1.
(2024高三下·武汉月考)
一种弹珠游戏可以简化为如图所示模型:小球A质量为m,小球B质量为3m,B球左侧水平面粗糙,右侧光滑,A球与粗糙水平面间动摩擦因数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%BC%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmath%3E)
, 轻质弹簧放置在粗糙水平面上,左端固定在竖直墙壁,右端与A球接触但不栓接,此时A、B两球间距离为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
。现沿弹簧轴线向左移动小球A使之压紧弹簧,当弹簧压缩量为0.5l时将装置锁定,弹簧的劲度系数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ek%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Eg%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
。将系统释放,A球向右运动与B球发生弹性正撞,碰后B球沿光滑水平面匀速运动一段距离后进入固定在光滑水平面上的两平行挡板EF、GH之间,两挡板间距为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmi%3El%3C%2Fmi%3E%3C%2Fmath%3E)
, 挡板均为粗糙弹性挡板,两挡板垂直水平面平行固定放置,两挡板与B球速度方向的夹角均为30°,乙图为俯视图。小球B进入到两挡板间先与GH挡板发生碰撞,且每次碰撞时垂直挡板方向上的分速度等大反向,小球B受到挡板的摩擦力是其与挡板压力的
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
倍。已知重力加速度为g,小球B与挡板的碰撞时间远小于小球B在两挡板间运动的时间,小球A、B可视为质点。求:
![](//tikupic.21cnjy.com/2024/06/15/07/54/0754d2c9f9f0126b3e90c94beb202ac8_457x162.png)