题目内容
如图所示,传送带以v为l0m/s速度向左匀速运行,BC段长L为2m,半径R为1.8m的光滑圆弧槽在B点与水平传送带相切.质量m为0.2kg的小滑块与传送带间的动摩擦因数为0.5,g取l0m/s2,不计小滑块通过连接处的能量损失.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241240576095420.jpg)
(1) 小滑块从M处无初速度滑下,到达底端B时的速度;
(2) 小滑块从M处无初速度滑下后,在传送带上向右运动的最大距离及此过程产生的
热量;
(3) 将小滑块无初速度放在传送带C端,要使小滑块能通过N点,传送带BC段至少为多长?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241240576095420.jpg)
(1) 小滑块从M处无初速度滑下,到达底端B时的速度;
(2) 小滑块从M处无初速度滑下后,在传送带上向右运动的最大距离及此过程产生的
热量;
(3) 将小滑块无初速度放在传送带C端,要使小滑块能通过N点,传送带BC段至少为多长?
解:(1)由机械能守恒定律可知:mgR(1-cos600)=
m![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057656249.gif)
得vB=3
m/s
(2)小滑块做匀减速运动至停止时距离最大
0-
="-2aS " a="µg=5m/s2 " S="1.8m " t=
=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057749222.gif)
s
Sm=vt+
vBt="10.2m " Q=fSm=10.2J
(3)小滑块能通过N点临界条件:m
="mgsin300 " V=3m/s
由机械能守恒定律: -mgR(1+sin300)=
mv2-
m
vB=
m/s
小滑块在传送带上加速过程:
="2aS " S=6.3m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057640225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057656249.gif)
得vB=3
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057702225.gif)
(2)小滑块做匀减速运动至停止时距离最大
0-
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057656249.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057734251.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057749222.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057702225.gif)
Sm=vt+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057640225.gif)
(3)小滑块能通过N点临界条件:m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057796267.gif)
由机械能守恒定律: -mgR(1+sin300)=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057640225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057640225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057656249.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057843261.gif)
小滑块在传送带上加速过程:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124057656249.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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