2013泛珠三角及中华名校物理奥林匹克邀请赛答案

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1、Part-IQ1(9points)l2l223mRotationalinertiaofthebeam杆的转动惯量的一般表达式:Ill(,)lmLdl/l.12l13Ll1m2a)II(0,)LL3Conservationofangularmomentum角动量守恒:2Lmv003vImLmLv.02ILm4LEnergylost动能损失:12121222EmvImLmv/8.(3points)00222231721122L127b)II(L,L)mL,orImLmmLmL4448124

2、121648Conservationofmomentumandangularmomentum角动量、动量守恒:mv2mv,6v00,LL25L.Immv40vv/240Energylost动能损失:212121L222EmvImmvmv/10.(3points)0022241112c)II(L,L)mL2212Conservationofmomentum,angularmomentumandenergy角动量、动量、能量守恒:12v0mv0mv1mv2

3、5LLL2v0Imv2mv0v1(3points)225121212123v0Imvmvmvv210222225Q2(10points)mmmm1212a)mrGG(rr),mr(rr).(1point)1133212212

4、rr

5、

6、rr

7、1212mm21b)rrr,rrr.12ccmmmm12121(mmr)0r012ccmmmmmm(2points)121212rGrrGr33mm

8、

9、r

10、

11、r12c)r0.(1point)cd)Theequationforrist

12、hesameasauniformcircularmotion，r满足的方程与匀速圆周运动满足的方程一致.Therefore因此,Gm(12m)2Gm(12m)a.23/2aart()acos(tx)asin(ty).(3points)00e)mmm,121/31/33/22811302a2TGm9106.710410Ta222Gm44.(3points)1/32796.116101.810mQ3(12points)2a)q'QRx/,x'R/.x21Qq'1QRxf22224

13、(xx')4(xR)0022L1LQWfxdx().(3points)不用积分扣2分。08RR(22L)0b)Sincetheoutsidechargedoesnotcreateanyfieldinsidetheconductorsphere,theworkdonehereisnodifferentfromtheoneina):外电荷对导体内部无影响，所以结果与a)一样。221LeW.(2points)228RR(L)0c)ThestaticelectricfieldonthechargeqLQR/outsidetheconductings

14、phereisequivalenttoa2fieldgeneratedbythreepointcharges:qQat(0,0),imagechargeqqRx/at1222(lR/,0)l,andqqat(0,0).Therefore22球外qLQR/受的静电力来自以下三个点电荷:qQ在(0,0),镜像电荷qqRx/在21222(lR/,0)l,以及qq在(0,0)。2221qqqq()q1qxRqxq()Rq222122212fx().(2points)2222234ò(xx')x

15、4ò(xR)x00Andtheworkdonebyelectricfieldisthen电场做功2222RL/1LqLqLq(2Rq)2221fxdx()8òR3LR2R304222222422421LQL(2RLQ)1LL(2LR2RQ)8òR5RL32R552208ò0RR(L)(3points)d)WW(2points)inc)Q4(9points)rrcosa)tvcrrsincvsinv(2points)tcvcos