题目内容
如图所示,有一固定的且内壁光滑的半球面,球心为O,最低点为C,在其内壁上有两个质量相同的小球(可视为质点)A和B,在两个高度不同的水平面内做匀速圆周运动,A球的轨迹平面高于B球的轨迹平面,A、B两球与O点的连线与竖直线OC间的夹角分别为α=53°和β=37°,以最低点C所在的水平面为重力势能的参考平面,则(sin 37°=
,cos 37°=
)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036076374184.jpg)
A.A、B两球所受支持力的大小之比为4∶3
B.A、B两球运动的周期之比为4∶3
C.A、B两球的动能之比为16∶9
D.A、B两球的机械能之比为112∶51
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607590369.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607606346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036076374184.jpg)
A.A、B两球所受支持力的大小之比为4∶3
B.A、B两球运动的周期之比为4∶3
C.A、B两球的动能之比为16∶9
D.A、B两球的机械能之比为112∶51
AD
由题意可知FN=
,所以
=
=
,A选项正确;mgtan θ=m
Rsin θ,所以
=
=
,B选项错误;Ek∝v2,v=
Rsin θ,所以
=
=
,C选项错误;Ep=mgR(1-cos θ),所以
=
=
,D选项正确.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607715624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607731600.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607762692.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607777373.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607793575.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607809459.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607824766.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607840462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607855504.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607871528.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036078871007.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607918512.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607933476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607949819.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003607965445.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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