《动力学》课后答案

1、l 32229所以质点的加速度为：a a a ,tnyvvaavannvyv2nxocv2avnys L v s l x2220Fs v， 2xx0sv（x vs02Axxx3AN mx Fmy F Fxlcos2x,y 00 x lx lx22223l02xx3（a）B22xAxRRxR 22222222223222x R x24x224aAA22 2ABNFARNmgmx F2422xx2,m R x24225F,N2222v v vaeraealvcos v e2当 45 杆上C v a0l2lCv v va1e1a2e2r2M v v a2a1e1r1e2r2xv v v 000030

2、02122M AaerOAOC1v v000，aearvR1，eaar1arCtea a a a，1 r321 vaAAMM；evaaerv v v，MAaerevA11ana a a a a aerCa Cra00eC163m/s ，ab ，a 2 v 8m/s2 22aCra rad/sa23，1lBMOvaArcos600ervv tanv 2r 2 ，v4r0eaer0BrM22r22O0a，aAa 2 v 8rr2a 14ravaveA绕OOeraer v v vreav v , v R ,，AaBeBARv v vm/sBRrABAOmrFOOrvvOMmgFv vOeaOrrMM

3、ataaervva a aecoscosaaera 0ea a arv2v2a。am(a a ) F F mgm(a sin a cos ) F cosm2FOaetMFerema ml mgsin F costreF ma ma,eed dl d gsind acos dl2 gcos asin c2c arOOreCdvma mrF cosdtreF mR2，rredvmv cosmRcosr2dRrvRr2r1R c222R R v 0c,OOOx 2MFyyFeMxxeePygeedydx，ytanPFP将Fy2ge1422xg243P1c2Fg fF fFN p m v m btx2

4、dpm b F fF m xdt2N12f 2 m 12m bf2 m 12p m v) mv12rx2r1212m b m F fF m xdt212N12m b2m m12p mv mv mv m v)rv1 11xp mx m l cos )x1F211211 mvv vaymrr2rdv 02dtFN Nrm m qtF0rfv q(v)x0r f q cqr0f c )qr0qvvr0fm0 图azJm lzveguMorollL 12rv v v。aerL L(mv) L(mv) L(mv)22a2e2rm Rcos ) sin)2 222e22rrr2zL Jm Rcos ) s

5、in) m(l Rcos cos mRsin u2 2 2 R 2lRcos R)mu2222 J m(l R )22LJOOldLOxO2PdtOlll 2Oll r x r x 2 grx2 2Oll令x 2x 02lJOltt12xt x 0c c020120 xrsin 2 r 2 2xlll0yyllllxPylF2 rx cht2，F P (2a 2 xch(2t)2 2oyll0112222Av CAC若v 是 ACrcA11122222CC， W，d m m dv dt22CCAAAdvmgaAA2，CCAm R 0A00vv e11 11T m v mv m v m vsin

6、) cos )22222aerr设0VmgRsin32mvm vsin) cos ) mgRsin2 2errp m v m(v vsin)x0 eereer14(1)中,且0e, vea ema m(a a a) F mgAARRFFBm gBmg0N0 e0Nm(a acos ) F mgsinnrev2rR0 eN0令0 Rm(R 2 mgR cos ) atm tgsinR)0FNm22maFi iyFm g 2mg(3cos2cos )2N0F0 Nm2cos002m1101而021v，rvzeLz0erzv r e2rrr m)r r0mh211 212120v vcos ) si

7、n)22errm r m vcos ) sin) 2mghn22rrvcosr 代入上式，可求得：v将rr由v vcos ) sin)22err1v v1 22arLr3gdsMO0 0rgO3r11 v cos ) c22221由初始条件确定积分常数c grv 2cosvAaervv vl，0eval3BaDr 4 3v v ，vl0ADDBCDrx v v v ，DBCDrA0 1 Crad/svAAC 2A，BCrad/sBIOB 4vvPBPv6rad/sI的角速度为：PI A v B0AB 4AB0atBAanBABtBABABA Aa a a ，a 2 r0nBABABB1 AtB

8、ABABAO At21BABAnO A2tyx n1BAa acos12r22yasin at，BA2AaaaaAO A2222ytOtO A2 II，22ata2121212anO1O A22acos a12，12212a a12 r)OO121vvDCR rvaR r R rRaOBata a a aBOana a a a aORBCtOCa a a aOORv2Cy B0 Pv4m/srCBatBanBBtBAatBABAxv2BrBBBBB，a 00。BBa a a a a aCBCBBC P，vAAPAB取 Caern3atBAr ABaCtBAnBAtBAnBAAaBCBaeaae

9、K00 aeKa 2 v223aO 1vaBve1aerA，vvv veetansinarO 1BO11vv v u001B1AuO11v v v 22BO11aeyx2，R r r1x yOx: 0 a a y: a a a 图Ca2r2O111a a a nBO0tBO0aBBxa a a a nBO0tBO0tByOaA2r，u2rB315（b） 取 套筒Aer3r3e 3r3e315（d） 取 套筒A PBCv v vaer8163tr22142 33 2 4v CPCr3 a a a a a a a aa BCCttBnBtCBCBCat2BAaerKaaCn, ea a a a a

