题目内容
一水平的浅色长传送带上放置一煤块(可视为质点),煤块与传送带之间的动摩擦因数为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346746355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250043467771233.png)
根据“传送带上有黑色痕迹”可知,煤块与传送带之间发生了相对滑动,煤块的加速度a小于传送带的加速度a0 ,根据牛顿运动定律,可得:
,设经历时间t,传送带由静止开始加速到速度等于v0,煤块则由静止加速到v,有:
;
。由于
,故
,煤块继续受到滑动摩擦力的作用。再经过时间
,煤块的速度由
增加到
,有 :
,此后,煤块与传送带运动速度相同,相对于传送带不再滑动,不再产生新的痕迹。
设在煤块的速度从0增加到v0的整个过程中,传送带和煤块移动的距离分别为
和s,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346980163.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004347027715.png)
传送带上留下的黑色痕迹的长度![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004347042507.png)
由以上各式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346793482.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346808566.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346824474.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346855484.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346871470.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346886291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346917323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346933391.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346949650.png)
设在煤块的速度从0增加到v0的整个过程中,传送带和煤块移动的距离分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346964363.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346980163.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004346995937.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004347027715.png)
传送带上留下的黑色痕迹的长度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004347042507.png)
由以上各式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250043470731236.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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