题目内容
如图所示,一小物块自平台上以速度
水平抛出,刚好落在邻近一倾角为
的粗糙斜面
顶端,并恰好沿该斜面下滑,已知斜面顶端与平台的高度差
m,小物块与斜面间的动摩擦因数为
,
点离
点所在平面的高度
m。有一半径为R的光滑圆轨道与斜面AB在B点平滑连接, 已知
,
,
取
m/s2。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028169846808.png)
(1)小物块水平抛出的初速度
是多少;
(2)小物块能够通过圆轨道,圆轨道半径R的最大值。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816797325.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816813508.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816828396.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816844562.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816859459.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816875300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816891309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816906442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816922658.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816937665.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816953273.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816969298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028169846808.png)
(1)小物块水平抛出的初速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002816797325.png)
(2)小物块能够通过圆轨道,圆轨道半径R的最大值。
(1)
m/s; (2)R最大值为
m
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817015507.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817031449.png)
试题分析:(1)小物块自平台做平抛运动,由平抛运动知识得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028170471145.png)
由于物块恰好沿斜面下滑,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817062784.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817015507.png)
(2)设小物块过圆轨道最高点的速度为v,受到圆轨道的压力为N。则由向心力公式得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817093886.png)
由功能关系得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250028171092825.png)
小物块能过圆轨道最高点,必有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817140478.png)
联立以上各式并代入数据得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817156587.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002817031449.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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