(формат)Тарг
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5. ECJIH }l.aHHaH CHCTeMa CHJI 3KBHBaJieHTHa O)l;HOH CHJie, TO ;na CHJia Ha3biBaeTcH paeHooet1cmey10wpl .n;armoil cncTeMhi cnJI.
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SblBaeTcH ypG13HOBewuea10wpl CIIJIOH.
6. CnJibi, .n;eii:CTBYIOill.IIe Ha .n;aHHoe TeJio (HJIII cncTeMy TeJI), MO*HO pa3)l;eJIHTb Ha BHeUIHHe II BHyTpeHHHe. 8HeUJHUMU Ha3biBa!OTCH CHJibi, KOTOpbie ,n;effCTBYIOT Ha 3TO TeJIO (HJIH Ha TeJia CHCTeMbi) CO CTOpOHbl .n.pyfHX TeJI, a BHympeHHUMU - CHJihl, C KOTOpbiMH qaCTH ,naHHOfO TeJia (HJIH TeJia }l.aHHOH CHCTeMbi) .n;eHCTBYIOT .n;pyr Ha .n.pyra.
7. CHJia, rrpnJiom:eHHaH K TeJiy B KaKoii-Hn6y.n.h o.n.Hoil era TO'lKe, ua3hlsaeTCH cocpeoomotteHFtoii. CIIJihi, .n.eiicTBYIOill.He Ha nee TO'IKII.n;aHHoro 06beMa llJIH i'l,aHHOHqaCTll IIOBepXHOCTH TeJia, Ha3biBaiOTCH pacnpe-
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B qacTHOCTH, paCCMaTpHBaeMaH B MeXaHHKe CHJia TSOKecTII, ,!l.eHCTnyrom;aH Ha .n;aHHoe TBep.n;oe TeJio, npe.n;cTaBJIHtT co6ofi paBHO,l(eficTBYIDill.YIO cii.rr TsuKeCTH, .n;eiicTBYIOill.HX Ha ero traCTHUhl. JliiHHH .n;eficTBHH
STOll paBHO,!I.eHCTBYIOill.efl npoXO)l;HT qepe3 TO'!Ky,Ha3hiBaeMyiO lfeFtmpo.M
*. 2 основные задачи, которые решает статика
3ai'l,a'laMHCTaTHKH HBJISIIOTCH: 1) npeo6pa3oBaHIIe CHCTeM CHJI, }IeHCTBytall.l,llX Ha TBepi'l,OeTeJIO, B CllCTeMbl liM 3KBHBaJieHTHble, B '!aCTHQCTH npHBei'l,eHHell.aHHOH CHCTeMbi CHJI K npoCTeHIIIeMy BII,ny; 2) onpe.n;e- JieHIIe YCJIO~HH paBHOBeCIISI CHCTeM CHJI, i'l,eHCTBYIOIIJ,HX Ha TBep.n.oe TeJIO.
PeiiiaTb 3ai'l,a'!HCTaTHKH MOJKHO HJIH rryTeM COOTBeTCTBYIOIIJ,HX reo-
MeTpHtieCKHX nocTpoeHIIH (reoMeTpHtieCKHH II rpaqm'leCKHH MeTO)l;hi), HJIH c noMOII~biO '!HCJieHHhiXpac'leTOB(aHaJIHTH'IeCKIIHMeTOi'I,).B Kypce
6y,!l.eT r JiaBHbiM: o6pa30M npHMeHSITbCSI aHaJIHTll'leCKHH MeTOi'l,, Oi'l,HaKO CJiei'l,yeTllMeTb B Blli'l.Y,'ITOHarJISii'l,HbiereoMeTpiiiieCKHe fiOCTpOeHIISI llf-
paiOT npn pewemm 3a.n;aq MexaHIIKII qpe3Bhl'laHHosaJKHYIO poJib.
