西安建筑科技大学精品课程：《大学物理 College Physics》课堂讨论会_学生讲演稿——带电小球对心碰撞（固定一球）

带电小球对心碰撞(固定一球) 电气0902李玮仓

带电小球对心碰撞（固定一球） 电气0902 李玮仑

十 十 R k 41q X 919 41q dx= mvdr (d-x) a-x

x d x22 2 1 1 2 ( ) dt d x m d x q q k = − v dx dv m dt dx dx dv m d x q q k 2 1 1 1 2 ( ) = = −   = − vv x dx m vdv d x kq q 1 2 2 1 0 1 ( ) 1 1 2 1 11 2 0 2 1 v v v m x m d x kq q    =   − 1 v R

2 kgg 1 kq, q d-x 2 2kq92 1.2 2kqq2 dx d-x are 2kg, q dx tk dx= dt a-x +k2 令k+k2=m X

2 2 1 2 1 1 2 1 1 2 1 2 v m v m d k q q d x k q q − = − − dt dx m d k q q v m d x k q q v + − = − = 1 2 1 2 1 1 1 2 2 1 2 1 1 2 1 2 m k q q k = m d k q q k v 1 2 1 2 2 1 2 = − 1 2 1 k d x k dt dx + − =   = + − x t dx dt k d x k 0 0 1 2 1 1 令 k m d x k + = − 1 2 1

2k, m-dm=2k1 dm积分上下限省写 2 (m2-k2) 令 sec sec 6 2k, √k2see=2kk2 j tan 0 de k. tan 0 2K k2 6d0- csc 0d0 sin 6 =2k,k,2 . 0X cOS 1c1 de- de 2sin0 2J sin e Sin 6 cos e =2kk,2 In(csc 0-cot 0) 2sin-0 2

dm m k dm k m k k m m   − = − 2 2 2 1 2 1 ( ) 1 2 ( ) 1 22 2 积分上下限省写 令 m = k2 sec        k d k k d k k   − = 3 23 2 1 2 2 3 2 1 tan sec sec 2 tan1 2   = − + −   = −     −−          k k d d k k d d sin1 sin1 21 2sin cos 2 csc sin1 2 2 23 1 2 3 23 1 2   = − − − − ln(csc cot ) 21 2sin cos 2 2 23 1 2     k k

代入积分上下限上限1k+k2=√k2sece k(d-x sec 6 ktk, d-x cos e h,(d-x) k1+k2(d-x) k k1+k2(d-x) sin e= CSc 6 k1+k2(d-x) k, cot 6= k 下限x=0有Mk+k2=Vk2sec sec0=k+h,d kd COS 6 k,+k,d

代入积分上下限 上限 sec 1 1 2 2 k k d x k + = − ( ) ( ) sec 2 1 2 k d x k k d x − + −  = ( ) ( ) cos 1 2 2 k k d x k d x + − −  = ( ) sin 1 2 1 k k d x k + −  = 1 1 2 ( ) csc k k + k d − x  = 1 2 ( ) cot k k d − x  = 下限 x = 0 有 sec 1 1 2 2 k k d k + = k d k k d 2 1 2 sec +  = k k d k d 1 2 2 cos +  =