题目内容
(16分)如图所示,A、B两球质量均为m,其间有压缩的轻短弹簧处于锁定状态。弹簧的长度、两球的大小均可忽略,整体视为质点。该装置从半径为R的竖直光滑圆轨道左侧与圆心等高处由静止下滑,滑至最低点时,解除对弹簧的锁定状态之后,B球恰好能到达轨道最高点,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050308181571.png)
(1)滑至最低点时,解除对弹簧的锁定状态之前A球和B球的速度v0的大小。
(2)最低点时,解除对弹簧的锁定状态之后A球和B球速度vA和vB的大小。
(3)弹簧处于锁定状态时的弹性势能。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050308181571.png)
(1)滑至最低点时,解除对弹簧的锁定状态之前A球和B球的速度v0的大小。
(2)最低点时,解除对弹簧的锁定状态之后A球和B球速度vA和vB的大小。
(3)弹簧处于锁定状态时的弹性势能。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030833618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030849898.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030864601.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050308801030.png)
试题分析:设A、B系统滑到圆轨道最低点时锁定为V0,解除弹簧锁定后A、B的速度分别为vA、vB,B到轨道最高点的速度为v,则有:
(1)根据系统机械能守恒有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030896913.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030833618.png)
(2)对B,在最高点重力提供向心力有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030927711.png)
解除锁定后在最低点由系统机械能守恒:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050309421034.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030864601.png)
对A.B组成系统由动量守恒有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030974727.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005030849898.png)
(3)由系统机械能守恒有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050310051226.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250050308801030.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目