题目内容
(16分)如图所示:矩形区域MNPQ内有水平向右的匀强电场,虚线框外为真空区域;半径为
、内壁光滑、内径很小的绝缘半圆管ADB固定在竖直平面内,直径AB垂直于水平虚线MN,圆心O为MN的中点,半圆管的一半处于电场中。一带正电的小球从半圆管的A点由静止开始滑入管内,小球可视为质点,质量为
,电量为
,当小球达到B点时,对管壁的压力为
,重力加速度为
,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025512953343.png)
(1)匀强电场的电场强度
;(2)若小球能从矩形框的右边界NP离开电场,矩形区域MNPQ的最小面积
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551202303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551217337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551249310.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551264656.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551280273.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025512953343.png)
(1)匀强电场的电场强度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551327318.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551342321.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551373755.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551358660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551373755.png)
试题分析:(1)设小球从B点滑出时的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551405323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551420928.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551436621.png)
A到B,由动能定理有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025514511038.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551358660.png)
(2)小球从B点滑出后,在水平方向做变速直线运动,竖直方向做自由落体运动
水平方向:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551483767.png)
竖直方向:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551498462.png)
设向左减速时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551514291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551529921.png)
小球向左运动的最大距离:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551545712.png)
虚线框MNPQ的最小宽度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551561455.png)
设向左减速时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551576327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551592684.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551607720.png)
小球出电场时,下落的高度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025516231275.png)
虚线框MNPQ高度应满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551639557.png)
故虚线框MNPQ的最小面积
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002551670995.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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