Чтобы это осуществить - используют ряд положений
§ 2. HCXO,!J;HbiE OOJIO)I(EHH51 CTATHI(H ОНИ ОПРЕДЕЛЯЮТСЯ
НЕКОТОРЫМИ ОСНОВНЫМИ АКСИОМАМИ
npu ll3JIOa<eHHH CTaTHKH MOJKHO lli'l,Tlli'l.BYMH nyTHMH: 1) HCXOi'l,HTb 03 ypaBHeliHH, KOTOpbie noJiytiaiOTCSI B i'l,IIHaMHKeKaK CJie}I.CTBHH OCHOBHhiX 3aKOHOB MeXaHHKH (CM. § 120); 2) H3JiaraTh CTaTHKY He3aBHCHMO OT )J.HHaMHKll HCXO,l(H ll3 HeKOTOpbiX 06ll.I,HX 3aKOHOB MexaHHKll II llOJIOJKe-
* Bonpoc 00 onpell,eJieHHI! UeHTpOB TSilKeCTII TeJI oy.n.er p.accMotpeH B rJI. VIII. Ope.n.BaputeJihHO aaMeTHM, 'ITOec.1u o.n.nopoJIHOe TeJio HMeeT ueHTP cHMMeTprrH (rrpl!- uoyroJihffhlfi 6pyc, U!!JII!F!;:(p, map II T, IT.), TO ueHTp TSIJKeCTII TaKOrO TeJia llaXO,ll.IITCS! B ero IJ.eHTpe CHMMeTpiiR.
11
HHH, H33hiBaeMhiX 3KCHOM3MH HJIH npiiHU.Hna;..m CT3THKH, XOT51 nocyIUeCTBY OHH 5IBJI5IIOTC51 He He3aBHCllMhiMll aKCllOM3\1ll, a cJie,n:CTBH51Mif TeX 2Ke OCHOBHhiX 33KOHOB MeXaHHKll (C~I. § 120). B yqe6Hh!X KypcaX, Kar{ n B .n.aHHOM, o6hiiiHO n,n:yT BTopuM rryTeM, TaK KaK no p5I,n:y rrpiitrHH OK33h!BaeTC51 He06XO.IJ:IIMhiM H3llllH3Th H3ytieHHe MeXaHHKll CO CT3TllKH, T. e • .no Taro, KaK 6y,n:eT H3JI02KeHa JI.HHaMHKa. DoJio2KeHH51 (IIJIJI aKciioMhi), H3 KoTophix rrpn 3ToM ncxo,n:HT, M02KHO ccpopMyJinposaTb cJie.n.yiOIUHM o6pa30M.
1. Ec.llu Ha ceo6oaHoe a6CO.!l10mHO meepaoe me.llo aeiicm6ytom aee CU.Ilbl, mo meAo Mo:JICem HaxoaumbCflB paeHo6ecuu moziJa u moAbKO mo2aa, K02da smu cu.llbt paeHbl no .M.oayAto (F1=F 2) u HanpaeAeHbt 600.Ilb oaHou npJlMOtl e npomueonoAO'JICHbte cmopOHbt (pnc. 2).
2. /l.eucmeue aaHHou cucmeMbt cuA Ha a6coAtomHo m6epaoe mMO He U3olteHJwmcR, ecAu K Heu npu6aeumb uAu om Hee omHHmb ypaeHoeemeHnyto cucmeAty cuA.
Pnc. 2 |
Puc. 3 |
Hnbi\!H CJIOKI~H 3To 03HatraeT, tiTO .nne cni::Te:Mbi CHJI, OTJIHIImomue-
CR Ha ypaBHOBeUieHHYlO CHCTe"'IY, 3 KBHB3.1eHTHbl .n.pyr ,n:pyry.
C JI e .IJ: C T B H e: aeiicmeue CU./lbl Ha a6C0/110mHO meepiJoe me.llo He U3MeHUmCJl, eC/IU nepeHecmu moliKY npU.IlOJICeHUJl CU.Ilbt 600./lb ee .llUHUU iJetl-
т.е. для абсолютно твер-го тела действующая сила является
Cm6IUl 8 ;uo6yto opyclj10 moliKlj meAa.вектором скользящим
B caM oM ,n:eJie, rrycTh Ha TBep,n:oe TeJio ,n:efiCTnyeT rrpnJio2KeHHa51 B TO'l:- Ke A CHJia F (pnc. 3). Bo3hMeM Ha JIHHHH ,n:elicTBHH 3TOM CHJibi npous-
BOJihHYIO TOtiKY B u npHJI02KHM B Heii i'l,BeypaBHoBerneHHhre CHJihi F1 n
F2, TaKne, tiTO F1 F nF2 =-F. OT 3Toro,n:eiicTBne CHJihi F Ha TeJio He U3MeHHTCfl. Ho CHJihi F n F 2 TaK2Ke o6pa3yiOT ypanHoserneHHyiO cncTe-
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Ha 30COJIIOTHO TBep,n:oe TeJIO. Ilpu llH2KeHepHhiX paC'leTaX HM M02KHO llOJib30B3TbCH JIHUJb TOr,ll,a, Kor,n:a onpei'l,eJIHIOTCfl yCJIOBllH paBHOBeCIIH
Toil HJIH nnoii KOHCTPYKU.HH II He paccMaTpHBaiOTCH B03HHKUJIIe B ee 'laCTHX BHyTpeHHHe ycHJIHH.
