题目内容
)一绝缘“?”形杆由两段相互平行的足够长的水平直杆PQ、MN和一半径为R的光滑半圆环MAP组成,固定在竖直平面内,其中MN杆是光滑的,PQ杆是粗糙的.现将一质量为m的带正电荷的小环套在MN杆上,小环所受的电场力为重力的
.
(1)若将小环由D点静止释放,则刚好能到达P点,求DM间的距离;
(2)若将小环由M点右侧5R处静止释放,设小环与PQ杆间的动摩擦因数为μ,小环所受最大静摩擦力与滑动摩擦力大小相等,求小环在整个运动过程中克服摩擦力所做的功.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112398338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021124148335.jpg)
(1)若将小环由D点静止释放,则刚好能到达P点,求DM间的距离;
(2)若将小环由M点右侧5R处静止释放,设小环与PQ杆间的动摩擦因数为μ,小环所受最大静摩擦力与滑动摩擦力大小相等,求小环在整个运动过程中克服摩擦力所做的功.
(1) DM间的距离j4R;(2)若μ≥
,整个运动过程中克服摩擦力所做的功为
若μ<
,克服摩擦力做功![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112461849.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112398338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112445916.png)
若μ<
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112398338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112461849.png)
试题分析: (1)小球刚好到达P点时,速度为零,对小球从D点到P点过程,由动能定理得
qEx-2mgR=0-0
又由题意,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112476729.png)
联立解得,x=4R
若μ≥
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112398338.png)
设小球到达P点左侧
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112507300.png)
qE(5R-
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112507300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112507300.png)
又f=μN=μmg
联立解得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112554667.png)
所以整个运动过程中克服摩擦力所做的功为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250021125701084.png)
若μ<
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112398338.png)
小环经过往复运动,最后在P点速度为0,
据动能定理qE·5R-mg·2R-W2=0
克服摩擦力做功
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002112461849.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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