题目内容
(10分)如图所示,长为
=5m的竖直杆上端距地面H=50m,杆正下方距杆下端
="12" m处有一薄圆环.杆由静止释放,1s后圆环也由静止释放,杆和环均不转动,不计空气阻力,取10g=
,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250018546344981.png)
(l)杆追上圆环后穿过环所用的时间;
(2)杆穿过圆环后,杆上端与圆环的最大距离,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001854463314.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001854603337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001854603489.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250018546344981.png)
(l)杆追上圆环后穿过环所用的时间;
(2)杆穿过圆环后,杆上端与圆环的最大距离,
(1)0.5s (2)8m
试题分析:(1)杆和圆环释放后均做自由落体运动,设杆下落后经时间t1下端追上圆环,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001854650972.png)
设经时间t2杆上端离开圆环,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250018546661059.png)
所以穿过圆环时间:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001854697629.png)
(2)杆落地时两者距离最远,设杆经t3落地,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001854712773.png)
圆环下降的距离:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250018547751026.png)
最大距离为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250018547901137.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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