题目内容
(9分)两物块A、B用轻弹簧相连,质量均为2 kg,初始时弹簧处于原长,A、B两物块都以v=6 m/s的速度在光滑的水平地面上运动,质量4 kg的物块C静止在前方,如图所示。B与C碰撞后二者会粘在一起运动。求在以后的运动中:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250041373441392.png)
(1)当弹簧的弹性势能最大时,物块A的速度为多大?
(2)系统中弹性势能的最大值是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250041373441392.png)
(1)当弹簧的弹性势能最大时,物块A的速度为多大?
(2)系统中弹性势能的最大值是多少?
3m/s 12J
试题分析:(1)当A、B、C三者的速度相等时弹簧的弹性势能最大.
由A、B、C三者组成的系统动量守恒,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137359944.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250041373751265.png)
(2)B、C碰撞时B、C组成的系统动量守恒,设碰后瞬间B、C两者速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137390405.png)
mBv=(mB+mC)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137390405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137390405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137437560.png)
设物ABC速度相同时弹簧的弹性势能最大为Ep,?
根据能量守恒Ep=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137453338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137468439.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137453338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137453338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137515497.png)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137453338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137453338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004137453338.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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