. 34.23. q = PB$/(4R) =
= 125 MKK.'1. 34.24. BOSMo>Kllbi JlBa cJlY'laSi (pHC. 283, a, 0): I) ql =
= :r.r 2 B/(2R) = O,56MKJI;q2 = :tr 2 BIR=I,3MK.'1;2) q\ = 1tr 2 B/(2R)=
= 0,56 MKJI; q2 = 0. 34,25. IF AI = IFI!HI = D2[2vIR. 34.26. F =
= (B2PV + kmgR)/[R (cos a + k sin a)}, r,lte a - yroJi Me:JKAY clinoH
F II rOpIlJOIITOlof. 34.27. 1= B1v (R) + R 2 )/(RR 1 + RR 2 + R 1 R 2 ).
34.28. v = mgR/(B2(Z) = 8.7 wc; TOK B nepelllbl'lKe Te'leT cnpaBa Ha-
JleBO, 34.29. v = mgR/(B2[2 sin a) = 17.4 wc. 34.30. v =
= Dpg sin alB2 = 46 cwc. r.lle D - n.'10THOCTb MeAH; p - Y.lleJJbHoe
COnpOTnB.'IClIJiC Melill. 34.31. a) 1= $IR = '0,50 A; 6) 1= ($+
+ Bvl)IR = 0,70 A; B) 1= ($ - Bvl)IR = 0,30 A; v = $/(BI) =.
= 10 wc, B.'IeBO. 3,32. v = 5,0 wc, MeBO. 34.33. w = 2$/(B(Z) =
= 4,O.I()2 pawc. 34.34: 1) 1= U/ R = 5,0 A; 2) v = V/(D!)-
- ....mgR/(B-r-) = 2,0 wc; 3) P = JlmgU/(B!) = 49 BT; 4) P TeUlI =
 p.mg ( J.l mgR )
= [J.lmg'(Bl)J- R = 48 BT; 5) P Mex = 81 V -"Ifl = 1,0 BT.
34.35. Kor,lta pa60TaeT. 34.37. L = 5,0 Mfu. 34.38, B = LJ/(nS) =
= 2,01111.1.34.39. L = (!I!I = O.10 "lfH. 34.40. W = LJ2/2 = IO,U>K;
YBc;rHQHTCSI D .. pa:!3. 34.41. W = f])J/2 = 1,25 .n. 34.42. Q =
= L$21 (2r 2 ) = 0,60 .u.>K. ...
201

:! 8 ' ' 8 "
, \ , \
I I I I
\ r \ r
\ , \ I
, I, "
" " .......: ...,
....
t11
....
61

I a'
PHC. 283
PHe. 284
35.1. CD = BS cos (2 nvl + (J'o); 8 = BS 2n vsin (2n vi + (J'o),
35.2, 8 M &RC = BS2nv; I) 8 NaRc BOJpSCTeT B N pa3; 2) 8 NaRc B03-
paCTeT B n pa3; nepHoJ{ YMeHbWHTCH B n pa3. 35.3, I = 0,25 X
Xsin(100 nl + (J'o); IN&RC = O,25A; v = 50 fu. 35.5. ,,=500 MHH-l.
35,6. VI = 0,20 KB; V.=O; V, = - 0,20 KB. 35,7. V = V o sin wi;
I = V. sin wlIR; P = VI sin l wiIR. 35.8, V = 310 B, 35.9. V =
= 707 HB. 35.10. V = 180 sin 100nl; 1= 5,6 sin 100 nl; P NaRc =
= 2P = 1,0 KBT. 35.11. !.. = I -  arcsin V 2 2 = 0,50, 35,14.
T n
I. B03pacracT, VI YMeHbwaeTcH; II B03pacraeT, VI npaKTH'IecKH He
MeHHCTCH. 35,15. II B03paCTeT; I. yyeHbUlHTcH. 35.17. k = 0,20;
n2 = 3,5,103; DJ"JepDoA 35,18, nl = 2,5.10 2 ;"2 = 1,4, WI. 35.19. TJ =
o II nl (VI + P R) 
= kV 2 ,I00 '¥olV I = 9 6%. 35.20'"2 = VI V = 72, 3a.21,
V = p"'If P R - 60 KB. 35.22. I) nl = 1- PRIV2 = 0,19;
Y (I - n)
"2 = 0,99; 2) Vi = VI - PRI VI = 120 B; V; = 6,15 KB. 35,23.
