2.
在高度为h的光滑水平平台左侧竖直面内固定一光滑
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
圆弧轨道,轨道与平台相切于最低点。平台右侧是一下挖深度为d的光滑水平槽,在水平槽上放置一个厚度为d的长木板,长木板质量
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 长木板左端放置一个质量为m的小物块(可视为质点),如图。一质量为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的小球从光滑
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
圆弧轨道最高点由静止释放,小球运动到平台后与长木板上的小物块发生弹性碰撞,碰撞后小物块获得水平向右的速度
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 小球反弹后被立即拿走。当小物块在长木板上滑动到长木板最右端时,小物块与长木板恰好达到共速,长木板右端到达平台边缘后立即被锁定,小物块水平飞出。已知重力加速度为g,小物块与长木板间的动摩擦因数为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%CE%BC%3C%2Fmi%3E%3C%2Fmath%3E)
, 空气阻力不计。求:
![](http://tikupic.21cnjy.com/ct20241o/c5/68/c56898177ef7493cbcf518d13070c7c1.png)