1.
(2024高三下·长沙模拟)
如图所示,倾角为θ的固定斜面的底端安装一个弹性挡板P,质量分别为
m和4
m的物块a、b置于斜面上,二者初始位置距离挡板足够远,物块a与斜面间无摩擦,物块b与斜面间的动摩擦因数为
![](//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%3Et%3C%2Fmn%3E%3Cmn%3Ea%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmtext%3E%CE%B8%3C%2Fmtext%3E%3C%2Fmath%3E)
。两物块间夹有一个劲度系数很大且处于压缩状态的轻质极短弹簧,弹簧被锁定,锁定时弹簧的弹性势能为
![](//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%3E0%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmath%3E)
。现给两物块一大小为
![](//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%3C%2Fmath%3E)
、方向沿斜面向下的初速度的同时,解除弹簧锁定,弹簧迅速完全释放弹性势能,并立即拿走弹簧。物块a、b与挡板P之间的碰撞均为弹性碰撞,重力加速度为
g(弹簧长度可以忽略不计)。求:
![](//tikupic.21cnjy.com/2024/06/01/03/9d/039de0ccca193cda6325eb78b1b2fc34_m_217x131.png)