* 0T6po111eHHble H.IIH nepeHeCeHHble Cll•1hl oy)leM Ha pHCYIIKaX nepeqepKHBa'fb.
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HarrpnMep, nso6pameHHhiH Ha pnc. 4, a cTep}f(eHh AB 6yp;er HaxoAHTbCH B paBHOsecuu, ecJin F1 =F 2· ITpn rrepeHoce TO'leKrrpnJiomeHHH OOellX CHJ! B KaKyio-HH6y,ll,b TO'IKYC CTepmHH (puc. 4, 6) HJ!ll npn nepe-
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cmpoeHHOcO Ha amux cu.llax, KaK rta cmopoHax.
PHc. 5 |
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BeKTop R, paBHhiH .n.rraroHaJin napaJIJieJiorpaMMa, rrocTpoeHHoro na BeKTOpax F1 n f 2 (pnc. 5), Ha3hiBaeTCH zeoMemputieCKOu cyMAwu eeKmopoe F1 n F 2: Величина этой силыглавный вектор
R=F1 +F2 • или аналитически
CIIJia Q He MmKeT 3aMeHIITb .n:eiicTBHe cnJI F1 u F 2 Ha )J.aHHoe reJio, r.n:e 6bl OHa HH 6hiJia npiiJI02KeHa. B ~aJibHeihneM 6y~eT e~e cTporo ~oKasa· HO (§ 29, 3a~aqa 38), liTO 3TH )U3e CllJ!bl He IIMeiOT paBHO~eHCTByJOIUefl:.
3aKOH paBeHCTBa ~eHCTBll51 ll npOTllBO,ZJ.efl:- C T B II 51: npu 6CRKOM aeucmeuu OOHOcO Mamepua.llbiWcO me.lla f{Q opyeoe wteem Mecmo max:oe CI/Ce rtuc.lleHHO, HO npomueono.lloCIICHae no Hanpae.lleHU/0 npomueooeucmeue.
3TOT 3aKOH 51BJI51eTC51 O,'I.HHM ll3 OCHOBHbiX 3aKOHOB MeXaHHKII. }h Hero cJie,'l.yeT,'lTOec.11rr TeJio A .n.eiicTByeT Ha TeJio B c HeKoTopoif ciinoii
F, To O,'I.HoBpeM:eHHOTeJio B ,'l.eifcTByeTHa TeJio A c TaKoii 2Ke no MO,'I.yJIJO H HanpaBJieHIIOH B,'I.OJibTOll 2Ke IIp51MOH, HO B npOTHBOIIOJ!OlKHYIO CTOpoHY CIIJIOH F' =-F (puc. 7). 3aMeTHM, liTO CHJibi F n F', KaK rrpiiJIO"iKeH• Hble K pa3HbiM TeJiaM, He o6pa3yiOT ypaBHOBerneHHYIO CIICTeMy CIIJ!.
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P11c. 7
§ 3. CBSI3H H HX PEAI(l(HH
I1o onpe,n:eJieHHIO, TeJio, KOTopoe Mom:eT cosepruaTh Hs .n:annoro no-
.noJKeHuH JII06ble nepeMell{eHHfl B IIpocrpaHCTBO, Ha3biBaeTC51 ceo6001iblM
(nanpHMep, sos.n:yruHblii map B sos.n:yxe). TeJio, IIepeMeiUeHHHM KOToporo B IIpOCTpaHCTBe npeiiHTCTBYIOT K8Kife-HH6y,n:h ,n:pyme, CKpenJieHHhie HJIH COIIpHK3C310ll.I,HeC5I C HUM, TeJia, Ha3biBaeTC51 HeCB0600Hbi.M.
