题目内容
一个内壁光滑的圆锥筒的轴线竖直,圆锥固定,有质量相同的两个小球A和B贴着筒的内壁在水平面内做匀速圆周运动,如图所示,A的半径较大,则 ( ).
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037225803441.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037225803441.jpg)
A.A球的向心力大于B球的向心力 |
B.A球对筒壁的压力大于B球对筒壁的压力 |
C.A球的运动周期大于B球的运动周期 |
D.A球的角速度小于B球的角速度 |
CD
两球贴着筒壁在水平面内做匀速圆周运动时,受到重力和筒壁对它的支持力,其中N的分力F提供球做匀速圆周运动的向心力,如图所示,由图可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037225953328.jpg)
F向=F=
①
N=
②
由上述两式可以看出,由于两个小球的质量相同,θ为定值,故A、B两球所受的向心力和它们对筒壁的压力大小是相等的,选项A、B错误.由向心力的计算公式F=mrω2和F=
mr
得
=mrω2,ω=
③
=mr
,T=2π
④
由④可知TA>TB,所以C正确.
由③可知ωA<ωB,所以D正确.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037225953328.jpg)
F向=F=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722611701.png)
N=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722626677.png)
由上述两式可以看出,由于两个小球的质量相同,θ为定值,故A、B两球所受的向心力和它们对筒壁的压力大小是相等的,选项A、B错误.由向心力的计算公式F=mrω2和F=
mr
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722642575.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722611701.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722673725.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722611701.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722642575.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003722720734.png)
由④可知TA>TB,所以C正确.
由③可知ωA<ωB,所以D正确.
![](http://thumb2018.1010pic.com/images/loading.gif)
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