题目内容
(10分)如图所示,空间存在水平向右的匀强电场. 在竖直平面内建立平面直角坐标系,在坐标系的一象限内固定绝缘光滑的半径为
的1/4圆周轨道
,轨道的两端在坐标轴上。质量为
的带正电的小球从轨道的
端由静止开始滚下,已知重力为电场力的2倍,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241449198572678.png)
求:(1)小球在轨道最低点
时对轨道的压力;
(2)小球脱离
点后开始计时,经过多长时间小球运动到
点的正下方?并求出此时小球距
的竖直高度
是多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144919467303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144919514396.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144919592337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144919670300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241449198572678.png)
求:(1)小球在轨道最低点
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920013309.png)
(2)小球脱离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920013309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920013309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920013309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920466313.png)
(1)2mg (2)
8R
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920653571.png)
试题分析:(1) 小球从释放到运动至轨道最低点的过程中,由动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241449207311043.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920856729.png)
在轨道最低点时,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144920965892.png)
联立上述各式得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921043505.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921168665.png)
(2)小球的运动,在竖直方向是自由落体运动,水平方向是往返运动。
由运动的分解可知,当水平速度变为零时,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921230678.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921277724.png)
设经历
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921339267.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921386822.png)
在竖直方向上,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824144921745824.png)
点评:此题较难。解决此类问题只需要把电场力看成一个普通的恒力分析就行了;分析问题时一定要弄清物体的运动轨迹,是什么运动。
![](http://thumb2018.1010pic.com/images/loading.gif)
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