题目内容
平板小车静止在光滑的水平面上,其质量为M ,一质量为m的小物块以水平初速v0沿小车表面向右滑去,如图所示。由于小物块与平板小车表面间存在着摩擦,使小物块最终相对于平板小车静止。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241251426391222.png)
(1)最终平板小车的速度是多大?
(2)小物块的动量减小了多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241251426391222.png)
(1)最终平板小车的速度是多大?
(2)小物块的动量减小了多少?
(1)mv0/(M+m)(2)v0- mv0/(M+m)
本题考查动量守恒定律
(1)因为平板小车静止在光滑的水平面上,所以由
组成的系统在水平方向上动量守恒。
设小物块最终相对于平板小车静止时小车的速度为
,则有
,解得
.
即最终平板小车的速度是![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142810676.png)
(2)小物块的初动量为
,小物块最终相对于平板小车静止时动量为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142920750.png)
,所以小物块动量的减少量为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241251429511300.png)
即物块动量的减少量为
.
(1)因为平板小车静止在光滑的水平面上,所以由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142701484.png)
设小物块最终相对于平板小车静止时小车的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142717252.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142764778.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142810676.png)
即最终平板小车的速度是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142810676.png)
(2)小物块的初动量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142904414.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142920750.png)
,所以小物块动量的减少量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241251429511300.png)
即物块动量的减少量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125142998651.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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