题目内容
(16分)质量为m的钢板与直立轻弹簧的上端连接,弹簧下端固定在地上.平衡时, 弹簧的压缩量为x0,如右图所示.一物块从钢板正上方距离为3x0的A处自由落下,打在钢板上并立刻与钢板一起向下运动,但不粘连.它们到达最低点后又向上运动.已知物块质量也为m时,它们恰能回到O点.若物块质量为M,仍从A处自由落下,则物块与钢板回到O点时,还具有向上的速度.物块向上运动到达的最高点与O点的距离h=
x0.求M与m的关系式。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025163206151.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516289338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025163206151.jpg)
M=2m
试题分析:在自由下落的过程中,两种情况下落至钢板的速度相同,
即v
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516320293.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516367552.png)
在碰撞时,因时间极短,故动量守恒.分别有:
mv0=2mv1(2分)
Mv0=(M+m)v2(2分)
在压缩弹簧后至回到O处的过程中机械能守恒,分别有:
Ep+
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516289338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516398281.png)
Ep+
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516289338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516414244.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516289338.png)
在第二种情况下,两者在O处分离后,物块做竖直上抛运动,其最大高度
h=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516445518.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002516289338.png)
解得:M=2m(2分)
![](http://thumb2018.1010pic.com/images/loading.gif)
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