题目内容
如图所示,长12m的木板右端固定一立柱,板和立柱的总质量为50kg,木板置于水平地面上,木板与地面间的动摩擦因数为0.1,质量为50kg的人立于木板左端,木板与人均静止,人以4m/s2匀加速向右奔跑至板的右端并立即抱住立柱,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241148174962647.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817511362.gif)
(1)人从开始奔跑至到达木板右端所经历的时间;
(2)木板的总位移。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241148174962647.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817511362.gif)
(1)人从开始奔跑至到达木板右端所经历的时间;
(2)木板的总位移。
(1)2s (2)2m;方向向左
:(1)在人相对木板奔跑时,设人的质量为m,加速度为
,木板的质量为M,加速度为
,人与板间的相互作用力大小为F
对人有:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817542460.gif)
对板有:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817558556.gif)
由几何关系得:
∴t=2s
(2)当人奔跑至木板右端时,人的速度:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817605346.gif)
板的速度:
板的位移![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817620390.gif)
人抱立柱过程中,系统动量守恒![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817636468.gif)
方向与人原来的运动方向一致
在随后的滑行过程中,对人与板构成的整体,根据动能定理得:
方向向左
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817527224.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817542226.gif)
对人有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817542460.gif)
对板有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817558556.gif)
由几何关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817589442.gif)
(2)当人奔跑至木板右端时,人的速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817605346.gif)
板的速度:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817605348.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817620390.gif)
人抱立柱过程中,系统动量守恒
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817636468.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817652312.gif)
在随后的滑行过程中,对人与板构成的整体,根据动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817667627.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114817683418.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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