题目内容
如图6-8-27所示,细绳一端系着质量
kg的物体,静止于水平面,另一端通过光滑小孔吊着质量
kg的物体,M的中点与圆孔距离为0.2m,并知M和水平面的最大静摩擦力为2N,现使此平面绕中心轴线转动,问角速度
在什么范围m会处于静止状态?(
)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152326963135.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232634385.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232634371.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232665316.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232681188.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241152326963135.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232728531.gif)
要使m静止,M应与平面相对静止,考虑M能与水平面相对静止的两个极端状态:当
为所求范围的最小值时,M有向圆心运动的趋势,水平面对M的静摩擦力方向背离圆心;当
为所求范围的最大值时,M有远离圆心运动的趋势,水平面对M的摩擦力方向指向圆心。要使m静止,M应与平面相对静止,考虑M能与水平面相对静止的两个极端状态:
当
为所求范围的最小值时,M有向圆心运动的趋势,水平面对M的静摩擦力方向背离圆心,大小等于最大静摩擦力2N,此时对M有:
且 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232852374.gif)
解得:
rad/s.
当
为所求范围的最大值时,M有远离圆心运动的趋势,水平面对M的摩擦力方向指向圆心,且大小也为2N,此时:
且 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232852374.gif)
解得:
rad/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232665316.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232665316.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232665316.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232806465.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232852374.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232884384.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232665316.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232915471.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115232852374.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115233055385.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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