题目内容
如图所示,倾角为45°的粗糙斜面AB底端与半径R=0.4m的光滑半圆轨道BC平滑相接,O为轨道圆心,BC为圆轨道直径且处于竖直平面内,A、C两点等高.质量m=1kg的滑块从A点由静止开始下滑,恰能滑到与O等高的D点,g取10m/s2.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011435124324.jpg)
(1)求滑块与斜面间的动摩擦因数μ;
(2)若使滑块能到达C点,求滑块至少从离地多高处由静止开始下滑;
(3)若滑块离开C处后恰能垂直打在斜面上,求滑块经过C点时对轨道的压力.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011435124324.jpg)
(1)求滑块与斜面间的动摩擦因数μ;
(2)若使滑块能到达C点,求滑块至少从离地多高处由静止开始下滑;
(3)若滑块离开C处后恰能垂直打在斜面上,求滑块经过C点时对轨道的压力.
(1)0.5 (2)2m(3)3.3N
试题分析:(1)由A到D,根据动能定理可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011435281429.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143543459.png)
(2)若滑块恰能到达C点,根据牛顿定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143559736.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143574820.png)
从高为H的最高点到C的过程,根据动能定理
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250011435901715.png)
(3)l离开C点后滑块做平抛运动,垂直打到斜面上时有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143606515.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143621864.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143637791.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143652883.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143668831.png)
在C点,根据牛顿第二定律有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143684947.png)
求得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143699655.png)
由牛顿第三定律可知,滑块对轨道的压力为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001143715740.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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