(формат)Тарг

~H MOMeHThi orrpe,ZJ;eJIHIOTCH TaK me, KaK H MOMeHThl CHJihi (eM. § 8, 14

H 28).

TaKl!M o6pa30M, MOMeHmOM K0J7Uilecmea aeu:J/CeHUfl moliKU OmHOCU· me1tbHO HeKOmOp020 l{eHmpa 0 HCl3btBaemCH BeKmOpHafl BeAUf.WHa tno (mv),

onpeoeAHe.MaH paeeHcmeo.M
mo (mv) = rX mv,	(35)

r)~e r - pa)I.IIYC·BeKTOp ABH)I{Yll.\eHCH TOqKH, rrpoBe,ZJ;eHHhiH H3 UeHTpa 0.

llpH 3TOM BeKTOp m0 (mv) HarrpaMeH rreprreH,ZJ;HKYJIHpHO ITJIOCKOCTH,

IIpOXO,ZJ;HIUefi qepe3 mV H ueHTp 0, a imo (mv)\ =mv ·h (pHC. 224; )I.JIH cpaBHeHHH Ha HeM IIOKa3aH H BeKTOp m0 (}')-rXF).

l\1oMeHT KOJIHqecTBa )I.BH)I{eHHH TOqKH OTHOCHTeJihHO KaKOH·HHOY,ZJ;h OCH Oz, rrpOXO)l;HIII,ell: qepe3 uemp 0, oyAeT paBeH rrpoeKUIIH BeKTOpa mo (mv) Ha 3TY OCh:

mz (mv) = [m	0	(mv)]z = 1 0 (mv) 1cosy,	(36)
		m

r,ZJ;e y - yroJI Me*)l;Y BeKTopoM m0 (mv) H ochJO Oz.

TeopeMa MOMeHTOB ycTaHasmmaeT, KaK II3MeHHeTCH co BpeMeHeM

BeKTop m0 (mv). lho6hi ,ZJ;OKa3aTh ee, rrpo,ll;HqxpepeHuHpyeM no BpeMeHH Bblpa)l{eHHe (35). lloJiyqHM

:t (rX nW)= (~;Xmv) + (rXm ~n =(VX mV) +(rX ma).

Ho vX mv-0 KaK BeKTOpHoe npoH3Be)l.eHIIe ,ZJ;Byx rrapaJIJieJibHhtX BeKTOpOB, a ma=F, r,ZJ;e rrpH ,ZJ;eHCTBHH HeCKOJihKHX CHJI F='i.Fft.

CJie,ZJ;oBaTeJihHO,

d -	-	- -	d -	-	-	-	(37)
d[(r X mv) =		r X F	HJIH dt [m0 (mv)] = m0			(F).
B pesyJihTaTe	Mhi	)I.OKa3a.!fn cJie)l.yJOmyJO		Teo p	eM y		MoM e H·
T 0 B 0 T H 0 C II T e JI h H 0			U e H T p a: npoU3BOOHaH no BpeMeHu om

J.WMeHma KOAuiiecmea aeu:J!CeHUH moliKU, 83Hmozo omHocumeAbHO KaKOzoHU6yob Henoaeu:JICH020 l{eHmpa, paeHa Mo.MeHmy OeiicmeyiOU{eU Ha mOiiKY CUAbt OmHOCUmeAbHO m020 :J/Ce l{eHmpa.

CpaBHHBaH ypaBHeHHH (37) H (32), BH)I.HM, qTO MOMeHThl BeKTOpOB mv

llF CBH3aHhl TaKOH me 3aBHCI1MOCThJO, KaKOH CBH3aHbl caMH BeKTOpb! mv

IIF.

ECJIH crrpoeKTHpoBaTh ooe qacTII paBeHCTBa (37) Ha KaKyJO·HIIOY,ZJ;h ochOz, rrpoxo,ZJ;Hll.\YJO qepe3 ueHTp 0, TO, y~H cooTHOilleHHe (36), rroJiy· llJIM

d	-	-	(38)
dt [mz (mv)] =- m., (F).

3'fo paBeHCTBO Bbipa)l{aeT meope.My .MOJteHmOB OmHOCUtne!lbHO OCU.

