题目内容
如图所示,光滑水平面AB与一半圆开轨道在B点相连,轨道位于竖直面内,其半径为R,一个质量为m的物块静止在水平面上,现向左推物块使其压紧轻质弹簧,然后放手,物块在弹力作用下获得一速度,当它经B点进入半圆轨道瞬间,对轨道的压力为其重力的8倍,之后向上运动恰好能完成半圆周运动到达C点,重力加速度为g。求;
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242249521093839.png)
(1)弹簧弹力对物块做的功
(2)物块从B到C摩擦阻力做的功
( 3)物块离开C点后,再落回到水平面上时相对于C点的水平距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242249521093839.png)
(1)弹簧弹力对物块做的功
(2)物块从B到C摩擦阻力做的功
( 3)物块离开C点后,再落回到水平面上时相对于C点的水平距离
(1) 3.5mgR (2) -mgR (3)2R
试题分析:(1)物块到达B点瞬间,根据向心力公式有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224953575944.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224954417598.png)
弹簧对物块的弹力做的功等于物块获得的动能,所以有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242249553071240.png)
(2)物块恰能到达C点,重力提供向心力,根据向心力公式有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224956227770.png)
物块从B运动到C,根据动能定理有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242249575841239.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824224959472720.png)
(3)物体从C点做平抛运动,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225000798474.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225002249676.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824225004043465.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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