题目内容
如图甲所示,足够长的固定光滑细杆与地面成一定倾角,在杆上套有一个光滑小环,沿杆方向给环施加一个拉力
,使环由静止开始自底端沿杆向上运动,已知拉力
及小环速度
随时间
变化的规律如图乙所示(重力加速度
取10 m/s2)。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241513153726788.png)
(1)求小环的质量大小
(2)若在1.5s末撤除力F,则撤除力F后物体经多长时间回到细杆底端
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151314888303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151314888303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315028265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315091267.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315294306.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241513153726788.png)
(1)求小环的质量大小
(2)若在1.5s末撤除力F,则撤除力F后物体经多长时间回到细杆底端
(1)2kg (2)1s
试题分析:(1)分析小环受力:重力mg,沿杆子拉力F,杆子的弹力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315590409.png)
设杆子与水平方向倾角为θ,在0~1s内有F=5N,小环匀加速运动,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241513156992092.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315762804.png)
1s后F=4N,小环匀速运动,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315840793.png)
由图像知,0~1s内加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151315980669.png)
解得m=2kg
(2) 0~1s内小环向上匀加速运动的位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316105897.png)
在1~1.5s内匀速运动的位移
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316308718.png)
撤除力F后,小环运动加速度大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316386345.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316510741.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316635617.png)
撤除力F后小环继续向上减速运动,初速度v=0.5m/s,到达最高点的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316869758.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151316978291.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151317119929.png)
到达最高点后,小环向下加速运动,设小环由最高点到底端时间为t2
有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151317197865.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151317306575.png)
撤除力F后小环运动到杆子底端总时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824151317368639.png)
点评:中等难度。多过程问题可以把每个小过程分开研究,把一个大题拆成多个小题研究可以使问题简化。
![](http://thumb2018.1010pic.com/images/loading.gif)
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