113 ypaBHeHHH (37) CJie)l.yeT, qTO eCJIH mo(F)=O, TO mo(mv)=const,

205

T. e. eCAU .MOMeHm aeuCtn6Ytot«eit CU/lbt OmHOCumeAbHO HeKOmopozo tfeHm· pa paseH HYAIO, mo .MOMeHm KOAUt-leCmea aeu:J!CeHUfl moll1W omHocume/lbHO &moeo WHmpa ecrnb ee/lulluHa nocmoJIHHaH. TaKoii pesyJihTaT IIMeeT MecTo B npaKTHqecKII BaJKHOM CJiyqae ABHJKeHIIH IIOA AeiicTBHeM ueHT· paJihHOH CHJihi (CM. § 86),

Puc. 224

§ 87. PAEOTA CI-IJ1bl. MOUJ,HOCTb

,UJIH xapaKTepHCTHK!I ,AeHCTBHJI, OKa3biBaeMoro Cl!JIOH Ha TeJIO rrpll HeKOTOpOM ero rrepeMemeHHll, BBO,A!ITCH IIOHHTHe 0 paooTe CliJlbl, ll!HpOKO liCIIOJib3yeMOe He TOJibKO B MeXaHHKe. CHaqaJia BBe,AeM llOHJITHe 00

3JieMeHTapHoli pa6oTe.

	3/leMeHmapHoii pa6omou cHJibi F,			npHJIOLKeHHoli	B	ToqKe	M
(pHC. 228), Ha3b!BaeTCH			CKaJIHpHaH BeJiuqHHa *
			dA=F,ds,				(40)
r,Ae	F't -	rrpoeKUHH CHJihi F Ha KacareJibHyio M't K rpaeKTOprrH ToqKrr
M,	HarrpasJieHHYIO B		cropoHy rrepeMemeHHR 3Toli ToqKH			(HJIH	npo-
eKuHH F na HarrpasJieHHe cKopocTH vTOtJKH M); ds- MO.AYJih 3JieMeH-
TapHoro		rrepeMemeHHH	ToqKn M.
	TaKoe	orrpe.n.eJienrre	coorsercTsyeT rrpe,rr,crasJieHHIO		o	pa6ore	KaK
0 Mepe TOfO JI.eHCTB!IH CHJibi, KOTOpoe				IIpMBO,AHT K H3MeHeHHIO MO.AYJI51

CKopocnr ToqKrr. EcJIH pa3JIOLKHTb CHJIY F Ha cocTaBJIHIOili,He F-r; rr Fn,

TO H3MeHHTb MO.AYJib CKOpOCTH					oy.n.eT F't• TaK		KaK F-r;=ma-r;=m ·dvldt
(cocraBJIHIOIUaH		Fn	H3MeHHeT		HJIII HanpasJieHHe BeKTOpa v, HJIH rrpii
HeCBOOOJI.HOM	,ABHJKeHMH -			CHJIY		)J.8BJieHHR	Ha CBH3b).
3aMeqaH,	tJTO	F-r;=F cos a, r.n.e a - yroJI					MeLKJI.Y F H M't, noJiy-
qHM H3 (40)	,Apyroe		BbipaLKeHHe			.AJIH dA:
			dA =Fds cos a.				(41)
EcJIH yroJI a		ocTpbili, TO paooTa noJioLKnTeJibHa. B qacTnocrn, npH
a=O 3JieMeHTapHaH			paooTa	dA =Fds.
EcJIH yroJI a Tyrroil:, TO pa6oTa oTpnuaTeJibHa. B qacTHOCTH, rrpH
a= 180° 3JieMeHTapHaa paooTa						dA =-Fds.
EcJIH yroJI a =90°, T. e. ec11u					cu11a Hanpae/leHa nepneHauKyllRpHo ne-

pe.!.teU{eHuJO, mo B/leMeHmapHaR pa6oma cu,7bt paeHa HY/110.

3HaK paOOTbl HMeeT CJieJI.yiOJUHH CMb!CJI: pa6oTa IIOJIOLKIITeJibHa, KOf)J.a COCTaBJI5IIOJUaH ~ HarrpaBJieHa B CTOpOHy JI.BHLKeHIIH (CHJia ycKopHeT ,n;BHLKeHue); paooTa oTpuuaTeJibHa, Kor.n.a cocraBJIHIOIUaH

F 't uanpaBJieHa rrpoTHBOIIOJIOLKHO HarrpasJieHHIO JI.BHLKeHHH (cHJia 3aMe)J;JIHeT JI.BHLKeHHe).

