题目内容
(18分)如图21所示,一根长0.1m的细线,一端系着一个质量为0.18kg的小球,拉住线的另一端,使球在光滑的水平桌面上作匀速圆周运动,使小球的转速很缓慢地增加,当小球的转速增加到开始时转速的3倍时,细线断开,线断开前的瞬间线的拉力比开始时大40N,求:
(1)线断开前的瞬间,线的拉力大小。
(2)线断开的瞬间,小球运动的线速度。
(3)如果小球离开桌面时,速度方向与桌边的夹角为
,桌面高出地面0.8m,求小球飞出后的落地点距桌边的水平距离。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107835959.png)
(1)线断开前的瞬间,线的拉力大小。
(2)线断开的瞬间,小球运动的线速度。
(3)如果小球离开桌面时,速度方向与桌边的夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107850399.png)
(1) F=45N(6分) (2)
(6分) (3)
(6分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107866559.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107882536.png)
试题分析:(1)设开始时角速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107897379.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107913356.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107928325.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001107991302.png)
线的拉力等于向心力有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108006734.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108038640.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108053811.png)
又因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108069687.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108084562.png)
(2)设线断开时速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108116265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108131680.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011081471364.png)
(3)设桌面高度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108162313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108178266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108194877.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108209593.png)
则抛出点到桌边的水平距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001108225891.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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