题目内容
如图所示,左侧为一个半径为R的半球形的碗固定在水平桌面上,碗口水平,O点为球心,碗的内表面及碗口光滑。右侧是一个固定光滑斜面,斜面足够长,倾角θ=30°。一根不可伸长、不计质量的细绳跨在碗口及光滑斜面顶端的光滑定滑轮两端上,线的两端分别系有可视为质点的小球m1和m2,且m1>m2。开始时m1恰在碗口水平直径右端A处,m2在斜面上且距离斜面顶端足够远,此时连接两球的细绳与斜面平行且恰好伸直。当m1由静止释放运动到圆心O的正下方B点时细绳突然断开,不计细绳断开瞬间的能量损失。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500040226610648.png)
(1)求小球m2沿斜面上升的最大距离s;
(2)若已知细绳断开后小球m1沿碗的内侧上升的最大高度为
,求
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500040226610648.png)
(1)求小球m2沿斜面上升的最大距离s;
(2)若已知细绳断开后小球m1沿碗的内侧上升的最大高度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402266414.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402297443.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402328321.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250004023131295.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402328321.png)
试题分析:(1)设重力加速度为g,小球m1到达最低点B时m1、m2速度大小分别为v1、v2,由运动合成与分解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402328526.png)
对m1、m2组成的系统由功能关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250004023601204.png)
根据几何关系得:h=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402375344.png)
设细绳断后m2沿斜面上升的距离为s′,对m2由机械能守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250004023911085.png)
根据几何关系得:小球
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402406386.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402375344.png)
联立①②③④⑤解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250004024381387.png)
(2)对m1由机械能守恒定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402453892.png)
联立①②③⑦得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000402469944.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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