题目内容
一辆机车挂着车厢由静止开始在水平轨道上匀加速行驶,前10s走了40m,突然机车与车厢脱钩,又过了10s,机车与车厢相距60m,若机车牵引力保持不变,求机车与车厢的质量比?(动摩擦因数为0.02,空气阻力不计,取g=10m/s2)
M:m =" 5:" 1
设机车和车厢的质量分别为M和m,机车和车厢构成的系统,在脱钩前、后受到的合外力F合不变。
F合=(M+m)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
由运动规律得,脱钩前机车和车厢的共同加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756147383.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756147307.gif)
脱钩后机车和车厢的加速度分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
F合=M
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
由(1)(2)式和
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756350368.gif)
由运动学公式得ΔS = S机-S厢 =
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756366338.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115756038309.gif)
解(3)式得M:m =" 5:" 1
![](http://thumb2018.1010pic.com/images/loading.gif)
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