T 2 = Ti2 = 10 MKC. 35.24, v = 10 Mtu, IMBUC = 8 YCIL ==
= 9,4 MA, 1 8 e!> =  Yc/(2L) = 6,6 MA. 35.25. P = lJICR/(2L) =
= 5,0 MKBT. 35,26. 1= TI8, 35.27. v = 2n/n, 35.28. 01' 71 Kfu
11.0 0,71 Mfu; OT 0,42 KY 1J.0 4,2 KM. 35,29. n = d(/'.) = 2,O.I()3.
35.30. tup = 2nvSlc = n/5. 35,31. SM&ICC = d(2{) = 37 KM; "=
= '(Cn. = 4,O,l()3,
X.I. I = 8Spg tg a1 B = 27 A. X.2. (J'c - (J'D = I B/(nla).
I 4 meVo ( 4:t2 E2 )
X.3. R T = meVD' (eB) + eElt"/(meBvo); R T = - I + ---;- =
eB B v
 gBR sin 2 q> V I?
='2,2 CM. X.4. Cl = _ = 2,6 B. X.5, w =
2 cos (J'
=8/(B1)I. X.6. P=5lJ2/(3R). X,7. AtIA'+T = (I-2nRVCiL)-I=
= 1,03.
36.2. 26° H 64° c nOBepxHocrblO CTO.la (pHC. 284, a, 6). 36.3. 2a.
36.4. VI = 3 cwc OT JepKaJla. 36,5. v = 200/. 36.6. VOTP =
= V(2v)1 + u = 5 cwc; IX = arctg (2vlu) = 53° C HSnpaBJleHHCM
1(DH)f{eHHH HCTO'lHHKa. 36.8, h = HJ2. 36.9. CM. pHC. 285; TaKSH CII-
CTeMa aepK8J\ Jl,aeT ,ABa HJ06pa)f{CHHH. LJTo6b1 YBH,AeTb HX O.llHOBpeMeH-
HO, rJlaJ lIaMIO.llaTeJlJl .ll0Jl)f{eH haXO;tHTbCH B O.llHoii H3 TO'leK nOJlOCbI,
OrpaHH'IellHOii JlY'IaMH 0' A H O.B. 36.10. 12 CM. 36,11, 132° 36.12,
202

3; 6eCKOHe'lIlOe QHCJlC; 3601a - I. 36.13. OTpa>KeHHe OT np03paQHblX
TeJl Bcer.lla Mellbwe, '1eM OT lIenp03pa'lHI>IX TeJl. 36.14, He 1!3I11eHHTCH.
nc
36,15. B IICO.llIIOpO,AIIOii. d6.16. i = a,ctg nb = 52°. 36.17. a = 87";
i = 34°. 36.18. n = 1,5. 36.19. XI = 0,75 M; x 2 = 2 III. 36,20, Cu.
pHC. 286. 36,21, d = 34 CM. 36,32. h = 13 CM. 36.23. h = 2,7 M.
36.24. 1= 3,7 CM; i = 60". 36,25. h =
A = 5 c'-t. 36.26. n = 1,5. 36.27. 6 =
=arcsin (n sin a) - a = 19". 36.28. 6=
= 2 arc sin In sin (a/2)] - a = 25°.
B
I'
<"'"
J'-'-
o -<.< . a"
\I ):-_
\I "
1-';'
PIIC. 285
Pile. 286
37,1. )l.UI YBeJlH'IeIlHJI 0630pa. 37.5, a) )leiicTDHTe.1bHOe; (5)
MHH\lOe. 37.6. a) BorHYToe; 6) BorHYToe; B) DblnYKJlOe. 37.7. YllleHb-
WHrCJI JlpKOcrb. 37,9. I = V XIX 2 = 18 CM. 37.10. Ha paccToHHHH
a = R (k + 1)lk.= 60 C\I OT 3CpKa.'la, 37,11,  = Ra/(R + 2al) =
= IOCM; )l.a. 37.12, R = 2a 1 a.j(al +) = 40CM. 37.13. al = kal =
= 45 CM; R = 2ka/(1 + k) = 36 C. 37,14. 1= [kl(k! - I) = 24 CM.
