题目内容
如图所示,一根不可伸长的轻绳两端各系一个小球a和b,跨在两根固定在同一高度的光滑水平细杆C和D上,质量为ma的a球置于地面上,质量为mb的b球从水平位置静止释放.当b球摆过的角度为90°时,a球对地面压力刚好为零,下列结论正确的是( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017438737166.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250017438737166.png)
A.ma∶mb=2∶1 |
B.ma∶mb=3∶1 |
C.若只将细杆D水平向左移动少许,则当b球摆过的角度为小于90°的某值时,a球对地面的压力刚好为零 |
D.若只将细杆D水平向左移动少许,则当b球摆过的角度仍为90°时,a球对地面的压力刚好为零 |
BD
试题分析:设b球下摆时的摆线长为L,根据机械能守恒,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001743888773.png)
到达最低点时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001743904849.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001743919623.png)
而此时a对地面的压力恰好为零,因此
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001743935563.png)
因此ma∶mb=3∶1,B正确,A错误;由以上各式可知,摆到最低点时,绳子拉力大小均为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001743919623.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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