EcJIH yqecTh, qTo ds= !dr\, r.n;e dr- se1nop 3JieMeHTapHoro rrepeMe-

memm TOqKH, li BOCI10Jlb30BaTbCH H3BeCTHbiM H3 BeKTOpHOU aJire6pbi IIOHHTHeM 0 CKaJI51pHOM npOH3BeJI.eHHH JI.BYX BeKTOpOB, TO paBeHCTBO

(41) MOLKHO npeJI.CTaBHTb B BHJI.e * ~
dA=F·dr.	(42)

* 3AeC:b dA (KaK u"clS B § 83)- CHMBOJI SJie\leHTapHOH BeJIHqHHbl, HO He ]].Hpcpe-

peHUHa,'Ja• .Uu¢¢epeHUHaJioM KaKoli-HH6YAh (PYHKUHH Be.'IHqHHa dA Bo06lll.e MO)KeT He 6b!Tb (CM. § J26).

** CKamiphbi\1 npousBeJJ.eHneM AByx BeKTopoBa nb HashJBaeTCH cKaJIHpHaH BeJiuquHa, onpeJJ.eJIHCM3l! paBeHCTBOM a• b=ab COS a, fJ].e a - yroJI Me)KJJ.Y BeKTOpaMH a

H b Bblp31K€1-1He CKa.'IHpHororrpoil3Be)l,eHHll qepe3 IIpOCKUHH BeKTOpOB aH b Ha KOOp)l,H-

H3T!-lble OCH !!MeeT BRAa•b=a_.bx+ayby+azbz..

208

209

CJie,IJ;oBaTeJibHO, aAe.MeHmapHWl pa6oma cu!lbl paeHa cJWARpHo.My npouseeaeHUIO CU/lbt Ha eeKmop a!leMeHmapHoco nepe.MeU{eHWl moll1W ee npUAOJJCeHUfl.

EcJirr B ¢opMyJie (42) Bhrpa3HTb cKaJIHpHoe rrpoH3Be,IJ;eHrre tiepes

rrpoeKU.HH BeKTOpOB F li r Ha KOOp,D;HHaTHbie OC!I II ytJeCTb, tiTO rx=X, fy=y, fz=Z, TO IIOJIYtiHM aHa!lUmUiieCKOe BbtpaJJCeHue aAe.MeHmapHOU

pa6ombt
dA =Fxdx+ Fydy+ Fzdz,	(43)
B KOTOpOM X, y, Z - KOOp,li;HHaTbl TOtiKH IIpHJIO}!{eHHH	CHJibl F.

1

Pnc. 228

Pnc. 229

PaooTa cHJihi Ha mo6oM KOHetiHOM rrepeMemeHrrH MoM1 (prrc. 228)

BbltJHCJIHeTCH KaK rrpe,D;eJI HHTerpaJibHOH cyMMbl COOTBeTCTBYIOlll,liX S>JieMeHTapHbiX paooT

(M,)
A(M,M,) = ~ Fr ds,	(44)
(M,)
HJIII
(1\1 ,)
A(M,M,)= ~ (Fxdx+Fydy+Fzdz).	(44')

(M,)

CJie,IJ;oBaTeJibHO, pa6oma CU!lbt Ha AI060Jrt nepeMeU{eHuu MoMt paeHa B3RtnOMY eaoAb amoco nepe.Meu~eHUH uHmecpally om &Ae.MeHtnapH.oll

pa6ombt. Dpe,D;eJibl liHTerpaJia cooTBeTcrByiOT sHatieHHHM rrepeMeHHhiX HHTerpHposaHHH B TOtiKax Mo D: Mt (TOtiHee rosop51, HHTerpaJI 6epeTC51

B,IJ;OJih KpHBOH MoM to	T. e. 51BJIHeTCH KpHBOJIImell:HbiM).
EcJirr sem-FmHa Fe rroCTOHHHa (Ft=const), TO 113 (44),		ooosHatJa51
rrepeMemeHHe MoM 1	tiepes s11 rroJiytiHM
	A(M,M,) = FTh·	(45)