37.15. 1= k1k....b/(k.... - k l ) = 10 CM. 37.16. R = (b 2 - a 2 )/a = 10 CM.
37.17.  = a 1 (R- al)/(2al- R) = 60 CM. 37.18, YKIl3aHue. Boc-
flOJlbJOBaTbCH nOHJlTHCM nooo'lHoii OnTH'IeCKOH OCH. 37.19. CIII. YKa-
3aHHe K J3.lla'le 37.18. 37.20. CM. YKaJaHHe K aa)l.a'le 37.18. 37.22. YKa-
saHue. BOCnOJlbJOBaTbCH cBoiicTBOM clJOKyca JlHHSbI. 37.23, MO>KHO,
nOMeCTHB ee B cpe.llY C n > nCT' 37.24. R = I (n - I) = 8 CM. 37.2p.
"1 - I + k
n2 = k = 1,5, r.llC "1 - nOKa3aTe.1b npeJlOMJleHHH clJnllHT-
r.1aca. 37.26. RI = (n - I) (k - 1)/(kD) = 0,75 M; R 2 = kR I =
= I I CM. 37,27. YBeJIII'IHTCSI B (1IRB - I) nJ(1IRB - "B) = 3,42 pa-
aa. 37.28. a = 1/2, HJ06paJKCliHe .llCiiCTBHTeJlbHOe, 37.30. II =
= ka/(I + k) = 7,5 CM; 1 2 = ka/(k - I) = 15 CM. 37.31. D =
= (I + k)'-IClk) = 3,6 .llnTp; Ha paCCTOJlflllH a = 11(1 + k) = I M OT
npcAllleTa. 37.32. 1= 120 CM. 37.33. I = (I' - a) 1(4/) = 16 CM.
37.34, DI = - 2,25 AnTp. 37.35. 1= RI(2n) = 20 CM. 37.36.  =
= alll(2a l - n = - 30 CM, T. e. H306paJKeflHe IIIHHMoe. 37.37. -1\.\HH-
IIIOC BOCblllHl<paTHOe YBe.1H'IeHHe. YI\asaHue. Ih06pa>KeHHe, .llaBaeMOe
ncpBoii JlHIIJoii, JlBJlReTCR HCTO'lHIIKOM ltJlH BTOpoii JIHH3b1. 37.38.
B_12 CIII OT BTOpoii JlHHSbI; 0,9 CM. CM. 3a.llny 37.37, 37.39. 100 CM.
YKasaHue. HJ06pa>KeHHe, ;J:aeacllloc JlHHJoii, JlBJlHeTCJI HCTO'lHHKOM
)I..1H 3CrKa,1a. KOTopoe, OTpa>KaH _lY'IH, nOCbI.aeT 'HX CHOBa Ha JlHHJY.
37.40. R = 2na 1 a/(al - a) = 72 CM.
38.1. h' = II (a-nil = 36 M. 38.2, Jl.tOJKIIO. 38.3. 'I = al!.xDlv=
= 10 CM. 38.4. Q' = a/(I+aD) = 19 CM. 38.5. a = (hi + nllz}/(Dh l +
+ Dnh 2 - 11) = II CIII. 38.6. a = (k + I) Ilk = 18 CM, r.l1c k-
203

-
k - JllllieHHOe YBeJUlqchke npoekuilohJloro annapaTa. 38.7, k = (a-
- f)/I = 29. 38,8. 1= ah/(h' + h) = 20 CM. 38.9. YBeJIHtlHTCJI.
38.10. TaK KaK nOKa3aTeJlb npeJIOMJleHHJI BO,AbI 6.18JOK K nOKaJaTCJlIO
npeJIOMJleHHH poroBHUbI (xpycTaJlHKa) H JlyqH npaKTHqCCKH He npeJIOM-
JlJJIOTCJJ. 38.11. g = al = 1,5 MM. 38.12. BJlH30PYK. HY>KHa pacceH-
BaJOII1aJJ JlBS3a C D = - 4 ,AnTp. YKa3QHUe. JJ.JlB. rJlaJa C HOpldaJlb-
HbiM SpeHBeJI- raccroHHHe HaHJlyqWero JpeHHH COCTaBJIHeT 25 CM. LJTO-
6b1 Bocn00ll8",", HeAOCTaTOK SpeHHJJ. qeJIOBeK HOCHT OqKH TaKOH OUTH-
qecKoA CBJlY, 'lT06b1 JlyqH, naAalOII1He OT TOqeK, YAaJlCIlHYX Ha 25 CM,
4K>XycHpOBaJlHCb OnTHqecKoH cHcreMoR OqKH-r.1asa Iia CeT'IaTKe.
