题目内容
(10分)如图所示,一根长为1.8m,可绕
轴在竖直平面内无摩擦转动的细杆AB,两端分别固定质量1kg相等的两个球,已知OB=0.6m。现由水平位置自由释放,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025295491192.png)
(1)轻杆转到竖直位置时两球的速度?
(2)轻杆转到竖直位置时轴O受到杆的力是多大?
(3)求在从A到A’的过程轻杆对A球做的功?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529518292.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025295491192.png)
(1)轻杆转到竖直位置时两球的速度?
(2)轻杆转到竖直位置时轴O受到杆的力是多大?
(3)求在从A到A’的过程轻杆对A球做的功?
(1)1.414m/s 2.828m/s (2 )70/3N (3)8J
试题分析:(1)当轻杆转到竖直位置的过程中,据机械能守恒定律有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025295651201.png)
据圆周运动过程线速度与角速度关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529611472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529627530.png)
代入数据求得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529643681.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529658668.png)
(2)据圆周运动规律,合力提供圆周运动的向心力,则,
A球有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529674907.png)
由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529736960.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529752890.png)
所以有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529767595.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529861615.png)
则转动轴的受力为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529908797.png)
(3)当球A从A位置运动到A’位置的过程中,据动能定理有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025299231017.png)
代入数据计算得杆对球A做的功为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002529939549.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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