B tJaCTHOCTH, TaKOH cJiytJal! MO}!{eT HMeTb MeCTO, KOr,IJ;a ,IJ;ell:cTBYJOlll,aH CHJia IIOCTOHHHa ITO MO,ll;yJIIO II HarrpaBJieHHIO (F=const), a TOtJKa,

K KOTOpOfi IIp!IJIOLKeHa	CIIJia, ,li;BH}!{eTCH IIpHMOJIIIHeHHO (pHC.	229).
B 3TOM cJiyqae F-r.=Fcos a=const H
	A< tr, It,)= Fs1 cos a.	(45')
E,IJ;HHHU.efl usMepeHHH paooTbr HBJIHeTcH B CH - 1 ,IJ;21WYJih (1		.U2K=
=lH ·M=l Kr ·M2/c 2), a	B CHCTeMe .MKfCC- 1 Kf •M.
	I

X 106

f p a	cjJ	H q e C K H ii:	C II 0 C 0 6 B bl q li C JI e H li li p a 6 0 T bl, ECJI!i CHJI3
33BHCHT	OT	paccTOl!Hl'lllS	H H3BeCTeH rpacjlliK 3aBiiC!iMOCTH f 'fOT S (puc. 230), TOp&-

	6oTy CHJibl MOIKHO BblqliCJIIiTb rpacjluqecKH.			TiycTb B IIOJIOtKeHHH M 0 TOqKa H3XO,ll;HTCll
	OT naqaJia oTCqeTa na paccToliHHH So, a B			rroJiotKenuu M 1 -		na paccTOliHiili s1. Tpr.D:a
		no ¢opMyJie (44), yquTb!Ball				reoMeTp!iqecKKii cMhlCJI
		liHTerpaJia,		rroJJyqKM
					s,
				Auu.M,>= ~ Fr; ds=a,
		r,ll;e 0' -	BeJJHquna 3aii!TpHXOB3HHOK				Ha p!iC, 230 IIJIO•
		UJ:3.1IH, YMHOIKeHHOK Ha M3CIIIT36HbiK					KOScpcpH~HeHT.
	Puc. 230	M o Ill, Hoc T h.			MomHOCThiO			Ha3hiBaeTcH
		BeJmqrma, orrpe.D;eJIHIOUJ,aH paoOTy, cosepwae-
		MYIO	CHJIOH B e,!I,HHHUY BpeMeHH. EcJIH pa6oTa
	coBepwaeTCH paBHOMepHo, TO		MOili.HOCTh N =Ait1 , r,IJ;e				t1 -	BpeMH, B
	Teqerme KOToporo rrpoH3Be)l.eHa paooTa A. B				ooUJ,eM cJiyqae
		N = dA!dt =Fe ds;dt = FT.v.						(46)

CJie.D;oBaTeJihHO, MOU{HOCmb paeHa npou3eeaeHUIO KacamellbHou cocmae/lHIOU{eu cu/lbt Ha cKopocmb.

E.D;HHHuell: II3MepeHHH MOUJ,HOCTH B CI1 HBJIHeTCH eamm (1 BT = =l.U2K/c), a B cHcTeMe MKfCC- 1 Kf ·M/c. B TeXHHKe 3a e,IJ;IIHHUY MOUJ,HOCTH qacTo npHHHMaeTca 1 Jl. c., paBHaH 736 BT (HJIH 75 Kf ·M/c).

PaoOTy, rrpoH3Be,IJ;eHHYIO MarniiHOH, M02KHO H3MepRTh npoH3Be,IJ;eHIIeM ee MOUI,HOCTH Ha BpeMH paoOThi. 0rCIO,IJ;a B03HHKJia yrrOTpe6IITeJibHaH B

TeXHHKe e)l.HHHua II3MepeHHH pa6oThi KHJIOBaTr-qac (1 KBT ·q=3,6x

.il.2K~3671QQ Kf •M).

l13'paBeHcTBa N =FT.v BH.D;HO, qro y )l.BHraTeJIH, HMeiOmero ,IJ;aHHYIO MOUJ,HOCTh N. CHJia THfH F'T: oy.D;eT TeM OOJib-IDe, qeM MeHbUie CKOpOCTh v.