38.13. 80 CM. CM. sa,Aatly 38.12. 38.14. 12,5 CM, 38.15. YMCHbWHTCH B
,ABa paJa. 38.18. D = klao = 8 Amp, f,!te 00 - paccToRHHe lIaHJlY'I-
wero SpeHHB.; k - YBeJIH'IeHHe Jlynbl. 38,17. JJ.anbHOJOpKOMY. 38.18.
x = f/(a - /) = 0,59 CM, 38.19. fofS = 60 CM; lOR = - 6 CM; OTO.llBH-
UYTb Ha 0,6 CM. 38.20, 1= 1,1 M; d = 3,5 CM. 38.21. k = Ilao = 10,
r,AC 00 - pacc'loHHHe lIaH.'IY'lwero SpeHHJJ. 38.22, MmKllo. HaAo BbI-
.llBHHYTb OKYJlHp Tax, qT06b1 OH AaBaJi .lleACTBHTeJlbHOe Hs06pa)l{eHHe.
38.23. k = 116; 1= 27 CM, 38.24. 4,1 NM, 38,25. k = 80.
39,2. (1) = 2:n1 = 0,16. 1()3 JIM. 39.3. E 1 = 11h z = O,I6.!<f' JlK;
E" = IhI(h " + R!)3/2 = 8 0 JlK. 39,4. A.h = h - V l/ E = 0,2 M,
39.5. I=V(lhlE)2/3 - h 2 = 81d. 39.6. h = RIVi = O,7R, r,!te R-
paJtHYc C'lOJIa. 39.7. (1) = O,75.I()3 JIM; R = 6,O.I()3 JlK. 39.8. E =
= 400 JlK, 39,9. a = 1 - RIE = 0,95. 39.10. Ha paccToRHKH 1=
( + h 2 )3/2 + h 3
= 0,53 M OT nepBoA JlaMnbl. 39,11. E = I J/2 27 JlK.
(+h2) h2
39.12. YMeHbWHTCJJ .llO '1"2 -= '1"1 (r - 1)2/r" = 4 c. 39.13. YMeHbwHT-
CH HpKOCTb. 39.14. BiB2 = df/d = 625. 39,15. E = 100 JlK; R =
= 80 JlK. 39.16. E = cD (a - 1)2/(SF) = 9 JlK, r.lle S - nJlOIl1a.llb
,AHaUOJHTHBa; R = Ep = 6,8 JlK. 39.17. 06'bCKTHB DbI.llOHIIYTb. 3KC-
nOJHUHIO YBe.1H'IHTb. 39.18. YBeJlH'IHTCSI B
 1,1 paJa. YKa3aHue. n.10cKoe SepKaJlO npHBo-
1(HT K nOJlB.1CIIHIO eIl1e O.llHorO HCTO'iHHKa S', SlB-
__!:I:'-- JlJlIOII1erOCH OTpa)l{eHHeM HCTO'lHHKa S. 39.19,
-r==r-S w (R/2)2 + (1-RI2)2
- E = Eo (RI2)2 400 JlK. Y"aJaHue,
TaK KaK HCTO'lHHK HaXO;J;HJlCH B 4JoKYCC BorHY-
Toro SepKaJla, OTpa)l{aeTCH napaJlJleJlbHblH ny-
PHe:. 287 '10K. 9Ta .llonOJlHHTeJIbHaSi oCBcw.eHHOCTb TaKaR
)I{e, KaK oCBcw.eHHOCTb caMoro SepKaJla. 39,20.
I = 10 = F/(f - al)" = 250 K;I.. J'KaJaIiUi!.
CBeToBoii nOTOK BHYTPH Te.'IeClloro yr.1a U) H U)' O.llHH H TOT )I{e
(pHC. 287). 39.21. E = If/(aJ + II - a 1 l)2 = O,62.1()3 JlK.
