题目内容
一卡车拖挂一相同质量的车厢,在水平直道上以
的速度匀速行驶,其所受阻力可视为与车重成正比,与速度无关。某时刻,车厢脱落,并以大小为
的加速度减速滑行。在车厢脱落
后,司机才发觉并紧急刹车,刹车时阻力为正常行驶时的3倍。假设刹车前牵引力不变,求卡车和车厢都停下后两者之间的距离。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414153647.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414277616.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414355424.png)
36m
设卡车的质量为M,车所受阻力与车重之比为
;刹车前卡车牵引力的大小为
,
卡车刹车前后加速度的大小分别为
和
。重力加速度大小为g。由牛顿第二定律有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241514149791928.png)
设车厢脱落后,
内卡车行驶的路程为
,末速度为
,根据运动学公式有
⑤
⑥
⑦
式中,
是卡车在刹车后减速行驶的路程。设车厢脱落后滑行的路程为
,有
⑧
卡车和车厢都停下来后相距
⑨
由①至⑨式得
10
带入题给数据得
11
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414480301.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414589302.png)
卡车刹车前后加速度的大小分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414714315.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414901344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241514149791928.png)
设车厢脱落后,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151414355424.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151415182283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151415323298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151415494782.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151415713569.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151415806600.png)
式中,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151415931316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151416040286.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151416181570.png)
卡车和车厢都停下来后相距
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151416259582.png)
由①至⑨式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241514164461119.png)
带入题给数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151416586636.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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