题目内容
(14分)为把货箱送到高处,搭成如图所示的传动装置,先用机械杆把货箱推至皮带底端,然后经传送带把货箱送至预定位置。A处每隔1秒就有静止的质量
的货物(可视为质点)被机械杆向左推出,机械杆对货物的推力F为恒力,大小为
,与水平面间夹角
,行至B点时撤掉F,因水平面与皮带间有转角,货物经B点时速度会突减一半,传送带若不转动,货物到达顶端的C点时速度恰好为零,C点处的工人立刻将货物搬走。已知AB的长度L=16m,货物与水平面间的动摩擦因数
,传送带BC的长度
,动传送带与水平面间倾角
,(
)试求:
(1)传送带与货箱之间的动摩擦因数
;
(2)为了加快货物的传送速度,C点处的工人转身去开动传送带开关,使传送带立刻获得
的速度逆时针转动,传送带开始动转时恰好有一货箱到达了C点,工人却未能及时将其搬走而造成与下一个货箱在传送带上相撞。求这两个货物箱在传送带上相撞的位置到C点的距离
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000806968585.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000806968576.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000806984506.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000806999458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807015520.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807030491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807046657.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008070625978.jpg)
(1)传送带与货箱之间的动摩擦因数
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807062355.png)
(2)为了加快货物的传送速度,C点处的工人转身去开动传送带开关,使传送带立刻获得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807077558.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807108321.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008071401008.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807124568.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008071401008.png)
试题分析:(1)设货箱在AB段运动的加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807155315.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807171351.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807202344.png)
AB段根据牛顿第二定律水平方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008072181001.png)
竖直方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807233909.png)
根据匀变速直线运动规律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807249618.png)
设货物进入皮带时速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807264384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807280562.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807296651.png)
在皮带上受力分析可知沿皮带方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008073111124.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807124568.png)
(2)皮带未转时,货箱从B点至C点用时为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807342737.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807358352.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807374334.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807405291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807420375.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807420343.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807436447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008074671052.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807483609.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807498896.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807514720.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807530752.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807545337.png)
接下货箱1按原状态继续沿斜面匀加速,货箱2将以不同于原加速度沿斜面向上匀减速,设加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807576346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807592327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807608431.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008076231632.png)
两货箱相碰的位置与C点距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000807639901.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008071401008.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目