X 1.1. I = 0012 - din = I 1,5 C\!, r.lle ao - paccToRHHe HaHJlY'I-
. sin {lp/2)
wero 3pCIIHJJ, XI.2. lup = 60°. xl.a. y = 2 arcsin n
= 76°, r.lle n - nOKaJaTeJIb npCJlOMJleHHH BO,AbI. XI.5. a =
I. aF ° ( 1 ) Z ( YMF ) _
-= 2 arcsin b (0 + d- F) = 15. XU. J=F 1'-r + 'l'T 1+0;;--
= 26 CN, r.lle Do - paCCTOSlHHe HaH.'IY'IWCro 3peHUR.
204

40.1. A = 0,38 MKM; 3eo1CHbli\. 40.5. 8 = 0,55°. 40.6, {, = 7,4°.
40.7. l!f = R t!.n/(2 (nl - I) (n! - I)J = 1,6 CM. 40.8. nOJlOCbl CTa-
JIF wHpe B .llBa paJa. 40,9. t!.q> = 11/2.40,10, t!.y = 3,6 MM. 40.12.
d"ntH = A/(4n) = 0,1 MKM, r.lle n - nOKaJaTe.1b npeJ10MJleHHH BO;r.bI.
40,14. a= 'J../(2ns) = 5.10- 5 pa,;(. 40,15. no.'10CbI cTallYT WHpC.
40,16. d = 2 MK\!. 40.17. k = 28.
41.1. E 1 = 2,6,10- 1 ' .lI.>K; E2=5,2.IO-18.!I.>K;ml=2,9.IO-a8 i<rj
m2 = 5,8.10- 38 Kr.41.2. m = 2,2.10- 33 Kr; p=6,6.10-:! Kr'M/c.
41.3. p = 1,6.10- 27 Kr'N/c. 41.4. A = 2,42 JIM. 41.5. A = 1,32 X
X 10- 15 M. 41.6. ,. = hlV 2m e eV = 0,55 HM. 41.7, n = WA /(hcSJ) =
= 2,5.10 20 I/(cM 2 .c), r1(c c - CKOpOC'ib CBeTa. 41.8. t!.M = 6,0.10' Kr.
41.9. HCT. 41,10. V=20,5 KB 41,11. AI{=0,577 &lXM; AnJI=0,235 MKM.
41.12. Her. 41.13. v=2,2.IOs we, 41.14. ,,=4,87.10 15 fl.{.
41.15. A = 340 HM. 41.16, Va = 5,05 B. 41.17. nCpBLlii; tg a = hie.
41.18. N-= 4,3.10 7 .
42.1. q = 3,8.10- 19 K.'1. 42.2, A.11O\!JIHHH. 42.3. R = 0,53 X
X 10- 8 C\I; V = 2,2, 1()8 CM/C. 42.4. E = 5,13, 1011 B/M; cp = 27,2 B.
42.5. F = 82 HH; FIF T = 2,3. 109. 42.6. En = - 27,2 98; EM =
= 13,6 3B; E = - 13,6 3B. 42.7. cp = 13,6 B. 42.8. «fl = 10,2 B.
42.9. v = 8,10 5 'Allc. 42.10, Becb cneKTp. 42.11. 122 HM; 103 HM;
0,66 MKI. 42.12. '}.. = 90 HM. 42.13. E = 3,04.10- 1 ' .D.>K. 42.14. Al =
= 810 JIM; "2 = 1,9 1-IKM.
43.4. 29,4 !>bB. 43.5. 225 1\bB. 43.6. 39,2 M9B. 43.7. 1.1 M3B;
8 1\bB; i,25 J.bB. 43.8, 4,4i M3B. 43.9. 20,6 M3B. 43.10. 7,28 M3B.
43,14. I) BblJlCJlRCTCR; 2) BbI.llCJlSlCTCR; 3) nor.10w.aCTCJI; 4) BbI.IlCJlSI-
eTCSI. 43,15. 17.35 1>\3B. 43.16. 17,6 .\bB,

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 9, 3aKoHbI coxpaHCIIHH B MexaHHKC
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 13. KHHCMaTHKa rapMOIIH'IeCKoro KOJle6aTeJlbIiOrO.ABH>KeHIIH
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 15. BOJlHbI. 3BYK .
