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T. e. npu nocmynameAbHOM nepertocrtoM iJouO/Certuu a6coAromnoe yCiwpertue mOLtKu paerto zeoMempuLtecKotl cyMMe omnocumeAbrtozo u nepertoc-
noco |
ycKopertuii. |
PesyJihTaT |
3AeCh aHaJiornqeH |
TOMy, KOTopbiH |
AaeT |
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TeopeMa 0 |
CJIO)!{eHHH |
CKOpOCTefr. |
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B hi q H C Jl |
e H H e |
0 T H 0 C H T e Jl h H 0 ro, |
IT e p e H 0 C H O- |
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r o |
n |
K o p n o JI n c o B a |
y c K o p e H n li. |
0THOCHTeJihnoe |
ycKo- |
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penne, |
llOCKOJihKY |
np H |
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ero |
Haxo~eHHH ABHJKeaJ |
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HHe |
nOABH)!{HbiX |
ocefr |
BO |
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BHHMaHHe |
He |
npHHHMa- |
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eTC5!, BhlqHCJI5IeTC5I 06biq- |
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HhiMH |
MeTOAaMH KHHeMa- |
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THKH TOqKH (§ 40, 43). Oe- |
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peHOCHOe ycKopeHHe |
Bhi- |
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qnCJI5IeTC5! KaK ycKOpeHHe |
PHc. |
190 |
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TOqKH,HeH3MeHHOCB5!3aH- |
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HOH c nOABH)!{HbiMH ocwvm,
T. e. KaK ycKopeHne ToqKH HeKoToporo TBepAoro TeJia, no cpopMyJiaM, noJiyqeHHbiM AJI5! ycKopeHHH ToqeK TBepAOrO TeJia B § 51, 58, 62, 63, KopnoJincoso ycKopenHe BhrqucJI5IeTC5I no cpopMyJie (g4). MoAyJih
KopnoJincosa ycKopeHH5!, ecJIH yroJI Me)!{AY seKTopaMH w n V0 -r |
o6os- |
naqHTh qepes a, 6yAeT paseH |
|
aKop = 21 w I·IV0 -r Isin a. |
(g6) |
HanpaBJieH BeKTOp aKop TaK )!{e, KaK H BeKTop w X V0 n T. e. |
nep- |
neHAIIKYJI5IpHo rrJiocKocTH, npoXOA5IW.eii qe~s ~KTOphr w H voT• |
B TY |
CTOpoHy, OTKyAa KpaTqafrruee COB\ielll,eHHe W C V0 -r BHAHO npOHCXOA5Ilii,HM npOTHB XOAa qacoBOH CTpeJIKH (p HC. }gO, a).
Hs pnc. 1go, a BHAHO TaK)!{e, qTo nanpaBJieHHe BeKTopa aKOP MO)!{HO onpeAeJIHTh, cnpoeKTHposas BeKTop V0 r Ha nJioCKOCTh IT, nepneHAHKYJI5IpHyiO w, H nosepHys :ny npoeKUHIO O:r:I. Ha goo B CTopoHy nepeHOCHoro Bpalll,eHH5!.
EcJIH OTHOCHTeJihHa5! TpaeKTOpH5! - nJiocKa5! KPHBa5! n nepeMelii,a-
eTC5I BCe BpeM5! B CBOefr nJIOCKOCTH, TO yroJI a=gQo (pHC, }gO, 6) |
H B |
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&TOM cJiyqae |
no |
MOAYJIIO |
|
aKop = 21 w 1·1 Vo-r I· |
(g6') |
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KpoMe Toro, |
KaK |
BHAHO H3 pHc. 1g0, 6, nanpasJieHrre G:ov MO)!{HO B |
|
3TOM CJiyqae |
HaHTH, nosepHyB BeKTOp OTHOCHTeJihHOH CKOpOCTH |
0:,-r |
|
Ha goo B cTopoHy |
nepeHocuoro spaw.eHH5! (T. e. no XOAY HJIH npoTHB |
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qacOBOH CTpeJIKH, |
B SaBHCHMOCTH OT HanpaBJieHH5! Bpalll,eHH5!). |
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Ha pHc. 1g1 AJI5! HJIJIIOCTpaunrr npnBeAeHHhiX npaBHJI noKa3aHo HanpasJierme KopHoJincosa ycKopeHHH wapnKa M, ABH)!{ylii,eroc5! BAO.llh
Tpy6KH AB B cJiyqa5Ix, KOrAa Tpy6Ka spaw.aeTC5! B nJioCKOCTH qepTe)!{a (pnc. 1g1, a) n Kor;~,a ona npn spaw.ennn orrnchiBaeT KoHyc (pnc. 1g1, 6).
