题目内容
一根长为L、质量不计的硬杆OA,杆的中点C及A端各固定一个质量均为m的小球,杆、球系统可在竖直平面内绕O端的水平轴转动,如图所示.若开始时杆处于水平位置,并由静止释放,当该系统在转动过程中通过竖直位置时,A端小球的速度
为多大?中点小球的机械能比在水平位置时减少了多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242315497252068.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231548867352.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242315497252068.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231550536782.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231551456826.png)
试题分析:在转动过程中,A、C两球的角速度相同,设A球的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231548867352.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231554030339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231554904524.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231555871654.png)
于是有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231556339525.png)
以A、C和杆组成的系统中,只有重力势能和动能相互转化,机械能守恒,由机械能守恒定律,并选最低点为零势能参考平面,则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231556947787.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242315574311145.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231558726460.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231559209974.png)
由①②两式联立解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231550536782.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824231601705739.png)
中点小球C的机械能减少量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242316029531604.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目