题目内容
如图所示,水平面放一质量为0.5kg的长条形金属盒,盒宽
,它与水平面间的动摩擦因数是0.2,在盒的A端有一个与盒质量相等的小球。球与盒无摩擦,现在盒的A端迅速打击一下金属盒,给盒以
的向右的冲量,设球与盒间的碰撞没有能量损失,且碰撞时间极短,求球与盒组成的系统从开始运动到完全停止所用时间。(
)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146165172291.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616471381.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616486356.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616502471.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146165172291.jpg)
1秒
设打击后金属盒的速度为v0,由I=mv0解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616533554.gif)
由于盒子与球碰撞时间极短,因而盒子与球组成的系统动量应该守恒,则有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616549545.gif)
由于碰撞过程没有能量损失,则有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616564794.gif)
且有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616580391.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616595521.gif)
球在盒子内做匀速运动,经时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616611526.gif)
定律可得碰撞后盒子的速度为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616627526.gif)
盒子克服摩擦做功,则由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616627702.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616658672.gif)
前球不再与盒子相碰,设盒子滑行的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616658204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616673610.gif)
则可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616845824.gif)
球与盒组成的系统从开始运动到完全停止所用时间为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114616861322.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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