l13 cpopMyJib! (g6) BII,.QHO, qTO KOp HOJIHCOBO ycKopeHHe MOLKeT o6palii,aThC5! B HYJib B cJieAYIOI11HX cJJyqafiXl
163
(1}=0, T. e. KOr,I~a nepeHOCHOe ABHLKeHIIe HBJIHeTCH llOCTY· naTeJibHh!M (cpOpMyJia (95)] HJIH eCJIH nepeHOCHaH yrJIOBaH CKOpOCTb B ,D.aHHhiH MOMeHT BpeMeHH o6par.u;aeTcH B HYJih;
a) g B |
OJ |
I aKoo 1
Pnc. |
191 |
||||
2) KOrAa |
V0 TH=0, T. e. KOfAa |
OTHOCHTeJibH3H |
CKOpOCTb B AaHHbiH |
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MOMeHT BpeMeHH |
o6par.u;aeTC5! |
B |
HyJih; |
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3) KOfA3 a=O, HJIH a= 180°, |
T. e. K0fA3 OTHOCHTeJihHOe ABHLKeHHe |
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npOHCXOAHT |
no |
HanpaBJieHHIO, |
napaJIJieJibHOMy |
OCH nepeHOCHOfO |
|
Bpar.u;eHH5!, HJIH eCJIH B )l.3HHbiH MOMeHT BpeMeH!l BeKTOp V0 -r napaJIJieJieH :JTOH OCH.
Pa3,IJ.eJI Tpendi
):(HHAMHKA TOlfKH
fJiasa XV
BBE,L\EHHE B )J.HHAMHI(Y. 3AI(OHbl )J.HHAMHI(H
§ 73. OCHOBHbiE noH~TH~ H OnPE,ll,EJIEHH~
P,UHG.MUKOU Ha3biBaeTCH pas,n;eJI MeXaHIIKII, B KOTOpOM II3y'laeTCSI )J.Bll)KeHIIe MaTepua,'IbHbiX TeJI ITO,!\ ,n;eiicTBIIeM CIIJI.
,UBII2KeHIIe TeJI C 'IHCTOreoMeTpH'leCKOH TOqKH 3peHHH paCCMaTpH-
BaJIOCb B KHHeM:aTITKe. B )l;HHaMHKe, B OTJIH'lHe OT KHHeMaTIIKH, npK II3y'leHIIII)l;BH2KeHIIH TeJI npHHHMaiOT BO BHHMaHIIe KaK ,n;eHCTBYIO~He
Ha HHX CHJibi, TaK H HHepTHOCTb CaMIIX MaTepiiaJibHbiX TeJI. 00H5.!THe 0 eiiJie, KaK 06 OeHOBHOH Mepe MeXaHH'leeKOfO)J.eHCTBHH,
OKa3hiBaeMOfO Ha MaTepiiaJibHOe TeJio, 6hiJIO BBe,n;eHO B CTaTHKe. Ho B eTaTHKe Mbi He KaCaJIIIeb Bonpoea 0 B03M02KHbiX II3MeHeHIIHX ,n;eHCTByioUJ,IIX eiiJI C Te'leHIIeMspeMeHII, a npH perneHHII sa,n;aq C'lHTaJIIIBee CHJlbl noeTOHHHhiMII. Me2KAY Tel\! Ha ABH2KYUJ.eecH TeJio Hap HAY c noeTOHHHwvm CHJiaMII )l;eHCTBYIOT 06hi'IHO CHJibi nepeMeHHbie, MO)l;YJIIT H HanpaBJieHHll KOTOPhiX npH ABH2KeHIIH TeJia nsMeHHIOTCH. Dpii 3TOM nepeMeHHhiMll: MOfYT 6biTh II sa,n;aHHbie (aKTIIBHb!e) CHJlhi *, H peaKUJIH CBH3eH.
