题目内容
(9分)如图所示,竖直平面内的光滑半圆形轨道MN的半径为R,MP为粗糙水平面.两个小物块A、B可视为质点,在半圆形轨道圆心O的正下方M处,处于静止状态.若A、B之间夹有少量炸药,炸药爆炸后,A恰能经过半圆形轨道的最高点N,而B到达的最远位置恰好是A在水平面上的落点.已知粗糙水平面与B之间的动摩擦因数为μ,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029292752978.jpg)
(1)A在轨道最高点的速度大小;
(2)B到达的最远位置离M点的距离;
(3)A与B的质量之比.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029292752978.jpg)
(1)A在轨道最高点的速度大小;
(2)B到达的最远位置离M点的距离;
(3)A与B的质量之比.
(1)
(2)x=2R (3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929306816.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929290609.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929306816.png)
试题分析:(1)A恰能经过半圆形轨道的最高点
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929337892.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929290609.png)
(2)A做平抛运动,由平抛运动规律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929368533.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929384687.png)
B到达的最远位置离M点的距离即为 x=2R (3分)
(3)炸药爆炸过程由动量守恒定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929399712.png)
A上升到N的过程,由机械能守恒定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029294151166.png)
对B,由动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250029294311007.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002929306816.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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