Bee mo, ttmo ocpartuttusaem nepe.MellJ!!HUfl oartHOC!O me.lla 8 npocmpartcmse, Ha3b«Jatom CBfl3bto. B ,n:aJihHeiirneM 6y,n:eM paccMaTpHBaTh CB513H, peaJinsyeMble KaKHMH-HH6y.r.J;b TeJiaMll, ll H33hiB3Tb CB513HMH C3MJf 3TH TeJia.
DpHMepaMH necso6o)l.HbiX TeJI HBJI5IIOTC5I rpys, Jiem:aiUHH na cTo.ne, ,n:sepb, IIO.D;BerueHHafl Ha IIeTJIHX, ll T. II. CBH35IMH B 3TllX CJIY'I35IX6y.n;yT:
.!l:JIH rpysa - IIJIOCKOCTb CToJia, He ,n:aiOIUafl rpysy nepeMeiUaThCfl no BepTHKaJIH BHH3; .!l:Jifl ,n:Beprr - IIeTJIH, He ,n:aiOIUlle ,n:Bepu OTOHTH OT KOCHKa. •
TeJio, crpeMHCb IIO,n: ,n:eiicTsHeM npHJio)KeHHbiX CHJI ocYIUecTBHTh nepeMeiUeHne, KOTOpOMY npeii5ITCTBYeT CB513b, 6y,n:eT ,n:eifcTBOB3Tb Ha Hee c HeKoTopoii crrJioii, Ha3hiBaeMoii cu.lloii OaB.IlettuH rta CBH3b. O.n;nospeMeHHO IIO 3aKOHy 0 paBeHCTBe ,n:eiiCTBHH I1 IIpOTHBO,n:eHCTBllH CBH3b 6y,n;eT )l;eHCTBOBaTb Ha TeJIO C TaKOH JKe IIO MO.!l:YJIIO, HO IIpoTHBOIIOJIO)KHO HanpaBJieHHOH CHJIOH. Cu.lla, c KOmopou oaHHafl CBH3b oeucmeyem fia mello, npenHmcmeyH me.w, u.llu UHbtM eco nepeMeU{ertuHM, Ha3bl6aemcH cu.llou pellKt{UU (npomUBOiJeucmBUH) CBH3U HJIH IIpOCTO peaiCifUeU C8Jl3U.
3naqeHne peaKUHH CBH3ll 33BI1CIIT OT ,n:pyrnx ,n:eHCTBYIOIUllX CHJI H
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I1paBHJibHoe onpe.n;eJieHHe nanpasJieHHii peaKU.Hii cngseii HrpaeT npn pemeHHH sa.n;alf MexaHHKH otreHb BaLKHYIO poJih. PaccMOTprrM no-
15
BaThCH O,ll,HO OTHOCHTeJibHO ,n.pyroro BOKpyr 1.\eHTpa rnapHHpa. f1pHMefOM CJIY1KHT rrpHKpenJieHHe q>GTOannapaTa K IIITaTHBy C IIOMOlll.h!O mapOBOH IIHThl. ECJIH TeJIO npHKperiJieHo C IIOMOlll.h!O TaKOfO ruapHHpa K Heno,n.BHJKHoii onope (pHc. 11, a), TO TO'!Ka A TeJia, cosrra,n.aiOman C ueHTpOM ruapHHpa, He MOJKeT rrpH 3TOM COBepiiiHTh HIIKaKOfO rrepe-
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rnapHnpaMH, HBJIHeTcH cBH3biO (pHc. 12, a). Tor.n.a Ha cTep1KeHb 6yll.YT lJ,elicTBOBaTb TOJibKO ll,Be CIIJibi, rrpHJIOJKeHHbie B TO'lKaxA II B; rrpii paBHOBeCIIH 3TH CHJibl ,l],OJIJKHbi 6biTb HanpaBJieHbi B,ll,OJlb Oll,HOJI npHMOii, T. e. B,ll,OJib AB (eM. pHc. 4, a, e). Ho TOrlJ,a corJiaCHO saKOHY 0 .n.eikTBIIH II rrpOTHBOll,eHCTBIIll CTep1KeHh 6ylJ,eT lJ,eikTBOBaTb Ha TeJIO
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