人类为了开发外太空,需要模拟各种等效重力场下的逃生方式。如图所示,水平面xOy和竖直面yOz内分别固定着两个半径均为R的半圆形光滑绝缘轨道OMN和OPQ,整个空间存在着方向沿y轴正方向的匀强电场,质量均为m的逃生球A、B套在轨道上,其中绝缘的A球不带电,B球的电荷量为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmath%3E)
。已知匀强电场的电场强度大小为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Eg%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Eq%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
(g为重力加速度),B球从OMN轨道进入OPQ轨道时无能量损失,初始时B球静止在OMN轨道的中点处,A球以大小为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmi%3ER%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmath%3E)
的初速度从N点滑上轨道,A、B两球之间的碰撞为弹性碰撞,且碰撞过程中B球的电荷量不变,A、B两球均可视为质点,求:
![](http://tikupic.21cnjy.com/2024/04/16/d7/96/d7964f949e78cff0d134b747564b356c.png)