3a.lla'lH K rJlaBe IV . .
7
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35
36
40
46
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LJ a C 'I b B TOp a H. Mo.1cKyn:lpilaR c1JHJHKa
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lII.eCTB8 . , . . , . . .
 16. Macca H pasMcpbl MO.1CKyJl . .
 17. .l1BH>KCHHe ldoJleKYJl. BsaHMoAciiCToHe MOJleKY.
!i 18. TenJlOBOe pacwHpcHHe 'iDep.!lblX H >KH.'lKHX Te.1
F AaBa i'l. CcoAc'illa raJOB . . . .
 19. KHHeTH'lecKaH TeopHH raSOB . . .
 20, rasoBbie 3aKOHbI, YpaBHeHHe COCTOSlIIHR H1IC3J1bHOro
raJa . . . . . . . . . . . . , . . . . . . . . . . . .
76
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206

 21. CnoiicTBa napOB. Bna>KIIOCTb . . . . . , 86
33.;1.a'lH K r.1aBC V I . . . . 88
FAaaa VII. TennOT8 H paGoTa . . . . . 88
 22. IhMelleHHe BIIYTpcHHeii 3HeprHH nYTeN Tennoo6MeHa 88
 23. IhMcHeHHe BHYTpeHHeii 311eprHH B npouccce COBep-
wellHR pa60TbI . . . . . . . . . . . . . . . . 91
 24. npHMcncnHc nepooro lIa'la,a TepMo;J.HHaMHKH K rasaM 93
3a.lla'lH K r.30e V II 96
LJ 3 C 'I b 'I P C T.b R. 3neKTpH'IeCTIlO
FAa8a '1/111. 3.1eKTpOCTaTHKa . . . . . . . .. 98
 25. 3.1eKTpH'ICCKHC 3apSIlU>I. 3aKoH KynoHa . . . . .. 98
 26. 3neKTpH'IeCKOC nO.1e. H3npR)l..eHtiOCTb. PaooTa CHn
3neKTpH'IeCKOrO nonR. nOTeHUflaJi. . 100
 27. npOBO.llHHKH H ;J.H3neKTpHKH B 3neKTpH'IeCKOM none 1M
 28. 3.1cKTpoeMKocTb. KOIIAeHcaTopbl 106
3a.lla'iH K rmlBC VIII. . . , III
F AGaa IX. nOCTORHHblii TOK . . . . . 113
 29. CH.1a TOKa. 3aKoH O}!a ;l.1R Y'IacTKa uertH, Coc;J.HHeHHSI
npOBo.lllIIIKOB .. ........ 113
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 31. PaooT3 II MOW.HOCTb TOKa . . . . . . . 121
 32. 3neKTpH'ICCKHii TOK 0 pa3.1H'IHblX cpc,Aax 126
3a;r.a'lH K rnaBC IX,. . .. .... . 128
F AGa X. 3neKTpoll13rHCTH3M . . . . . . 129
 33. BsaHMoAeiicTBHe MarHHTHoro nonR C TOKOM 129
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 35. nepcMeHHblii TOK. 3.1cKTpOMarHH'illbie Kone6allHH H BonHbI 140.
3a;J,a'lH K r.1aBC X . , . . . . , . . . . . . 143
LJ a C 'I b 'I e 'I B e p 'I a R. OnTHKa, CTpoellHC aTOMa 145
FAG8a XI. feOMeTpH'IeCKaR onTHKa, 4>OTOMeTpHR . . .. 145
 36. OTpa>KeHlle H npenoMneHHe CBeTa lIa n,10cKoii rpaHHlle 145
 37. C<jJcpH'IeCKHe sepK3na H .nHH3b1 148
 38. OnTH'ICCKHe npH60pbl 153
 39. cJ>OTOIIICTpHH . 155
33.'1.a'lH K rnaBC XI . . . 157
FAoBa XII. BonHoobie II KoallTOBbie cBoiicTlla CIIeTa 158
 40. Bo.111oBaR npHpoAa CBeTa . 158
 41. KBaHTooaH npHpoAa CBeTa 159
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npH.10>KCHIIR . 163
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