10、tAaCry0C动点Aa a a a a atACnACaCrKaya a a a00Cr) r 为BCBCOaCCerKtetCO22a a a a atnCrK220CKa 0CCO 2 v 02 BC CBCxy3a2298C P，为AAAP 2RAB杆上B2vBAO yRv0AAPABAB取Axa a a a a anBAtBAnBABAAva a cos45a a a A2a a a2B 取DC C CaCeCrv v 3 rCeCrv v vDaDeDrv v CrDr3r023r02Caa a a a aDKCaayaa 3 raayD点aa a a a aCrDDaDeDrDK

11、xa a CrDra a a cos3002r0DaxDrDKaa a cos30 a 02r0DayDeDrDKCSaNCm F r Fr2S0F FFr(rcos r)SNa0C22，N2F0r22SNmg Fsin2022CAN1l2aCaA2aORanata a a atAOnAOAAO1OO1F221m R F R2222m g)S222m gF fF m SN121N12 m12A111P2222AB, v,ABCAA,ARRAA1 l2222T m1222 2 2 12 22 2 R212136412alW m g sin)02121lm 2 2202121323l221221

12、33lm l m l sin m l cos sin m g cos2222221221 450：112ca1 A2 Clv vC2AA22vA A1L3A)L2l2CC1111ml25ml22lI66C Cl 113L mvBCCBCml226I27ml mgk332ghv2m m 与 13mst32ghv2312222131322 22mg222k 22km 28mghk若。h313ht 0 杆上A1OCCAAt 0当 A B1m 232l 2 asin gcos C3Cg。2l asin gcos2g f()3f() 0 f()0若 杆f()f() asin gcosg) acos gs

13、in 0*g当agsin*22，*当sin*22，*g2g 0222222246 P ABlaCPBCP21ABMF12aCICmgAll22P23F mg cos ) 24AyACI3F mgsin cos 4BxCIB F ma IC0 xI0CCAF m a m a m mF FCIC CABIAB AABCaBFACICABIF 0mg F F 000 xaAAa a ACAaCxAxF 0 F F m g 0yF m g m a 0F fF NFC Cx a a )FN000C0200FCACIya 2AFFBa a ) 0AFA B ICIxa a 20，A 2222I1M12I2

14、1M 0 F r M F r 0， F mr ) N226AIBBF F F 0n 0 t 0 x1F mr( ) 22，00yBF 03 6rad/s，22 设 , OAABlF m , F m(2FFF11M221212ABFMOxI2，I2 M 0AFABFMgAxI2a a a aCA CAACantlatB2CC，IAA11M m r M2212AC，lF r M F sin) F rcosnCAFt2IAIAIAllAMtCAm g22IC CFIANPBCll222F r M F r F rcos F rsin 01122225r l cos l sin 02dl 0C 0111

15、224242A1v r , v r rl sin l4Alsin 5r2(3 1030g90|当,0ABAAB ,2()2l3 10FFAxAm gACF当 90 0,0llsin25r0。a r 0当 AAAF 0AyNICF 2mg F 2mg m27NNIC AtBAnBAtBABABtBtBABv2a a tBA0Bhv22B C FICla2C1M12F F 00IC，x00C00B，Aa r32A2，0033ar233BF 2maC22MP3B2F1FMF2AB21M F r F r F r 00mgC BB22FNB000，2 3F FP30 B，F22M 0ABAFmgNBF

16、r F 2r 2mgr000ICNB20IC23 2F 2mg F m r23 90MM1 22M gMa122211 I2Mx21W M gx M gx F x F x 011x xa a221212FFa122M2M g T M aT。a 1220取 V R d L L( ) 0dt1T mS22取S 0Sh222d L Lg( ) 0S S 0，A,S Asin( t ) 05-13质量为m r 1T m(r ) m(rsin)22220取 V )1L T V mr ( sin ) mgr cos)2 2222dtg( cos 02r1L T V mr ( sin ) mgr cos)2

17、22取；W M取QM；d L L( ) Q 0Mdtgrd L L( ) QM M M222 , 01 21 2OOO G l OO O GO度 G 33OJ23O O zyO G31 2aO Gy3a cos j sinzaO 33122221230取 12222123d L L( ) 0，J J cos mglsin2123v度 B BA Bv11s2222vx scos ) )1 2222Ax11122g1222x 11122g12222FF取Q F；F 取s P Ps 2dt s s22a x2A212楔块Bg112 222 12mm rAv v vOAOr12222x22A11 11

18、mx m rcos) (rsin) mr2222 22 241113 m mrcosx mr22 2211113L T V m mrcosx mr m g rsin2241111 m mrcos 01g1112 m g1 m ) cos 211M 12m m m m m，1231232Mm 12M121112222122221 m m m m )xx2x22123 1232 1 21取1V m m x)m x)2x2213(m m m m 12123123211L T V m m m m )xx222122312313211 m m m m m 011222322 m m m 03 123 2

19、223Mm m ) ma xg2 3123m m ) m11，1232 3M4m mm12312F M P PT x 1 2222g 2gs111222g12221xV ks21111L T V P P Ps ks2222gg 2g 21222F取；x 0,s 0取；d L L( ) Q Fdt x x P Ps 212d L L( ) Q 0FgPxs2 P) P)1212PPs P P212PFPFscospt22 P)k P)121 Pp212。FPa x1P P P121物体M F12MmmM l的杆 与22T mv m v21 A2 21 1m x m ) ()2222 21211 m m x m l22 2221222设112212222xL T m m l cosx x12211T V m m x m l m g cos )22 22212222mm2s v v vCBCBC1 1 11T mv ( ml) m v2222 21221 C11122221121122261211设s 0l1V m g cos m k22212L T V111T V m mlscos( ) ml22 22261211l1m g cos