题目内容
(14分)下图为仓库中常用的皮带传输装置示意图,它由两台皮带传送机组成,一台水平传送,A、B两端相距3m,另一台倾斜,传送带与地面的倾角θ=37°,C、D两端相距4.45m,B、C相距很近。水平部分AB以5m/s的速率顺时针转动。将质量为10kg的一袋大米放在A端,到达B端后,速度大小不变地传到倾斜的CD部分,米袋与传送带间的动摩擦因数均为0.5。试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030505206359.png)
(1)若CD部分传送带不运转,求米袋沿传送带所能上升的最大距离;
(2)若要米袋能被送到D端,求CD部分顺时针运转的速度应满足的条件
(3)在满足(2)问的情况下,求米袋从C 端到D 端所用时间的取值范围。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030505206359.png)
(1)若CD部分传送带不运转,求米袋沿传送带所能上升的最大距离;
(2)若要米袋能被送到D端,求CD部分顺时针运转的速度应满足的条件
(3)在满足(2)问的情况下,求米袋从C 端到D 端所用时间的取值范围。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050582624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050551825.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050566724.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050582624.png)
试题分析:(1)米袋在AB上加速时的加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050598972.png)
米袋的速度达到v0=5m/s时,滑行的距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030506291122.png)
因此米袋在到达B点之前就有了与传送带相同的速度 ,
设米袋在CD上运动的加速度大小为a,由牛顿第二定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050644898.png)
代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050676573.png)
所以能滑上的最大距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050551825.png)
(2)设CD部分运转速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050769298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050769298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030508161162.png)
米袋速度小于
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050769298.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030508631140.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030508781128.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050894555.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050566724.png)
(3)米袋恰能运到D点所用时间最长为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030509251066.png)
若CD部分传送带的速度较大,使米袋沿CD上滑时所受摩擦力一直沿皮带向上,则所用时间最短,此种情况米袋加速度一直为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050941344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250030509721061.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050988631.png)
所以,所求的时间t的范围为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003050582624.png)
(说明:若计算中选用
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003051019534.png)
先由由牛顿定律求得加速度,再由运动公式可以求得球3位移大小再由运动学公式求解
![](http://thumb2018.1010pic.com/images/loading.gif)
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