题目内容
(8分)如图所示,A、B两物体的质量都为m,拉A的细线与水平方向的夹角为30°时,物体A、B处于静止状态,设弹簧的劲度系数为k;某时刻悬线突然断开,A在水平面上做周期为T的简谐运动,B自由下落,当B落地时,A恰好将弹簧压缩到最短,,不计一切摩擦阻力,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241453509392461.jpg)
求:(1)A振动时的振幅;
(2)B落地时的速度.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241453509392461.jpg)
求:(1)A振动时的振幅;
(2)B落地时的速度.
(1)
(2) v=gt=
gT.(n=0,1,2…)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145350954709.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145351001637.png)
试题分析:(1)线断前,线的拉力F=mg
设此时弹簧伸长为x0,Fcos30°=kx0
则A做简谐运动的振幅为:A=x0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145350954709.png)
(2)A将弹簧压缩到最短经历的时间t=(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145351110338.png)
在t时间末,B落地,速度v=gt=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824145351001637.png)
点评:由于简谐运动的重复性使得本题的运动时间的多解,这是本题应该注意的问题
![](http://thumb2018.1010pic.com/images/loading.gif)
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