题目内容
(14分)如图所示,弧形轨道的下端与半径为R的圆轨道平滑连接。现在使小球从弧形轨道上端距地面2R的A点由静止滑下,进人圆轨道后沿圆轨道运动,轨道摩擦不计。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500264552121670.png)
试求:
(1)小球到达圆轨道最低点B时的速度大小;
(2)小球在最低点B时对轨道的压力大小;
(3)小球在某高处脱离圆轨道后能到达的最大高度。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500264552121670.png)
试求:
(1)小球到达圆轨道最低点B时的速度大小;
(2)小球在最低点B时对轨道的压力大小;
(3)小球在某高处脱离圆轨道后能到达的最大高度。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645568707.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645537591.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645552660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645568707.png)
试题分析:⑴小球从A到B的过程中,由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645584856.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645537591.png)
⑵在B点,由牛顿第二定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645615908.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645552660.png)
⑶根据机械能守恒,小球不可能到达圆周最高点,但在圆心一下的圆弧部分速度不等0,弹力不等于0,小球不会离开轨道。设小球在C点(OC与竖直方向的夹角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645708297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645740939.png)
小球从A到C的过程中,由机械能守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026457551260.png)
由③④得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645771643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645786770.png)
离开C点后做斜上抛运动,水平分速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645818552.png)
设小球离开圆轨道后能到达的最大高度h处为D点,则D点的速度即水平方向大小等于
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645818552.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250026458641284.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002645568707.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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