题目内容
如图所示,光滑半球的半径为R,球心为O,固定在水平面上,其上方有一个光滑曲面轨道AB,高度为R/2.轨道底端水平并与半球顶端相切.质量为m的小球由A点静止滑下.小球在水平面上的落点为C(重力加速度为g),则( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241452331417158.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241452331417158.png)
A.将沿半球表面做一段圆周运动后抛至C点 |
B.小球将从B点开始做平抛运动到达C点 |
C.OC之间的距离为![]() |
D.小球从A运动到C的时间等于(1+![]() ![]() |
BC
试题分析:如果小球在B点的速度足够大,则小球从B点开始做平抛运动,如果速度较小则会沿半球表面做一段圆周运动后抛至C点
A、小球在B开始做平抛运动的临界条件由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233594711.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233672505.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233734845.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233797532.png)
B、理由同A选项,B选项正确
C、小球从B点开始做平抛运动,由平抛运动规律
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233875641.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233937492.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145234015622.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145234093515.png)
D、小球从B运动到C的时间由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233875641.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145234374658.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145234452648.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233204336.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233485466.png)
故选BC
点评:较难。判断小球是否沿球面运动的临界条件是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145233672505.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145234779534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145234842531.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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