题目内容
如图所示,把一个质量为M的三角形物体放在粗糙的水平面上,三角形物体的斜面是光滑的,用一根轻绳OB吊一个质量为m的小球(可视为质点)放在斜面上,已知AO=AB。求
(1)当三角形物体静止时,绳OB对球的拉力多大?
(2)要求整个系统处于图示静止状态,物体与水平面间的摩擦因数不得小于多少?
(3)如果剪断绳子要求三角形物体保持静止状态,则物体与水平面间的摩擦因数又要求多大?(题中假设最大静摩擦力等于滑动摩擦力)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241226218235287.jpg)
(1)当三角形物体静止时,绳OB对球的拉力多大?
(2)要求整个系统处于图示静止状态,物体与水平面间的摩擦因数不得小于多少?
(3)如果剪断绳子要求三角形物体保持静止状态,则物体与水平面间的摩擦因数又要求多大?(题中假设最大静摩擦力等于滑动摩擦力)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241226218235287.jpg)
解:(1)对球如图有
F
·cos60°=F
·cos60°
F
·sin60°+F
·sin60°=mg
联立得F
=
mg
(2)对系统如图有
F
·cos60°=f![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621964129.gif)
F
+F
·sin60°=(M+m)g![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412262210473.gif)
f
≤![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
·F![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621979313.gif)
联立得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
≥![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622213570.gif)
(3)对M如图有
F
· sin30°= f![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244180.gif)
F
=Mg+F
·cos30°
f
≤![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
·F![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244308.gif)
F
=mg·cos30°
联立得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
≥![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622432572.gif)
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621839127.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621854195.gif)
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621839127.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621854195.gif)
联立得F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621839127.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621932267.gif)
(2)对系统如图有
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621839127.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621964129.gif)
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621979313.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621839127.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412262210473.gif)
f
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621964129.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621964129.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621979313.gif)
联立得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122621964129.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622213570.gif)
(3)对M如图有
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622229299.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244180.gif)
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244308.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622229299.gif)
f
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244180.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244180.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244308.gif)
F
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622229299.gif)
联立得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622135204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622244180.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122622432572.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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