题目内容
(09·广东物理·19)如图19所示,水平地面上静止放置着物块B和C,相距
="1.0m" 。物块A以速度
=10m/s沿水平方向与B正碰。碰撞后A和B牢固地粘在一起向右运动,并再与C发生正碰,碰后瞬间C的速度
="2.0m/s" 。已知A和B的质量均为m,C的质量为A质量的k倍,物块与地面的动摩擦因数
=0.45.(设碰撞时间很短,g取10m/s2)
(1)计算与C碰撞前瞬间AB的速度;
(2)根据AB与C的碰撞过程分析k的取值范围,并讨论与C碰撞后AB的可能运动方向。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241407449605413.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140744539280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140744586323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140744648265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140744851301.png)
(1)计算与C碰撞前瞬间AB的速度;
(2)根据AB与C的碰撞过程分析k的取值范围,并讨论与C碰撞后AB的可能运动方向。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241407449605413.png)
⑴
⑵当
时,AB的速度为0 ; 当
时,AB的运动方向与C相反
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745023615.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745070398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745116524.png)
:⑴设AB碰撞后的速度为v1,AB碰撞过程由动量守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745366583.png)
设与C碰撞前瞬间AB的速度为v2,由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745569981.png)
联立以上各式解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745023615.png)
⑵若AB与C发生完全非弹性碰撞,由动量守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745818772.png)
代入数据解得
此时AB的运动方向与C相同
若AB与C发生弹性碰撞,由动量守恒和能量守恒得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241407459741373.png)
联立以上两式解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746052959.png)
代入数据解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746099417.png)
此时AB的运动方向与C相反
若AB与C发生碰撞后AB的速度为0,由动量守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746271641.png)
代入数据解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745070398.png)
总上所述得 当
时,AB的运动方向与C相同
当
时,AB的速度为0
当
时,AB的运动方向与C相反
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745366583.png)
设与C碰撞前瞬间AB的速度为v2,由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745569981.png)
联立以上各式解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745023615.png)
⑵若AB与C发生完全非弹性碰撞,由动量守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745818772.png)
代入数据解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745881414.png)
此时AB的运动方向与C相同
若AB与C发生弹性碰撞,由动量守恒和能量守恒得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241407459741373.png)
联立以上两式解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746052959.png)
代入数据解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746099417.png)
此时AB的运动方向与C相反
若AB与C发生碰撞后AB的速度为0,由动量守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746271641.png)
代入数据解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745070398.png)
总上所述得 当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140746583522.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745070398.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140745116524.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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