题目内容
(12分)如图所示,在距水平地面高为0.4m处,水平固定一根长直光滑杆,杆上P处固定一定滑轮(大小不计),滑轮可绕水平轴无摩擦转动,在P点的右边,杆上套一质量m=3kg的滑块A。半径R=0.3m的光滑半圆形轨道竖直地固定在地面上,其圆心O在P点的正下方,在轨道上套有一质量m=3kg的小球B。用一条不可伸长的柔软细绳,通过定滑轮将两小球连接起来。杆和半圆形轨道在同一竖直面内,滑块和小球均可看作质点,且不计滑轮大小的影响。现给滑块A施加一个水平向右、大小为60N的恒力F,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008372944190.jpg)
(1)把小球B从地面拉到半圆形轨道顶点C的过程中力F做的功。
(2)小球B运动到C处时所受的向心力的大小。
(3)小球B被拉到离地多高时滑块A与小球B的速度大小相等?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008372944190.jpg)
(1)把小球B从地面拉到半圆形轨道顶点C的过程中力F做的功。
(2)小球B运动到C处时所受的向心力的大小。
(3)小球B被拉到离地多高时滑块A与小球B的速度大小相等?
(1)
;(2)
;(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837341554.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837310427.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837326458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837341554.png)
试题分析:(1)对于F的做功过程,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008373571306.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837372976.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837388853.png)
所以,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837404998.png)
(2)由于B球到达C处时,已无沿绳的分速度,所以此时滑块A的速度为零,
考察两球及绳子组成的系统的能量变化过程,由功能关系,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837419958.png)
代入已知量,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837450970.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837466653.png)
因为向心力公式为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837482675.png)
所以,代入已知量,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837497989.png)
(3)当绳与轨道相切时两球速度相等,
由相似三角形知识,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837497664.png)
代入已知量,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837528675.png)
所以,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000837544892.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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