Do::tTOMY, HarrpHMep, Ha no.D;beMe HJIH Ha IIJIOXOM yqacTKe .D;Opom y aBTOMOOHJIH BKJIIQqaiOT IIH3lliHe nepe,D;a qu, ll03BOJIHIOUJ,He rrp H IIOJIHOH MOUJ,HOCTH ,ll,BHraThCH c MeHbUiell: CKopocTh!O H pa3BHBaTh 66.nhUIYIO CHJIY T5Irii.

§. 88. nPHMEPbl BbllfHCJJEHH~ PA60Tbl

PaccMOTpeHHbre mnKe rrpHMephJ.D;aiOT pe3yJihTaTh!, KOTOphlMH MO:lKHO

Herrocpe.n.cTBeHHO	noJih30BaThCH rrpH peUiemm sa.n.aq,
1. P a 6 o T a	c H JI hi	T Sf >K e c T H. DycTh TOqKa M, Ha KOTopyiO
,IJ;eilcrsyer cHJia	TH2Kecnr	P,	nepeMemae-rc&	HS. noJio2Kem-IH M 0 (x0 ,
Yo, z0) B IIOJI02KeHHe M 1 (x1o Y1o			Z1 ). Bbr6epeM	KOOp,!UIHaTHh!e OCH TaK,

qTo6hr och Oz OhiJia HarrpaBJieHa BepTHKaJihHO ssepx (puc. 231). Tor.D;a p x=O, p y=O, p z=-P. Do,IJ;cTaBJIHH 3TH 3HatieHHH B <PopMyJiy (44'),

IIOJiyqHM1 yqHThiBa51, qro rrepeMeHHhiM HHTerpiipOBaHHH HBJIHeTCH z:

z,

A(M 0 M 1 )= ~ (-P)dz=P(z0 - Z1).

2'~

210

EcJIH roqKa M 0 Bhiiiie M 1 , TO z0- Z1 =h, r;I.e h - BepTHKaJihHOe nepeMern.eHne ToqKH; ecJIH 2Ke roqKa M 0 HH2Ke TOqKH M 1 , TO Zo-zl =::;

= - (zl-zo)=-h.

0KOHqaTeJibHO noJiyqaeM

A(M 0 M 1 ) =+Ph,

(47)

CJie,IJ;OBaTeJibHO, pa6oma cuAbl tmlJJCecmu paeHa 83flmo.My co 3Ha!WM nAIOC UAU ..MUHYC npou38eaeHUIO ..MoiJyAfl CUAbl Ha BepmUI«<JlbHOe nepe.Me- U{eHUe molltW ee npuAoJJCeHUfl. Pa6ora noJI02KHTeJibHa, ecJIH HaqaJibHaH TOqKa Bblute KOHeqHOH, H OTpHUaTeJibHa, ecJIH HaqaJibHaH TOqKa HUJ/Ce KOHeqHOH.

l-13 llOJiyqeHHOfO pe3yJlbTaTa CJie,IJ;yeT, qTO paooTa CHJibl TH2KeCTH He 3aBHCHT OT BH,IJ;a TOll TpaeKTOpHH, no KOTOpOH nepeMern.aeTCH TOqKa ee npHJI02KeHHH. CIIJihl, ooJia,IJ;arorn.ne TaKHM cBoHCTBOM, H83b!BarorcH nomeH4UaAbHbtMU (eM. § 126).

a}	t

Puc. 231	Puc. 232
2. P a 6 o T a	c H JI bl _ y n p y roc T H. PaccMoTpliM rpys M,

Jie2Karn.Hll: Ha ropH30HTaJibHOH nJIOCKOCTH H npHKperrJieHHbiH K cBo6o,IJ;- HOMY KOHUY HeKoropoll: npy2KHH:r.I (pHc. 232, a). Ha nJIOCKOCTH OTMe· THM TOqKOH 0 llOJI02KeHHe, 3aHl!MaeMoe KOHUOM npy2KHHbl, KOr,n,a OHa He HanpH2KeHa (A0=/0 - ,Il,JIHHa HeHanpH2KeHHOH npy2KHHbl), I1 npHMeM 3TY TOqKy 3a HaqaJIO KOOp,D;HHaT. ECJIH Terrepb OTTHHYTb rpy3 OT paBHOBeCHOro llOJI02KeHHH 0, paCTHHyB npy2KHHY ,li;O BeJIHqHHbl [,

TO rrpy2KHHa noJiyqHT Y,IJ;JIHHeHHe 'A=l-lo H Ha rpy3 oy,IJ;eT ,IJ;ell:cTBOBaTb

CHJia ynpyrocrn F, HanpaBJieHHaH K roqKe 0. TaK KaK B HarneM cJiyqae 'A=x, TO no ¢opMyJie (6) 113 § 76

F=c'A=clxl H Fx=-cx.