KaK noKa3hiBaeT orrhiT, nepeMeHHhre CHJihi MoryT onpe,n;eJieHHbiM oOpasoM :;asiiceTb OT speMetm, noJiomeHHn TeJia II ero CKopoCTH. B qaeTHoeTH, OT BpeMeHH 3aBIIeHT eHJia THfii 3JieKTpOB03a npii rroeTeneHHOM BhiKJ!IO'leHIIHHJIH BKJ!IO'leHHHpeocTaTa HJIII CIIJia, Bbi3biBaiOUJ,a5I KOJie6aHIIH 11YH,n;aMeHTa npii pa6oTe MOTOpa e llJIOXO IJ.eHTpiipOBaHHhiM BaJIOM; OT ITOJ!OllieHHH TeJia 3aBHeHT Hh!OTOHOBa CHJ!a THfOTeHHH IIJIK eiiJia yrrpyroeTII rrpymHHbi; OT eKopoeTII 3aBIIeHT eHJihl COnpOTIIBJieHIIll cpe.nhr (no,n;po6Hee eM. § 76). B saKJIIO'leHIIeOTMeTIIM, 'ITOsee BBe,n;eHHbie B eTaTHKe ITOHHTIIH II IIOJiy'leHHbieTaM pe3yJihTaTbi OTHOCHTeH 1J paBHOH Mepe II K rrepeMeHHbiM CIIJ!aM, TaK KaK YCJIOBHe nOCTOHHCTBa CIIJI HIIf,I\e B CTaTIIKe He HeiiOJ!h30BaJIOeb.
l1HepTHOeTh TeJia npOHBJIHeTCH B TOM, 'ITO OHO eoxpaHHeT eBoe )J.BIIllieHHe IIp!I OTeyTCTBIIII ,n;eileTBYIOW.HX CIIJI, a KOf,I\a Ha Hero Ha'lHHaeT )J.eHeTBOBaTh CHJia, TO CKOpOCTII TO'leKTeJia H3MeHHIOTC5I He MfHG-
* AKmU61iOU 06b!'!HOHa3blBa!OT CHJiy, KOTOpaS!, Ha'laB,u:eiiCTBOBaTb Ha ITQKOHW.eeCS! TeJio, MoJKeT rrpnaecnr ero B ,U:BIDKeHne.
180
BeHHO, a nocTenemw H TeM Me,n;JieHHee, qeVI 6oJibllle rmepTHOCTb ::noro TeJia. KoJinqecTBeHIIOli Mepoli: HHepTHOCTH MaTepnaJibHoro TeJia 5IBJI5IeTC5I G_)n3nqeCKa.H BeJinqnHa, Ha3biBaeMa5I .Maccou TeJia "', B KJiaccrrqecKofi MeXaHHKe MaCCa m paCCMaTpi1BaeTC5I KaK BeJIHqHHa CKaJI5IpHafl, TIOJIO)I{HTe.TibHaf! H TIOCT05IHHa5I )l;Jifl KaJK)l;OfO ,n;aHHOfO TeJia.
KpoMe cyMMapHoii MaCChi ,n;BHJKeHHe TeJia 3aBHCHT ew.e B o6w.eM cJiyqae OT <lJOpMbl TeJia, TQqHee OT B3aHMHOf0 paCTIOJIOJKeHH5I 06pa3y!Oll.I,HX ero qacTHU, T. e. OT pacnpe,n;eJieHHfl Mace B TeJie.
4T06bi npH nepBOHaqaJibHOM H3yqeHHH )l;HHaMHKH OTBJieqbCf! OT
y'leTaG_lopMbi TeJia (pacnpe,n;eJieHHfl Mace), BBO)l.5IT a6cTpaKTHoe noHHTHe o .MamepuaA.bH.Otl motfxe, KaK o TOqKe, o6Jia,n;aiOll.l,eii Maccoii, H Ha'IHH3IOTH3y'IeHHe)l;HHaMHKH C )l;HHaMHKH MaTepnaJibi-IOH ToqKH.
J.b KHHeMaTHKH H3BeCTHO, qTo )l.BHJKeHHe TeJia CJiaraeTC5I B 06W.eM cJiyqae H3 noCTynaTeJibHOro n Bpall.l,aTeJibHOro. DpH pellleHHH KOHKpeTHbiX 3a,n;aq MaTepHaJibHOe TeJIO MOJKHO paCCMaTpHBaTb KaK MaTepnaJibHYIO TO'IKYB TeX CJiyqaf!X, KOr)l.a TIO yCJIOBH5IM 3a,n;aqJ1 )l;OTiyCTHMO He npHHHMaTb BO BHHMaHHe Bpall.l,aTeJibHYIQ lJaCTb )l.BHJKeHH5I TeJia. HanpnMep, MaTepnaJibHOii ToqKoli MOJKHO cqnTaTb nJiaHeTy nprr H3Y- 'IeHHHee )l.BHJKNIH.H BoKpyr CoJIHUa HJIH apTHJIJiepnlicKnii CHap.H,n; npn onpe,n;eJieHHH ,n;aJibHOCTH ero noJieTa n T. n. CooTBeTCTBeHHo noCTynaTeJibHO )l;BHIKYIUeecf! TeJIO MOIKHO BCef)l.a paCCMaTpHBaTb KaK MaTepnaJibHYIO TOqKy c Maccoii, paBHOli Macce scero TeJra. CnpaBe)l.JIHBocTb 3THX yTsepJK)l.eHnii 6y)l.eT o6ocHOBaHa B § 107.
