题目内容
如图所示,半径分别为R和r(R>r)的甲乙两光滑圆轨道安置在同一竖直平面内,两轨道之间由一光滑水平轨道CD相连,在水平轨道CD上有一轻弹簧被a、b两个小球夹住,但不拴接.同时释放两小球,a、b球恰好能通过各自的圆轨道的最高点.(1)已知小球a的质量为m,求小球b的质量.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241426022823997.png)
(2)若ma=mb=m,且要求a、b都还能够通过各自的最高点,则弹簧在释放前至少具有多大的弹性势能.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241426022823997.png)
(2)若ma=mb=m,且要求a、b都还能够通过各自的最高点,则弹簧在释放前至少具有多大的弹性势能.
(1)
.(2) 5mgR.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602329607.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241426023751042.png)
mg=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602469656.png)
解得:va=
;同理可得:vb=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602578474.png)
又:mva=mbvb
所以:mb=
.
(2)由题意分析知,应该按照a球在轨道最顶点具有临界速度这一条件计算.依照上面结果可得:
va=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602516483.png)
mva=mvb
所以有:Ep=2×
5mgR.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241426023751042.png)
mg=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602469656.png)
解得:va=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602516483.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602578474.png)
又:mva=mbvb
所以:mb=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602329607.png)
(2)由题意分析知,应该按照a球在轨道最顶点具有临界速度这一条件计算.依照上面结果可得:
va=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602516483.png)
mva=mvb
所以有:Ep=2×
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824142602734653.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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