TiocJie,IJ;Hee paBeHcTBO cnpaBe,IJ;JIIIBO II npll x<O (rpys JieBee TOqKH 0);

ror,IJ;a CHJia F HanpaBJieHa BnpaBo H noJiyqHrca, KaK H ,IJ;OJIJKHO ob!Tb,

Fx>O.

Hall:,n,eM paoory, coBepwaeMyro cnJioll: ynpyroCTH npH nepeMern.e- HHH rpy3a H3 noJio2KeHHH M 0 (xo) B noJio2KeHHe M 1 (x1 ). TaK KaK B ,n,aH-

HOM CJiyqae Fx=-cx, F y=F z=O, TO, llO,IJ;CTaBJIHH 3Tll 3Ha'leHHH B

211

§ 89. TEOPEM.A 06 H3M.EHEHHH KHHETHIJECI(OA

9H EPfHH TOIJ KM

BBe)l.eM IIOHHTHe ern.e 00 O)I.HOH OCHOBHOH )I.HHaMHtieCKOH XapaKTepHCTHKe )I.BH}!{eHHH - o KIIHeTH'-leCIWH 3Hep rmr. KUHemwlecKOu EJHepeueu MamepuaAbHou motfKU HasbteaemcH CKaAHpHaH eeAutiuHa mv2/2, paeHaH noAoeuHe npou38eaeHUR Maccbt motLKu Ha KBaapam ee CKOpocmu.

EAHHHUa H3MepeHHH KHHeTH'-leCKOH 3Heprm-I Ta }!{e, tiTO H paoOTbi (B CI1 - 1 .U}!{). Haii)l.eM 3aBncH:O.IOCTh, KOTopoll. CBH3aHbl 3TH )!.Be BeJIH- ':IHHbi.

213

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CJie)!,OBaTeJibHO, rrp rr rrepeMeiii,eHrrrr no Herro)!,BH:iKHOH r Jia)!,KOH no·

BepXHOCTH (HJIH KpHBOH) li3MeHeHHe KHHeTrrqeCKOH ::mepmrr TOqKH paBHO cyMMe paoOT Ha 3TOM nepeMeiii,eHHH rrpHJIOX<eHHbiX K TQqKe

aKmUSHbtX CHJI.

EcJirr rrosepxHOCTh (KpHBaH} He HBJIHeTCH rJia)!,Koii 1 TO K paooTe aKTHBHhiX cnJI npH6asmc.H paoOTa cHJibi TpeHrrH (eM. § 88). EcJirr 2Ke no· BepXHOCTb (KpHBaH) )!,Bli2KeTCH, TO aoCOJIIOTHOe rrepeMeiiJ,eHrre TOqKrr M

M02Ket He obiTh nepneH)!,HKYJIHpHo N rr Tor)!,a paoOTa peaKU.HH N

He 6y)!,eT pasHa Hymo (HanpnMep, paoma peaKu.HH rrJianpopMbi Jinqrra).

P e Ill e H H e	s a )!, a	q, TeopeMa	o6	H3MeHeHrrn KHHeTnqecKoii
::mepnm [<lJopMyJia	(52))	II03BOJIHet,	3HaH	KaK IIpH )!,BH2KeHHH TOqKH

H3MeHHeTCH ee CKOpOCTb, orrpe)!,eJIHTb pa6oTy )!,eikTBYIOIIJ,HX CHJI (rrep· BaH 3a)!,aqa )!,HHa.MHKH) HJIH, 3Ha51 pa6oTy )!,~HCTBYIOIII,HX CHJI, orrpe)!,e·