J.J3yqaTb )l;HHaMHKy Mbl HalJHeM C )l;HHaMHKH MaTepnaJibHOll TO'IKI!, TaK KaK eCTeCTBeHHO, qTQ H3yqeHHe )l.BHJKeHHfl O)l.HOH TQqKH )l.OJIJKHO npe)l.IIJeCTBOBaTb H3y'IeHHIO)l.BHJKeHH5I CHCTeMbl TOqeK H, B 'IaCTHOCTH, TBep)l.OfO TeJia.
§ 74. 3AKOHbl )].HHAMHKH. 3A)].A4H )].HHAMHKH
MATEPHAJibHOfl T04KH
BocHoBe ,n;rrHaMnKH JieJKaT 3aKOHhi, yCTaHOBJieHHhle nyTeM o6o6ll.l,e- HH.H pe3yJibTaTOB ueJIOfO p5I,D;a OTibiTOB H Ha6JIIO)J,eHHH, TIOCB5IIIJ.eHHbiX H3y'IeHHIQ )J,BHJKeHHH TeJI, H npOBepeHHbie 06IIIHpHOH 06ll.l,eCTBeHHOnpOH3BO)J,CTBeHHOll npaKTHKOfi 'IeJioseqecTBa. CncTe\1aTH'IeCKH3aKoHbl ,n;nHaMHKH 6hiJIH snepshre H3JioJKeHhi 11. HbiOTOHOM B ero KJiaccnqecKO\I
CO'IHHeHHH«MaTeMaTHqeCKHe HaqaJia HaTypaJibHOH <lJHJIOCOcpHH», H3)J,aHHOM B 1687 r. **. QpopMyJIHpOBaTb 3TH 3aKOHbl MOJKHO CJie,n;yiOIUHM
o6pa30M.
D e p B bi ll 3 a K 0 H (3aKOH HHepUHH): U30AUpOeaH.H.aJ'l Om 8Heut-
H.UX eosaetlcmeuu ;uamepuaAbflaJ'l mottKa COXpaH.f/i!m ceoe COCmOJlfiUe noKOJ'l uAu paeH.oMepH.ozo npf'l.MOAUH.euH.ozo aeuJJCeH.uf'l ao mex nop, noKa npuAoJJCeH.H.ble CUAbl ne sacmaeJim ee us.Menumb amo cocmoJinue.
HHe, COBeplUaeMOe TQqKQll npH OTCYTCTBHH CHJI, Ha3biBaeTCfl )J,BHJKeHHeM
no UH.ept{UU.
* Macca HB.'IHCTCHeme Mepoil: rpaBHTaUHOHHbiX CBOHCTB TCJia (eM. § 76). "'*EcTb npeKpacHhiH pyccKHII rrepeBo,ll. c,l(eJiaHHbiH A. H. KpbiJIOBbiM. CM .. CoU-
paHHC TPYAOB aKa,ll. A. H. KpbiJioBa, T. VII. M.- Jl., 1936.
181
3aKOH IIHepUIIII OTpa>KaeT O)l.HO II3 OCHOBHbiX CBOHCTB MaTepim - npe6hlBaTb Heii3MeHHO B )l.BmKeHHH. Ba>KHO OTMeTIITb, qro pa3BHTHe ,lf[IHaMIIKII KaK HayKH CTaJIO B03MO>KHbiM JIIIlllb TIOCJie TOfO, KaK faJIIIJieeM 6biJI oTKpbiT 3TOT 3aKoH (1638 r.) II TeM caMhiM onposepmyra rocno)l.CTBOBaBlllafl co spe:v~en ApiiCToTeJifl roqKa 3peHII5I o TOM, 'lTO ,!J.BII>KeHIIe TeJia MO>KeT npoiiCXO)l.IITb TOJibKO nO)!. )l.eHCTBIIeM CIIJlbl.
