题目内容
如图所示,在倾角为θ=37°的粗糙斜面上,有一个质量为m=11kg的物体被水平力F推着静止于斜面上,已知物体与斜面间的动摩擦因数为μ=0.5,若物体静止不动,求推力F的范围。(设最大静摩擦力等于滑动摩擦力,取g=10m/s2,sin 37°=0.6,cos 37°=0.8)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022253916857.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022253916857.png)
20N≤F≤220N
试题分析:当物体恰好不下滑时,受力如图甲所示,(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022254063403.jpg)
由平衡条件得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002225438892.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002225453933.png)
由题意知最大静摩擦力等于滑动摩擦力,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002225469528.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022254841436.png)
当物体恰好不上滑时,受力如图乙所示,(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022255002750.jpg)
由平衡条件得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002225516882.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002225453933.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002225469528.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250022255621522.png)
故20N≤F≤220N (1分)
![](http://thumb2018.1010pic.com/images/loading.gif)
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