题目内容
真空中存在空间范围足够大的、水平向右的匀强电场。在电场中,若将一个质量为m、带正电的小球由静止释放后小球的运动速度与竖直方向夹角为37°(取
)。现将该小球从该电场中某点以初速度
竖直向上抛出。求抛出之后小
球的运动过程中:
(1)小球受到的电场力的大小及方向;
(2)小球从抛出点至最高点的电势能变化量;
(3)小球的最小动量的大小及方向。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259390681.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259406205.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412325942165.gif)
(1)小球受到的电场力的大小及方向;
(2)小球从抛出点至最高点的电势能变化量;
(3)小球的最小动量的大小及方向。
(1)
mg 水平向右 (2)
(3)
方向与电场力方向夹角为37°斜向上。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259452223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259484470.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259499419.gif)
(1)根据题设条件,电场力大小![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259515732.gif)
电场力的方向水平向右。
(2)小球沿竖直方向做匀减速运动,速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259530415.gif)
沿水平方向做初速度为0的匀加速运动,加速度为ax![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259546512.gif)
小球上升到最高点的时间
此过程小球沿电场方向位移 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259593592.gif)
电场力做功W=
小球上升到最高点的过程中,电势能减少![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259484470.gif)
(3)水平速度
,竖直速度
故小球的速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259655467.gif)
由以上各式得出![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259702833.gif)
解得当![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259718944.gif)
此时
·
,即与电场方向夹角为37°斜向上
小球动量的最小值为
最小动量的方向与电场方向夹角为37°,斜向上。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259515732.gif)
电场力的方向水平向右。
(2)小球沿竖直方向做匀减速运动,速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259530202.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259530415.gif)
沿水平方向做初速度为0的匀加速运动,加速度为ax
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259546512.gif)
小球上升到最高点的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259577403.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259593592.gif)
电场力做功W=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259608590.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259484470.gif)
(3)水平速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259640376.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259530415.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259655467.gif)
由以上各式得出
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259702833.gif)
解得当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259718944.gif)
此时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259749476.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259764776.gif)
小球动量的最小值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123259780655.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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