力学竞赛动力学课件1.ppt

1、CiimmvvpmzmzmymymxmxmmmmiiCiiCiiCiiiiiC,rrrOO1ABOvABOvvmiriOyxzriyxzCvirCii)(vrvMLiiiOOmmiCirrriiCiC)(vrvrvrrLiiiiiOmmmCivvmmiivrLiiCmCOmLvrLCCmiriOyxzriyxzCvirCirCivvvirCirCi)(vrvrvvrvrLiiiiiiiiCmmmm0CiimmrrCiiCmmLvrvrL iiiriAiiivmT221222121CiiimvvmT222121ziiiJvmT222212121PCCJJmvTiiiCiTTvmvmTre2r2i

2、21)(21v 图示坦克的履带质量为图示坦克的履带质量为 m，两个车轮的质量均为两个车轮的质量均为 m1。车轮车轮可视为均质圆盘，半径为可视为均质圆盘，半径为 R，两车轮间的距离为两车轮间的距离为 R。设坦克设坦克前进速度为前进速度为 v，计算此质点系的动能。计算此质点系的动能。212221212r2i)32(2121)(21212)2(2121)(21vmmmvRvRmvmmvmvmTiiiCi222222121OOOJmvT222222,2mRJRvRvOrOOO226mRT 22222211212121OOOOOJmvJT22212221,9232,3,mRJmRJRvvRvRvOOrO

3、ErOOEO22222629mRmRmRT222222112121212121OOOOOOJmvJmvT11,3OORv232,3222RvvRvRvrOErOrOErcos1249cos22222221222122RRRvvvvvrOOrOOO222222112121212121OOOOOOJmvJmvT11,3OORv2322RvvrOErOcos1249cos22222221222122RRRvvvvvrOOrOOO)cos1(641822222mRmRmRMiCdrCdriCicCidddrrriCiCiiidddWrFrFrFdMdCMFdiCiiiCi)(cosFrFdMddMdW

4、WCCRiCCii rFFrF)(dMdWCCCCR 212112rFOBCFFsFNOBCFSRSFmgMW)sin(12RSFrFSWcos12OCBPOACBPFFTFNmg2222222143)21(21210mRmRmRJTTCmgfsPsW212mgfsPsmR204322OCBPOACBPFFTFNmgmgfsPsmR204322)2(32mgfPmsR)(32mgfPmR222zyxOMMMM)(22222yxmrmJyzmJxzmJJMJJMJJMiiiziyzixzzzxzyzyyzxzx 其其 中：中：均质圆轮均质圆轮A和和B的半径均为的半径均为r，圆轮圆轮A和和B以及物

5、以及物块块D的重量均为的重量均为W，圆轮圆轮B上作用有力偶矩为上作用有力偶矩为M的力偶，且的力偶，且3Wr/2 MWr/2。圆轮圆轮A在斜面上作在斜面上作纯滚动。不计圆轮纯滚动。不计圆轮B的轴承的摩擦力。的轴承的摩擦力。求：求：1、物块、物块D的加速度；的加速度；2、二圆轮之间的绳索所受拉力；、二圆轮之间的绳索所受拉力；3、圆轮、圆轮B处的轴承约束力。处的轴承约束力。1sDsDiiWTT12222221221212121AOAABODDJvmJvmTMGADiiWWWW1222222)21(2121)21(2121TrgWvgWrgWvgWAABDBDDMsWWssin30sD1222222)

6、21(2121)21(2121TrgWvgWrgWvgWAABDBDDMsWWssin30rsrvsvvDDBADAD,DDsWrMTvgW)2(2312DDDvWrMavgW)2(3gWWrMaD32rFWMragWrgWDB)(21T2BDraT23FWrMagWD)23(21TrMWF。，不不合合理理时时时时，,023;023TTFWrMFWrM30sin230cos0TTFWFagWFFByDBx)253(121)23(4330cosTrMWFrMWFFByBxAO30C均质圆盘均质圆盘O放置在光滑的水平面放置在光滑的水平面上，质量为上，质量为m，半径为半径为R，匀质细匀质细杆杆OA长

7、为长为l，质量为质量为m。开始时杆开始时杆在铅垂位置，且系统静止。在铅垂位置，且系统静止。求：求：杆运动到图示位置时的角速度。杆运动到图示位置时的角速度。2xO，xAO30COvAO30COvOviiWTT122222212121CCOmvJmvTmgllmgWii41)30sin1(2lvlvvvvvvOOCAOCAOC214160cos2222222OOvmlmlmvT41612222AO30COvAO30COvOvmglvmlmlmvTTOO414161222120)60cos2(lvmmvOOlvO81lg2934OA0P0AOPCMmMROC,MmmRCP)()(22RMmMmL1C

