题目内容
如下图所示,现有一质量为
、电荷量
的带电小球在水平光滑绝缘桌面上向右以
的速度匀速直线运动,某时从桌边缘D水平飞出,之后小球恰好从竖直放置的有等量异种电荷的平行金属板P、Q上端E处进入两板间,又沿直线运动碰到Q板上的F点,不计各种阻力,已知DE之间的竖直高度
,两板间的距离
,匀强电场只存在于M、N之间,取
。求:
(1)判断两板带电正负情况,求出两极板间的电势差
。
(2)小球由D到F所用总时间
。
(3)小球到达F点时的动能
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145078933964.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507768508.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507784503.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507799423.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507815430.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507815306.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507831476.gif)
(1)判断两板带电正负情况,求出两极板间的电势差
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507846350.gif)
(2)小球由D到F所用总时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507862228.gif)
(3)小球到达F点时的动能
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507877342.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145078933964.jpg)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507893561.gif)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507909439.gif)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507924476.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507893561.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507909439.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507924476.gif)
(1)小球进入电场后沿直线运动到F,此过程受力为重力和电场力,可知二者的合力一定沿EF方向,即电场力应该水平向右,因此得P板带正电,Q板带负电。
小球刚刚进入电场时,竖直方向的速度为
,则![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507955593.gif)
设小球在电场中做直线运动时,运动方向与水平方向夹角为
,
则
,
,
。
(2)小球平抛运动过程的时间为
,则
,
。
进入电场后,在水平方向上,
,
,
,
。
(3)小球到达F点时的水平速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508236577.gif)
竖直分速度
,
。
或从D到F由动能定理知:
。
小球刚刚进入电场时,竖直方向的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507940202.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507955593.gif)
设小球在电场中做直线运动时,运动方向与水平方向夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114507971200.gif)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508049742.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508080480.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145081111533.gif)
(2)小球平抛运动过程的时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508127199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508143479.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508158654.gif)
进入电场后,在水平方向上,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508174631.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508189565.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508205411.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508221544.gif)
(3)小球到达F点时的水平速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508236577.gif)
竖直分速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508252595.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114508267984.gif)
或从D到F由动能定理知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145082991610.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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