题目内容
如图所示,一质量m1=0.2kg的小球,从光滑水平轨道上的一端A处,以v1=2.5m/s的速度水平向右运动. 轨道的另一端B处固定放置一竖直光滑半圆环轨道(圆环半径比细管的内径大得多),轨道的半径R=10cm,圆环轨道的最低点与水平轨道相切;空中有一固定长为15cm
的木板DF,F端在轨道最高点C的正下方,竖直距离为5cm。水平轨道的另一端B处有一质量m
2=0.2kg的小球,m1、m2两小球在B处发生的是完全弹性碰撞,重力加速度为g=10m/s2. 求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241243076042901.gif)
(1)经过C点时,小球m2对轨道的作用力的大小及方向?
(2)m2小球打到木板DF上的位置?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430757372.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430758872.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241243076042901.gif)
(1)经过C点时,小球m2对轨道的作用力的大小及方向?
(2)m2小球打到木板DF上的位置?
(1)在B处m1与m2发生的是完全弹性碰撞,
有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241243076042901.gif)
①(2分)
②(2分)
由①②式解得:
(1分)
(或:因m1与m2发生的是完全弹性碰撞,且
,所以,两球交换速度。得:
。同样给这5分)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430811973.gif)
由B到C的过程,机械能守恒,有
③(2分)
由③代入数据得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308197508.gif)
在C点
,对m2根据牛顿第二定律
:
④(2分)
由④代入数据得:
(2分)
据牛顿第三定律知:小球
对轨道的作用力大小为2.5N,方向竖直向上(1分,没有指明方向不给这1分)
(2)小球从C飞出做平抛运动,有
⑤(2分)
⑥(2分)
由⑤⑥解得:
,所以物体刚好落在木板的D点上(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430761972.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241243076042901.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124307697570.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124307713786.gif)
由①②式解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124307729371.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124307744563.gif)
(或:因m1与m2发生的是完全弹性碰撞,且
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124307760391.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124307729371.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308087517.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430811973.gif)
由B到C的过程,机械能守恒,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308181825.gif)
由③代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308197508.gif)
在C点
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430824372.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430824372.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308275631.gif)
由④代入数据得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308290458.gif)
据牛顿第三定律知:小球
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412430757372.gif)
(2)小球从C飞出做平抛运动,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308321371.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308337504.gif)
由⑤⑥解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124308353530.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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