题目内容
如下图所示,质量
kg的木块A套在水平杆上,并用轻绳将木块与质量
kg的小球B相连。今用跟水平方向成α=30°角的力
N,拉着球带动木块一起向右匀速运动,运动中M、m相对位置保持不变,取g=10m/s2。求:
小题1:运动过程中轻绳与水平方向夹角θ;
小题2:木块与水平杆间的动摩擦因数μ。
小题3:当
为多大时,使球和木块一起向右匀速运动的拉力最小?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241301027271940.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102586497.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102617407.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102680454.png)
小题1:运动过程中轻绳与水平方向夹角θ;
小题2:木块与水平杆间的动摩擦因数μ。
小题3:当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102695266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241301027271940.jpg)
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102742412.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102773481.png)
小题3:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102805649.png)
(1)对B进行受力分析,设细绳对B的拉力为T,由平衡条件可得
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241301028832277.jpg)
(1分)解得:
(1分)
,即
(1分)
(2)对A进行受力分析,由平衡条件有
(1分)
(1分)解得
(1分)
(3)对A进行受力分析,由平衡条件有
(1分)
(1分)
解得:
(1分)
令
,
,即
则:
(1分)
显然,当
时F有最小值,所以
时F的值最小。(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102836624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241301028832277.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102898786.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102929451.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102961572.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102742412.png)
(2)对A进行受力分析,由平衡条件有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103007733.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103101601.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102773481.png)
(3)对A进行受力分析,由平衡条件有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103179875.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103210569.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241301033821010.png)
令
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103413659.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103444682.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103460551.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241301035221435.png)
显然,当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130103569495.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824130102805649.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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