题目内容
如右图所示,光滑细圆管轨道AB部分平直,BC部分是处于竖直平面内半径为R的半圆,C为半圆的最高点。有一质量为m,半径较管道略小的光滑的小球以水平初速度v0射入圆管.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242018506301123.png)
(1)若要小球从C端出来,初速度v0应满足什么条件?
(2)在小球从C端出来瞬间,对管壁压力有哪几种情况,初速度v0各应满足什么条件?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242018506301123.png)
(1)若要小球从C端出来,初速度v0应满足什么条件?
(2)在小球从C端出来瞬间,对管壁压力有哪几种情况,初速度v0各应满足什么条件?
(1)v0>
(2)有三种可能,
<v0<
.对轨道内有压力,v0=
正好没有压力,v0>
对轨道外侧有压力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201851457279.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201852720277.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201853921275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201853921275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201853921275.png)
试题分析:(1)小球恰好能达到最高点的条件是vC=0,
由机械能守恒定律,此时需要初速度v0满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201856542222.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201851457279.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201851457279.png)
(2)小球从C端出来瞬间,对管壁作用力可以有三种情况:
①刚好对管壁无作用力,此时重力恰好充当向心力,由圆周运动知识mg=m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201858913260.png)
由机械能守恒定律,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201856542222.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201856542222.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201853921275.png)
②对下管壁有作用力,此时应有mg>m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201858913260.png)
此时相应的入射速度v0应满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201852720277.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201853921275.png)
③对上管壁有作用力,此时应有mg<m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201858913260.png)
此时相应的入射速度v0应满足v0>
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824201853921275.png)
点评:本题借助机械能守恒定律求解到最高点的速度,并借助向心力知识分析对轨道压力情况。
![](http://thumb2018.1010pic.com/images/loading.gif)
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