题目内容
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154516154561.jpg)
在车厢顶上吊有一单摆,摆长为L,如下图所示,当小车向左运动时,悬线偏向竖直方向的左边一个恒定的角度,使这个单摆摆动,摆动的平面与小车的前进方向在同一平面内,测得振动周期为T,求放在该车厢地板上质量为M的物体在相对车厢静止时受到的摩擦力的大小和方向。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451630903.gif)
悬线偏离竖直方向左侧,意味着小车具有一个向右的加速度,
设车的加速度为
,球与小车相对静止时偏角为
,绳拉力为
,
则由牛顿第二定律知
,
,即![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451708538.gif)
小球摆动时,以下图所示位置为平衡位置,其等效重力加速度![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451724373.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154517402119.jpg)
由
,得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451771493.gif)
解得
,方向向右
对M运用牛顿第二定律,则
,方向向右。
设车的加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451646192.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451662201.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451677206.gif)
则由牛顿第二定律知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451677491.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451693493.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451708538.gif)
小球摆动时,以下图所示位置为平衡位置,其等效重力加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451724373.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154517402119.jpg)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451755556.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451771493.gif)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451771708.gif)
对M运用牛顿第二定律,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115451630903.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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