题目内容
(20分) 一传送带装置示意图如图,其中传送带AB段是水平的,CD段是倾斜的,动摩擦因数均为
,AB段和CD段通过极短的BC段平滑连接.现将大量的质量均为m的小货箱一个一个在A处放到传送带上,放置时初速为零,经传送带运送到D处,D和A的高度差为h.稳定工作时传送带速度保持不变,始终为v,CD段上各箱等距排列,相邻两箱的距离为L.每个箱子在A处投放后,在到达B之前已经相对于传送带静止,且以后也不再滑动(忽略经BC段时的微小滑动).传送带由电动机带动,传送带与轮子间无相对滑动,不计轮轴处的摩擦.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003138753111.png)
(1)为了小货箱到达B点前相对于传动带静止,AB段至少多长?
(2)将每个小货箱从A点运送到D点,因摩擦产生了多少热量?
(3)求电动机的平均输出功率?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000313859311.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003138753111.png)
(1)为了小货箱到达B点前相对于传动带静止,AB段至少多长?
(2)将每个小货箱从A点运送到D点,因摩擦产生了多少热量?
(3)求电动机的平均输出功率?
(1)
;(2)
;(3)
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000313890579.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000313922534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000313937879.png)
试题分析:(1)直接运用动能定理求解:
刚开始小货箱相对于传送带有滑动,相对静止前,设货箱在传送带上滑行的距离为s,
由动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000313937848.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000313968640.png)
也可以运用运动学的知识求解:
货箱的加速度a=gμ,加速到速度为v时的时间为t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314046595.png)
传送带运动的距离为s1=vt=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314062514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314078338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314093594.png)
所以货箱在传送带上相对滑动的距离为s=s1-s2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314062514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314093594.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314093594.png)
(2) 每个小货箱从A点运送到D点只有在货箱与传送带发生相对运动时才产生热量,热量的大小等于摩擦力与相对运动距离的乘积。
Q=W=fs=mgμ×
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314093594.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314171572.png)
(3) 设T时间内运送货箱N个,,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314187576.png)
每个货箱由A点运到D点需要能量E
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000314218716.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250003142341535.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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