题目内容
(16分)物体A的质量
,静止在光滑水平面上的木板B的质量为
、长
,某时刻A以
的初速度滑上木板B的上表面,为使A不致于从B上滑落,在A滑上B的同时,给B施加一个水平向右的拉力F,若A与B之间的动摩擦因数
,试求拉力F应满足的条件。(忽略物体A的大小)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241454571771208.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145456771559.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145456849663.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145456911467.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457021622.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457067474.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241454571771208.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457239543.png)
试题分析:物体A滑上木板B以后,作匀减速运动,加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457301820.png)
木板B作匀加速运动,设加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457364348.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457411807.png)
A不从B的右端滑落的临界条件是A到达B的右端时,A、B具有共同的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457489324.png)
由位置关系,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457598975.png)
运动时间相等,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457723710.png)
由①③④式,可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457769817.png)
由②⑤式,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241454578631182.png)
代入数值,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457910503.png)
若F<1N,则A滑到B的右端时,速度仍大于B的速度,于是将从B上滑落,所以F必须大于等于1N。
当F较大时,在A到达B的右端之前,就与B具有相同的速度,之后,A必须相对B静止,才能不会从B的左端滑落。
当A相对B静止时,由牛顿第二定律
对A、B的整体,设加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457972283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145458175717.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145458612650.png)
联立解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145458893528.png)
若F大于3N,A就会相对B向左滑下。
使A不致于从B上滑落,力F应满足的条件是:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145457239543.png)
点评:难题。在分析动力学问题时,一定要注意:(1)过程分析,(2)运动状态分析,(3)受力分析.物体的运动可能经过几个过程,而在这几个过程,运动状态一般不同.因此要分析不同过程的运动状态和受力情况,从而利用不同的公式求解.
![](http://thumb2018.1010pic.com/images/loading.gif)
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