Cy!UeCTBeHHb!M 5IBJIHeTC51 Bonpoc 0 TOM, no OTHOllleHHIO K KaKOH CIICTeMe oTcqera cnpase)I.JIIIB 3aKOH IIHepUIIII. HbiOTOH npe,!l.nOJiaraJI, qro cymeCTByeT HeKoe HenO)l.BII>KHOe (a6COJIIOTHOe) npOCTpaHCTBO, nO OTHOllleHIIIO K KOTOpoMy 3TOT 3aKOH BblnOJIHHeTCH. Ho no cospeMeHHhiM B033peHII5IM npOCTpaHCTBO3TO <lJOpMa cymecTBOBaHII51 MaTepiiii, II KaKOfO-TO a6cOJIIQTHOf0 npOCTpaHCTBa, CBOHCTBa KOTOpOrO He 3aBIIC5IT OT )l.BII>KY!Ueiic51 B HeM MaTepiiH, He cy!UeCTByeT. Me>K)l.Y TeM, noCKOJibKY 3aKOH IIMeeT OnbiTHOe npOIICXO>K)l.eHIIe (e!Ue faJIIIJieii yKa3aJI, qTo K 3TOMY 3aKOHY MO>KHO npiiHTII, paccMaTp1IBa5I )l.BJI>KeHIIe lllapiiKa TI(} HaKJIOHHOH nJIOCKOCTII CO BCe y6hiBaiOIUIIM yrJIOM HaKJIOHa), )!;OJI>KHbl CyJUeCTBOBaTb CIICTeMbi OTCqeTa, B KOTOpbiX C TOll IIJIII IIHOH CTeneHb!O np1I6JIII>KeHII51 )l.aHHhiH saKOH 6y)l.eT BbiTIOJIHHTbCH. B CBH31I c 3TIIM B MexaHIIKe, nepeXO)l.H, KaK o6hrqHo, K nayqHoil a6crpaKUIIII, BBO)l.5IT TIOH5ITIIe 0 CIICTeMe OTcqeTa, B KOTOpOii cnpaBe,!I.JIIIB 3aKOH IIHepU,IIII, nocryJIIIPYIOT ee cymecTBoBaHIIe II na3biBaiOT unepl{UaAbHoii cucmeMoii
omcttema.
Mo>KHO JIII )l.aHHYIO peaJihHYIO CIICTeMy orcqeTa npii pellleHIIII rex IIJIH IIHbiX 3a)l,aq MeXaHIIKII paCCMaTpiiBaTb KaK IIHepuHaJibHYIO, ycTaHaBJIIIBaeTC51 nyTeM nposepKII TOfO, B KaKOU Mepe pe3yJibTaThi, noJiyqeHHbie B npe,ll,nOJIO>KeHIIII, qTo 3Ta CIICTeMa 5IBJI51eTC51 IIHepu,IIaJibHOH, TIO)l.TBep>K- )I.aiOTC5I OTibiTOM. flo )l.aHHbiM OnbiTa )l,Jl51 HallleiiCOJIHeqHOH CIICTeMbl IIHepUIIaJibHOH C BbiCOKOH CTeneHb!O TOqHOCTII MO>KHO cqHTaTb CIICTeMy OTcqeTa, HaqaJIO KOTOpOH HaXO,li,IITC51 B UeHTpe COJIHU,a, a OCII HanpaBJieHbl Ha TaK Ha3biBaeMbie HeTIO,li,BII>KHble 3Be3)1.bl. flpii pelllelfiiii 60JiblUIIHCTBa TeXHIIqeCKIIX 3a)l,aq IIHepu,IIaJlbHOH, C ,li,OCTaTOqHOll )I.JI5I npaKTIIKII ToqHOCTb!O, MO>KHO cqJITaTb CIICTeMy OTCqera, >KeCTKO CB513aHHYIO C 3eMJieii. Cnpase)l.JIIIBOCTb 3Toro yrsep>K,ll,eHIIH 6y)l.eT o6ocHOBaHa B § 92.
