题目内容
(18分)如图所示,质量为M的厚壁塑料管B内有一个质量为m的小塑料球A,塑料球A的直径略小于塑料管B的内径,且M ≥m; A和B之间有一根极短的轻弹簧,轻弹簧与A、B不连接。将此装置从B下端离地板的高度H处由静止释放,B触地后在极短时间内反弹,且其速度大小不变,接着A脱离B竖直上升,而B恰好停留在地板上。不计空气阻力及A与B内壁的摩擦。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010129851444.jpg)
(1)塑料球A上升的高度;
(2)弹簧中能达到的最大弹性势能。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010129851444.jpg)
(1)塑料球A上升的高度;
(2)弹簧中能达到的最大弹性势能。
①若M=m,A上升的高度
;弹簧能达到的最大弹性势能
。
②若M>m,A上升的高度为
;弹簧能达到的最大弹性势能
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013001491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013016895.png)
②若M>m,A上升的高度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013047994.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010130631022.png)
试题分析:(1)A和B一起自由下落H,处于完全失重状态,轻弹簧处于原长,A和B一起下落,满足机械能守恒:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010130941208.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013110631.png)
B自地面原速反弹后,A和B组成的系统动量守恒,以向上为矢量正方向,有:
①若M=m,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013125890.png)
解得v1=0 1分
在此条件下,A和B的初动能完全转化成弹簧的弹性势能,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010131411318.png)
弹簧弹开A和B,B静止在地面,A竖直上升,弹性势能转化为A的重力势能,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013157696.png)
解得A上升的高度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013001491.png)
②若M>m,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013266845.png)
解得A上升的初速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013328806.png)
可得A上升的高度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010133591577.png)
在A离开弹簧之前的某一时刻,A和B的速度大小相等时,弹簧的弹性势能最大,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013375889.png)
从A开始压缩弹簧到A和B速度相等,满足机械能守恒,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010133911286.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010130631022.png)
综上所述:①若M=m,A上升的高度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013001491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013016895.png)
②若M>m,A上升的高度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001013047994.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250010130631022.png)
综上所述部分正确再给 2分
![](http://thumb2018.1010pic.com/images/loading.gif)
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