题目内容
一半球形容器内壁光滑,半径为R,小球在容器内以ω的角速度在水平面内做匀速圆周运动,如图所示.则小球的轨道平面距离容器底的高度h为___________.不断增大ω,小球能爬到容器最高点吗?__________.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241159456603310.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241159456603310.jpg)
??h=R-
不能
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115945675265.gif)
??小球的受力如图所示,受到重力和支持力FN的作用,FN的水平分力提供小球做匀速圆周运动所需的向心力,竖直分力以平衡重力,FNcosθ=mrω2,FNsinθ=mg.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241159456912920.jpg)
??r为小球的轨道半径,由图可知r=(R-h)cotθ,代入方程,得ω2=
.所以h=
.当ω增大时,h增加,但不会等于R,因为mg需被FN的竖直分力平衡,如h=R,则θ=0°,重力无法被平衡,小球将又滑到偏低水平面运动.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241159456912920.jpg)
??r为小球的轨道半径,由图可知r=(R-h)cotθ,代入方程,得ω2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115945706304.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115945722327.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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