题目内容
如图所示,竖直光滑的杆子上套有一滑块A,滑块通过细绳绕过光滑滑轮连接物块B,B又通过一轻质弹簧连接物块C,C静止在地面上。开始用手托住A,使绳子刚好伸直处于水平位置但无张力,现将A由静止释放,当速度达到最大时,C也刚好同时离开地面,此时B还没有到达滑轮位置.已知:mA="1.2kg," mB="1kg," mc=1kg,滑轮与杆子的水平距离L=0.8m。试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242357432485908.jpg)
(1)A下降多大距离时速度最大
(2)弹簧的劲度系数
(3)A.B的最大速度是多少
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242357432485908.jpg)
(1)A下降多大距离时速度最大
(2)弹簧的劲度系数
(3)A.B的最大速度是多少
(1)
(2)
(3)
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235746259884.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235743669477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235744558606.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235745432898.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235746259884.png)
试题分析:(1)当A速度达到最大时,即加速度等于0的时候,此时C也刚好同时离开地面,那么对B和C整体分析只有绳子拉力,因此此时绳子拉力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235746945922.png)
A下降过程受力分析如图
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082423574878612077.png)
当A的速度最大加速度等于0时,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235750003743.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235751453464.png)
假设A下降的高度为h,则根据几何关系可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235752811654.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235754199842.png)
(2)根据第一问的几何关系如上图,A下降
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235743669477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235757007813.png)
那么绳子拉长的长度也就是B上升的高度就是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235758411606.png)
初始状态,绳子无张力,对B分析有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235759862617.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235801094550.png)
末状态,C刚好离开地面,对C分析有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235801968634.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235803450572.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235804682678.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235805634704.png)
(3)由第二问可知,初状态弹簧压缩
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235807131753.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235808301772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242358097681896.png)
有几何关系可得AB的速度关系有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235811250628.png)
带入计算得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235745432898.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824235746259884.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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