题目内容
(16分)如图所示,在光滑水平面右端拱点处连接一个竖直的半径为R的光滑半圆形轨道
,在距离B为x的A点,用一个较大的水平力向右瞬间弹击质量为m的小钢球,使其获得一个水平向右的初速度,质点到达廖点后沿半圆形轨道运动,经过C点后在空中飞行,正好又落回到A点。求:
(1)小钢球经过C时的速度有多大?
(2)小钢球经过B时的速度有多大?
(3)在4点,这个瞬间弹击小钢球的力的冲量需要有多大?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412130090222044.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300871650.jpg)
(1)小钢球经过C时的速度有多大?
(2)小钢球经过B时的速度有多大?
(3)在4点,这个瞬间弹击小钢球的力的冲量需要有多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412130090222044.gif)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300918547.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300933712.gif)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300949724.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300918547.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300933712.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300949724.gif)
(1)小钢球经过C做平抛运动又回到A,在C的速度设为vC,空中飞行时间设为t,则
在水平方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300965372.gif)
竖直方向上
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300980501.gif)
解①②有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300918547.gif)
(2)小钢球由B→C机械能守恒,所以有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121300996783.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121301011954.gif)
(3)设在A点力F瞬间弹击小钢球的冲量大小为I,则应用动量定理有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121301027399.gif)
由A到B小球做匀速直线运动,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121301043276.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121301058835.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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