B Top o ii 3 a K o H (ocHoBHOH 3aKOH )l.IIHaMIIKII) ycraHaBJIIIBaeT, KaK II3MeH5leTC51 CKOpOCTb TOqKII npii )l,eHCTBIIII Ha nee KaKOH-HII6y,ll,h
CIIJihi, a IIMeHHO: npouseeaenue MaGCbl MatnepUaAbHOU mottKU na ycKopenue, KOtnOpOe Ofia no!lyttaetn no() OeUctneUeM aaHHOU CU!lbl, paeHO no MOayAIO amou cu!le, a nanpaeAenue ycKopenufl coenaiJaem c nanpaeAenueM CU/lbl.
MaTeMaTIIqecKII 3TOT saKou Bbrpa>KaeTcH seKTOpHbiM pasencrsovr
ma=F. |
(1) |
flpii 3TOM Me>KAY MO)l.YJIHMH ycKopeHH51 II CIIJibi HMeeT MeCTO 3aBHCIIMOCTb
ma=F. |
(1') |
Bropoil saKOH )l.IIHaMIIKH, KaK II nepsbrfr, HMeer Mecro TOJibKo no OTHOllleHIIIO K IIHepu,HaJibHOH CIICTeMe OTcqeTa. lb 3TOf0 3aKOHa Henocpe,!I.CTBeHlfO BII,!I.HO, qro Mepoii IIHepTHOCTII MaTepiiaJibHOH TOqKII 51BJI51•
182
eTCH ee Macca, TIOCKOJibKY npH )J,eHCTBHH )l,annOH CHJihl TOqKa, Macca KOTOpOH OOJibiiie, T. e. 6oJiee nnepTnaf!, TIOJiyqnT Menbmee ycKopenne H Hao6opoT.
ECJIH na TOqKy )J,eHCTByeT O)l,nOBpeMeHnO neCKOJibKO CHJI, TO OnH, KaK 3TO CJie.I{yeT H3 3aKona napaJIJieJiorpaMMa CHJI, 6y)l.yT 3KBHBaJienTnbi
O)l.HOH cnJie, T. e. paBHO)l.eiicTBYIOIII.eli. R, pasnoii reoMeTpnqecKoii cyMMe )l.aHHbiX CHJI. YpasHeHne, BhlpaJKaiOIII.ee ocHOBHOii 3aKon )l.HnaMHKH, npHHHMaeT B 3TOM CJiyqae BH)l,
(2)
3TOT JKe pe3yJibTaT MOJKnO TIOJiyqHTb, HCTIOJib3Y51 BMeCTO 3aKona
napaJIJieJIOrpaMMa 3aKOH. H.e3G8UCU!r!OCmU aet1Cm8Uft CU;2, COfJiaCHO KOTO-
poMy npn O)l,HOBpeMeHHOM )l.eiicTBHH Ha TOqJ{y HeCKOJibKHX CHJI KaJK)l,a51 H3 nHX C006lll,aeT TOqKe TaKOe IKe ycKopenHe, KaKOe Ona C006lll,HJia 6bi,
.I{eHCTBYfl O.I{na.
T p e T n ii 3 a K o n (3aKoH pasencTsa .I{eiicTBHfl n npoTHBo)l.eficr-
BHH) ycTanaBJIHBaeT xapaKTep MexannqecKoro B3auMo)l.eiicTBH51 MeJK)l.Y MaTepnaJibHbiMH TeJiaMH. )lJif! )l.Byx MaTepnaJibHhlX ToqeK on rJiaCnT:
aee MamepuaAbflbte motiKU aet1cmey10m apyz H.a apyza CCUAGMU, pa8H.bl.MU no MoOYAIO u H.anpaeAeH.H.blMU BOOAb np!tMOU, coeaUH.ft10!1.{et1amu mottKU, 8 npomueonoAOJICH.bte cmopoH.bt.
3THM 3aKonoM Mbi yJKe nOJib30BaJIHCb B cTaTnKe. On nrpaeT 6oJibiiiYIO pOJib B ,I{HnaMHKe CHCTeMbi MaTepnaJibHbiX TOqeK, KaK ycTanaBJIHBaiCIII.HH 3aBHCHMOCTb MeJK)l,y )l,eHCTByiOill,HMH na 3TH TOqKH BHyTpeHniiMH cn.'IaMn.
