题目内容
如图所示,在光滑的水平面上,有两个质量都是M的小车A和B,两车间用轻质弹簧相连,它们以共同的速度向右运动,另有一质量为
的粘性物体,从高处自由下落,正好落至A车并与之粘合在一起,在此后的过程中,弹簧获得最大弹性势能为E,试求A、B车开始匀速运动的初速度
的大小.![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146435992877.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643568249.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643583224.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146435992877.jpg)
A、B车开始匀速运动的初速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643615939.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643615939.gif)
物体
落到车A上并与之共同前进,设其共同速度为
,
在水平方向动量守恒,有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643661412.gif)
所以![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643677429.gif)
物体
与A、B车共同压缩弹簧,最后以共同速度前进,设共同速度为
,根据动量守恒有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643724447.gif)
所以![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643724465.gif)
当弹簧被压缩至最大而获得弹性势能为E,根据能量守恒定律有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643739981.gif)
解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643615939.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643568249.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643646222.gif)
在水平方向动量守恒,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643661412.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643677429.gif)
物体
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643693249.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643708224.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643724447.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643724465.gif)
当弹簧被压缩至最大而获得弹性势能为E,根据能量守恒定律有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643739981.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114643615939.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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