题目内容
如图为某种鱼饵自动投放器中的投饵装置示意图,其上半部BC是半径为R的四分之一圆弧弯管,管口与水平方向垂直,下半部AB是一长为2R的竖直细管,AB管内有一原长为R、下端固定的轻质弹簧。投饵时,每次总将弹簧长度压缩到0.5R后锁定,在弹簧上端投放一粒鱼饵,解除锁定,弹簧可将鱼饵弹射出去。设质量为m的鱼饵到达管口C时,对管壁的作用力恰好为零。若不计鱼饵在运动过程中的机械能损失,且假设锁定和解除锁定时,均不改变弹簧的弹性势能。已知重力加速度为g。求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241720111331816.png)
(1)质量为m的鱼饵到达管口C时的速度v1;
(2)质量为m的鱼饵到达管口的过程中,弹簧的弹力做的功
为多少?
(3)已知地面与水面相距1.5R,若使该投饵器绕AB管的中轴线OO’在90°角的范围内来回缓慢转动,每次弹射时只投放一粒鱼饵,鱼饵的质量在
到
之间变化,且均能落到水面。持续投放足够长时间后,鱼饵能够落在水面的最大面积S是多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241720111331816.png)
(1)质量为m的鱼饵到达管口C时的速度v1;
(2)质量为m的鱼饵到达管口的过程中,弹簧的弹力做的功
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172011367467.png)
(3)已知地面与水面相距1.5R,若使该投饵器绕AB管的中轴线OO’在90°角的范围内来回缓慢转动,每次弹射时只投放一粒鱼饵,鱼饵的质量在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172011570514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172011789337.png)
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012912693.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012272526.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012491767.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012912693.png)
试题分析:(1)由于C点时,鱼饵对管壁的作用力恰好为零,因此有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172013115750.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012272526.png)
(2)根据动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241720140351044.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241720143941386.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012491767.png)
(3)做平抛运动的时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241720150961311.png)
鱼饵的质量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172011789337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172016063686.png)
鱼饵的质量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172011570514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241720165151593.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172016749640.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172016983715.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172017233624.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172017732637.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172017951830.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172012912693.png)
点评:此题的综合性较强,对题目的审题能力也强。题中的鱼饵在最高点时对管道的作用力为零,意味着此时的速度大小为一个特定值
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824172018824430.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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