flpn B3aHMO)J,eHCTBHH )J,ByX CB060,I{HbiX MaTepnaJibHhlX ToqeK, OHH,
COfJiaCnO TpeTbeMy H BTOpoMy 3aKOHaM .I{HnaMHKH, 6y)l.yT )l.BHfaTbC51 C
ycrmpeHH5lMH, |
o6paTnO npOnOpii,HOHaJibnbiMH |
HX MaCCaM. |
3 a )1, a q H |
)1, H H a M H K H • )lJif! CB06o,I{nOH MaTepHaJibnOH TOqKH |
|
3a.I{aqaMH )l,HnaMHKH 51BJ151IOTC5l CJie)l.yiOlll,He: 1) |
3Ha51 3aKOn )l,BHJKeHHfl |
|
roqKn, onpe)l.eJIHTb .I{eiicTBYIOIII.YIO na nee cnJiy (nepeaJt saaatta auH.a- MUKu); 2) 3na51 )l,eHCTBYIOlll,He Ha TO•IKy CHJibl, onpe)l.eJIHTb 3aKOH )l,BH-
JKenH5l roqKn ( emopa!t, HJIH ocH.oet-taR, saaatta auH.aMuKu).
)lJIH HeCB060)l,nOH MaTepnaJibHOH TOqKH, T. e. TOqKH, Ha KOTOpyro HaJioJKena CB513h, BbiHYJK)l.aiOlll,a5I ee )l.BHraTbCfl no 3a)l.aHHOH nosepxHOCTH HJIH KpHBOH, nepBaf! 3a)l,aqa ;zr;nnaMHKH 06hlqno COCTOHT B TOM, qro6bi, 3na51 .I{BHJKenne TOqKH II )l,eHCTBYIOIII.He na nee aKTHBnbre CHJibi, onpe.I{eJIHTb peaKUHIO CB5l3H. BTopaH (ocnosna5l) 3a)l.aqa )l,HnaMHKH npu HeCB060.I{nOM )l,BHJKenHH pacna)l,aeTCH na )],Be H COCTOHT B TOM, qT06bi, 3Ha5l ,I{eikTBYIOIII.He na TOqKy aKTHBnbre CHJibi, Onpe.I{eJIHTb: a) 3aKOH )l,BHJKenn5l TOqKH, 6) peaKII,HIO naJIOJKenHOH CB5l3H.
§ 75. CHCTEMbl E)l.HHHU
nJI51 H3MepenHH BCeX MexanHqecKHX BeJinqnn OKa3biBaeTC5l )l,OCTaToqnbiM BBeCTH He3aBHCHMble )l.pyr OT Apyra e)l,HnHI.J.bi H3MepenH51 KaKHX-Hn6y.I{b Tpex BeJinqnH. )lByM5I H3 nHX npHnHTO cqnTaTb e)l,HHHUbl )l.JIHHhi n speMeHn. B KaqeCTse TpeTbeii OKa3biBaeTC5l HaH6oJiee YA06HbiM Bbr6paTb e)l.nnuuy H3MepeHI15l nnn MaCChi, HJIH CHJihl. TaK KaK
te3
9TH BeJIHqHHhi CB5I3aHhl paBeHCTBOM (1), TO npOH3BOJlhHO e,li.HHHL(y H3Me-
peHHfl KaJK,li.Oll H3 HHX Bbi6paTh HeJih3f!. 0rCIQ,ll.a BbiTeKaeT B03MOJK•
HOCTh BBe,ll.eHH5I B MeXaHHKe ,li.ByX npHHl(HTIHaJihHO OTJHl'IHhiX,ll.pyr O'f
,11;pyra CHCTeM |
e,li.HI!Hl(. |
|||
n e p |
B hi H |
T H n |
c H c T e M |
e )1. H H H l(. B 3THX CllCTeMaX 3a |
OCHOBHble |
npmiHMaiOTC5l |
e)l.IIHHl(hi |
,li.JIHHh!, BpeMeHH H MaCChi, a CHJia |
|
H3MepHeTC51 npOH3BO,li.HOH e,li.HHffl(eH.
