如图所示,一滑环套在水平光滑杆上,杆上
P点处固定一挡板(挡板厚度不计)。长度为
L的轻绳一端连接半径不计的小滑环,另一端悬挂可视为质点、质量为
m的小球,轻绳能承受的最大拉力
![](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%3EF%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3Em%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3Ex%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmtext%3Em%3C%2Fmtext%3E%3Cmtext%3Eg%3C%2Fmtext%3E%3C%2Fmath%3E)
。水平面上固定有一倾角
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%B8%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmath%3E)
的斜面
AB , 斜面底端
A点与
P点在同一竖直线上。初始时,轻绳保持竖直,滑环和小球一起水平向右做匀速直线运动,一段时间后滑环与挡板碰撞,滑环立刻停止,小球的速度在滑环碰撞瞬间未受影响,轻绳恰好达到最大拉力而绷断,小球水平飞出,刚好能垂直打到斜面
AB上的
Q点(未画出)。不计空气阻力,重力加速度大小为
g ,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3Ei%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E8%3C%2Fmn%3E%3C%2Fmath%3E)
, 求:
![](http://tikupic.21cnjy.com/2024/05/06/1d/02/1d027a7704e7c8eaa9f1d75796fabed2.png)