题目内容
如图所示,一个小物块以一定初速从光滑斜面上的a点沿斜面上滑,能到达的最高点是b,c为ab的中点。已知小物块从a上滑到c的时间为t,求小物块从c点经b点再回到a点所用时间。已知上滑和下滑时小物块的加速度相等。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641727351.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641727351.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641743369.gif)
逆向分析小物块从a到b的运动,可以看成是初速度为零的匀加速运动。
根据特殊结论有:
,而![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641758301.gif)
又由于上滑和下滑时小物块的加速度相等,所以上滑过程和下滑过程是对称的即:
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641789275.gif)
小物块从c点经b点再回到a点所用时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641805352.gif)
由上几式可得:
, 即所求时间为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641743369.gif)
根据特殊结论有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641743393.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641758301.gif)
又由于上滑和下滑时小物块的加速度相等,所以上滑过程和下滑过程是对称的即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641774275.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641789275.gif)
小物块从c点经b点再回到a点所用时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641805352.gif)
由上几式可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641743369.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114641743369.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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