题目内容
如图,竖直放置的斜面下端与光滑的圆弧轨道BCD的B端相切,圆弧半径为R,∠COB=q,斜面倾角也为q,现有一质量为m的小物体从斜面上的A点无初速滑下,且恰能通过光滑圆形轨道的最高点D.已知小物体与斜面间的动摩擦因数为m,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508469582087.jpg)
(1)AB长度l应该多大。
(2)小物体第一次通过C点时对轨道的压力多大。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508469582087.jpg)
(1)AB长度l应该多大。
(2)小物体第一次通过C点时对轨道的压力多大。
(1)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508470041095.png)
试题分析:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508471144879.jpg)
(1)因恰能过最高点D:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824150847176718.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508473161014.png)
物体从A运动到D全程,由动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508473791501.png)
联立求得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508475661184.png)
(2)物体从C运动到D的过程,设C点速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824150847660316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241508478001014.png)
物体在C点时:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824150847925869.png)
联立求得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824150847987681.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824150848050528.png)
点评:中等难度。解决此类问题的常规思路是利用机械能守恒求速度和竖直平面内合外力等于向心力求外力,但如果机械能不守恒,一般用动能定理求解。
![](http://thumb2018.1010pic.com/images/loading.gif)
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