JIHTb, KaK H3MeHHeTCH IIpH )!,BH2KeHHli CKOpOCTb TOqKH (BTOpaH 3a)!,aqa )!,HHaMl!KH). Dprr pellleHnrr BTOpoii 3a,11,aqu, Kor,z~;a 3a)!,aHbl CHJihi, Ha)!,O

sblqHcJIHTh Hx paooTy. KaK BH)!,HO H3 ¢opMyJI (44), (44'), 3TO MOX<HO C)!,eJiaTb Jllllllb TOf)!,a, KOr)!,a CHJibl IIOCTOHHHbl HJIH 3aBHCHT TOJibKO 011 IIOJI02KeHHH (KOOp)!,HHaT) )!,BH2Kyiii,eHC5I TQqKH, KaK, HarrprrMep, CliJibl yrrpyrOCTH HJIH THfOTeHHH (eM. § 88).

TaKHM o6pa3oM, ¢opMyJiy (52) M02KHO Herrocpe)!,CTBeHHO ucrroJib30·

BaTb )!,JIH pellleHHH BTOpOH 3a)!,aqH )!,HHaMHKli, KOf)!,a B 3a)!,aqe B qHCJIO )!,aHHbiX H HCKOMbiX BeJIHqliH BXO)!,HT: ,D,eHCTBYIOIII,He CHJibl, nepe.MeWptue

mOilKU H ee HaqaJibHaH H KOHeqHaH CKOpOCTH (T. e. BeJirrqHHbl F, S,

Vo, V1 ), npuqeM CHJibl )!,OJI2KHbl Ob!Tb IIOCTOHHHbiMH HJIH 3aBHCHIII,liMll TOJibKO OT IIOJI02KeHIIH (KOOp)!,HHaT) TOqKH.

TeopeMy B )!,II<lJ<PepeHU.!IaJibHOH <lJopMe [<lJopMyJia (51)) MOlKHO, KO·

HeqHO, rrprrMeHHTb nprr JIIOObiX )!,eikTBYIOIII,liX CHJiaX.

3a.n.a'!a 98. fpys ~laCCOll m=2 Kf, 6poUieHHb!ll CO CKOpOCTbiO V0=20 M/C 1'13IIYHK• ra A, naxo.n.mn:erocH na BbiCore h=5 M (pnc. 235), liMeer B TO'IKerra.n.eHiiH C cKopocrh

v1 = 16M/c. Orrpe.n.eJIKTh, 'leMy paBna	pa6oT-a .n.eil-		7(
cTByiOill,eil na rpys rrp!i ero ABKJKeHiili	C!iJibi	conpo·
THBJieHKH B03Ayxa R.
P e UI e H li e. Ha rpys np!i ero ABKJKeHKH .n.eii·
CTBYIOT C!iJI3 THJKeCT!i p li CliJI3 conpOT!iBJieHiiH B03·
JJ.Yl\3 R. Tio reopeMe 06 li3MeHeHHH KI1HeTHtl€CKOH
sneprli!i, C'!HT3Hrpys MaTepH3JibHOll TO'!KOll,HMeeM
mv~/2-mv3/2= A (P) +A (R).
H3 ::nora paBeHCTBa, TaK KaK corJiacHo <!JopMy-
Jie (47) A (P)= Ph, naxo.n.KM			Puc. 235
A (R) = mvi/2- mvg/2-mgh= -242 )l)K.
3a.n.a'la 99. Tip!i ycJIOB!iHX sa.n.a'IK96 (eM.~§ 84) orrpe.n.eJIKTb,			KaKoil nyrh rrpoil.u.er
rpys .n.o ocTaHoBK!i (eM. p!ic, 223, r.n.e M0 -		ua'!aJibuoenoJioJKeHHe rpysa, a		M 1 -
Koneqnoe).
P e UI en H e. Ha rpys, KaK li B sa.n.aqe 96, .n.eilcTBYIOT CliJibl P, N, F. .[LJIH				onpe-
JJ.eJielilill TOpM03HOf0 IIYTii s1=M0M 1 ,	Y'IHTblB3511 'ITOB ycJIOBHll JJ.3HHOH 33,li,3'1HBX{)-

,li,HT s1o v0 , v1 H nocTOliHHaH cuJia F, BocnoJih3yeMCll TeopeMoii o6 H3MeHeHHH KHHeTii- '!ecKoii :;mepruH

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