8、222)()(MRRMmmML2COA0P0AOPC)()(22RMmMmL1C222)()(MRRMmmML2C02C1CLL0)(22MRRMmmMOA0P0AOPC02C1CLL0)(22MRRMmmM0)(22MRRMmmMMmMmmMM/21/2ABO2220)(2213121222lmglmglmmllg792OAABC2mglFmlAx1231030sin30cos)2(30cos2002000CxyNBAAyyNByxAxxMlFlmgFlFMmgFFFFFFF222CCCyyCxxJMmaFmaFABCOAAanAanAaAaCAaABnAaAaBAa1279laglaAnA

9、CAAnACaaaa060sinBAnAByaaalg7332BAAnABaaaa14960sin143360cos1gaaaglaaaCAnACyCAACxOAABC2mglFmlAx1231030sin30cos)2(30cos20)(02000CxyNBAAyyNByxAxxMlFlmgFlFMmgFFFFFFFF14960sin143360cos1gaaaglaaaCAnACyCAACx222CCCyyCxxJMmaFmaFOAABC2mgmgFmgFmgFlglglgNBAyAx49654996493373349397921OABCBAC260sin12160sin60cos2)()

10、(lFmlJmaFmgFmaFFACcyAeyCxAex60aAaCAaA2,0laaCAnCAnCACAACaaaa230sin,30coslaaaaACyAcxACBBAC260sin12160sin60cos2)()(lFmlJmaFmgFmaFFACcyAeyCxAex60ACaAaCAaA230sin,30coslaaaaACyAcx.132,1318,1332galgmgFAAOABCABCmiriOyxzriyxzAvirAivrLiiAm ACvLLmAAirvrLiiAm)(AiiriiiiAmmvvrvrL CCACvLLmAAAL0CCAAiiAiiiiAmmmmmmmd

11、tddtdMvvMvvvvMvrrarvrvrL CAiAiiiAiiiiiii)-()()()(eiACAAmdtdFMvvL)()(eiACAAmdtdFMvvLmgPFNAFNBPCFmRFRFmRJP342232cos23cos2312lglmgmlJP)()()(ACeiAAmdtdaFML定定 向向 爆爆 破破r21FFFFaeiCm跳高运动员的过杆姿势跳高运动员的过杆姿势CCfmgFFRmRFmaC2.,00tRgffgtvvRgfgfaCC.,00tRgffgtvvE000gftRfgtvRvvEfgRvt200RvRtRgfRvfgtvv22000000CEfgRvt200R

12、vRtRgfRvfgtvv22000000.0,000RvvRv:有有此此时时,:则则:若若E0,000vRv:则则:若若CC.,00tRgffgtvv.,0000RvRfgvtv时时:当当ttt时时:当当ttC继继续续无无滑滑动动的的滚滚动动.圆圆圈圈经经过过一一段段滑滑动动后后,:若若,00Rv 纯纯滚滚回回来来.经经过过一一段段时时间间后后,接接着着反反方方向向滑滑动动,轮轮心心速速度度降降为为零零,圆圆圈圈经经过过一一段段滑滑动动后后,:若若,00Rv 圆圆圈圈将将如如何何运运动动?:若若,00Rv 20)cos(cos2)coscoscos(22dlmgdlmgymgVC0)cos(

13、sin2dlmgddV.,.,0221ooo舍舍弃弃2 2为为其其平平衡衡位位置置为为其其平平衡衡位位置置0o为为其其平平衡衡位位置置0o)cos(cos2dlmgV)cos(cos222dlmgdVd随随遇遇平平衡衡状状态态非非稳稳定定平平衡衡状状态态稳稳定定平平衡衡状状态态0cos0cos0cos)cos(2022dldldldlmgdVdcos2221lddll221)2(21lmT)cos(cos2dlmgVEdlmglm)cos(cos2)2(21221sin0)cos(21ldlg 0)cos(21ldlg 1)cos(ldlgOCxycosMgdV0sinMgdddV.,0221ooo舍舍弃弃为为其其平平衡衡位位置置为为其其平平衡衡位位置置0ocos22MgddVd稳稳定定平平稳稳0022MgddVdOCxy为为其其平平衡衡位位置置0ocos22MgddVd稳稳定定平平稳稳0022MgddVdACAl02)2(mRJLz1zl2mvRlmJl2mvRl2mvJLr2zr2ez2z)(222l2mvl2mvRlmJLrr2z2z)(22arvv lmvmRJaz2)2(02222021212)2(21azmvTmRJT22022)2(azmvmRJmJRlz22