题目内容
如图12-1-6所示,一个光滑的圆弧形槽半径为R,放在水平地面上,圆弧所对的圆心角小于5°.AD的长为x,今有一小球m1以沿AD方向的初速度v从A点开始运动,要使小球m1可以与固定在D点的小球m2相碰撞,那么小球m1的速度v应满足什么条件?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415334923533.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415334923533.png)
v=
(n=1,2,3……)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533570570.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533648481.png)
把m1的运动分成两个分运动,其一是沿AD方向的匀速运
动,其二是沿AB圆弧的运动,实际相当于摆长等于圆弧槽半径
的单摆运动.
在AD方向上:x=vt ①
在AB弧上运动,等效成单摆运动:t=nT ②
又T=2π
③
由②③两式可得:t=2nπ
(n=1,2,3…)
代入①式得:v=
=
(n=1,2,3…).
动,其二是沿AB圆弧的运动,实际相当于摆长等于圆弧槽半径
的单摆运动.
在AD方向上:x=vt ①
在AB弧上运动,等效成单摆运动:t=nT ②
又T=2π
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533663490.png)
由②③两式可得:t=2nπ
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533663490.png)
代入①式得:v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533772375.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533570570.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141533648481.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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