K TaKHM CHCTe'viaM OTHOCHTCH MeJK)l.ynapO,li.Haf! cncTeMa e,li.HHHL(
H3MepeHH51 cpH3HqecKHX BeJIHqHH (ClJ), B KOTOpOH OCHOBHhiMH e,li.HHHIJ,aMH H3MepeH1-l5I MeXaHHqecKHX BeJIHqHH 5IBJI5IIOTC51 MeTp (M), KHliOrpaMM Macchi (Kr) H ceKyH.ll.a (c). E)l.HHHueil JKe H3MepeHHH cHJihi 5IBJif!eTC51
rrpOH3BO,li.Haf! e)l.HHHua - 1 HhiOTOH |
(H); 1 H - 3TO |
CHJia, coo6IIJ,aiO- |
maR Macce B 1 I{f ycKopenHe 1 Mlc 2 |
(1H=1 Kr·Mic2). |
0 TOM, qTo co6oii |
npe,ll.craBJIHIOT 1 M, 1 Kr H 1 c, H3BeCTHO H3 Kypca cpH3HKH. Me:tK.li.Y- napO,li.HaH cHCTeMa e,li.HHHIJ. (Cl1) BBe,ll.eHa B CCCP KaK npe)l.nOqTHTeJih-
Haf! C 1961 f. H B ,ll.aHHOM |
Kypce |
Mhl TIOJih3yeMC5l eiO. |
B T o p o il T H n c H |
c T e M |
e .ll. H H H u. B 3THX CHCTeMax 3a |
OCHOBHhie npHHHMalOTCH e,li.HHHUhi ,li.JIHHhi, BpeMeHH H CifJihi, a MaCCa
ll3MepHeTC5I npOH3BO,li.HOH e,li.HHHUeH.
K TaKHM CHCTeMaM OTHOCHTCH HMeBrnaH 6oJihUIOe pacrrpocrpaneniie B TeXnHKe CHCTeMa MKfCC, B KoTopoii: OCHOBHbiMH e,li.HnrruaMH HBJIHIOTCH MeTp (M), KHJIOrpaMM CHJihi (Kf) H CeKyH,ll.a (c). E,li.HHHUeH H3MepeHHH MaCChi B 3TOH CHCTeMe oy,ll.eT 1 Kf •C 2fM, T. e. Macca, KOTOpOH CHJia B } Kf
coo6maeT ycKopenHe 1 Mlc 2 • |
||
CoOTnornenHe MeJKAY |
e,li.HHMUaMH cnJihi B cncTeMax Cl1 n MKfCC |
|
Tarmso: 1 Kf=9,81 H |
HJIH |
1 H=0,102 Kf. |
B 3aKJIIOqenHe OTMeTHM, |
qro neo6xO,li.HMO pa3JIHqaTh nonf!THH pC13- |
|
Mept-wcmb BeJIHqHHhi H eaunuup ee U3Mepe1iUJl. Pa3MepHOCTh onpe,ll.eJIHeTCH TOJlhKO BH,li.OM ypaBHeHHH, Bhipa:tKaiOIIJ,ero 3HaqenHe ,ll.aHHOH BeJIHqlfHhi, a e)l.HHHL(a l13MepeHH51 3aBMCHT eiiJ,e OT BbiOOpa OCHOBHbiX e,li.HHHU. HanpHMep, ecJIH, KaK 3TO npHHHTO, o6o3HatJ:aTh pa3MepHOCTh ,li.JIHHLI, speMenu H MaCchi cooTBeTCTBeHHo CHMBoJiaMH L, T n M, TO pa3MepHOCTh cKopocnr LIT, a e,li.HHHueii H3MepeHHH MO:tKeT OhiTh 1 Mlc, 1 KMIII H T. ,ll..
§ 76. OCHOBHblE BH)l.bl CHJl.
DpH perneHHH 3a,ll.aq ,li.HHaMHKH Mbl oy,ll.eM B OCHOBHOM pacCMaTpH-
BaTh CJie,ll.yiOIIJ.He TIOCTOf!HHbie HJIH nepeMeHHbie CHJibi (3aKOHhl H3MeHe· HHH nepeMeHHbiX CHJI, KaK npaBHJIO, ycTaHaBJIHBalOTCfl OTihiTHhlM nyTeM).
C H Jl a T H :tK e C T H. |
3'foTIOCT05IHHa5I |
CHJia p, ,ll.eHCTBYIOIIJ.aH Ha |
|
JII06oe TeJio, naXO,li.HIIJ,eecf! |
s6JIH3H |
3eMHOH |
rrosepxnocTH (rro,ll.po6nee |
eM. § 92). Mo,ll.yJih CHJihi TH:tKecTrr |
pasen secy TeJia. |
||
OnhiTOM ycranosneHo, qTo no,ll. )J,eHCTBHeM CHJibi P Jno6oe TeJio np11 CB060,1J;HOM IIa,ll.eHim na 3eMJilO (c neoOJibiiiOH BhiCOThi ll B 6e3B03.ll.Yl11HOM npocrpaHcrse) HMeer o,u;no H To :tKe ycKopenne g, na3hiBaeMoe ycrwpe-
184