题目内容
(8分)如图所示,一质量为m=2kg的物体,由光滑的1/4圆弧轨道上端从静止开始下滑,然后沿粗糙水平面向右滑动4m的距离后停止.已知轨道半径R=0.8m,求:
(1)物体滑至圆弧轨道最低点B时的速度;
(2)在最低点B,物体对轨道的压力大小;
(3)在水平面上物体克服摩擦力做的功;
(4)物体与水平面间的动摩擦因数。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222519253981.jpg)
(1)物体滑至圆弧轨道最低点B时的速度;
(2)在最低点B,物体对轨道的压力大小;
(3)在水平面上物体克服摩擦力做的功;
(4)物体与水平面间的动摩擦因数。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222519253981.jpg)
(1)4m/s
(2)60N
(3)16J
(4)0.2
(2)60N
(3)16J
(4)0.2
(1)根据机械能守恒定律(以B点所在水平面势能为零)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122251940583.gif)
B点时速度为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122251972924.gif)
(2)B点时物体所受重力和支持力的合力提供向心力![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122251987571.gif)
物体对轨道的压力跟支持力大小相等为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222520031121.gif)
(3)根据动能定理:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252034532.gif)
可解得水平面上摩擦力做的功为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252050829.gif)
所以物体克服摩擦力做了16J的功。
(4)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252315183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252315510.gif)
物体与水平面间的动摩擦因数为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252518863.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122251940583.gif)
B点时速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122251972924.gif)
(2)B点时物体所受重力和支持力的合力提供向心力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122251987571.gif)
物体对轨道的压力跟支持力大小相等为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241222520031121.gif)
(3)根据动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252034532.gif)
可解得水平面上摩擦力做的功为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252050829.gif)
所以物体克服摩擦力做了16J的功。
(4)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252315183.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252315510.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252346128.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122252518863.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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