题目内容
如图12-1-10所示, A、B两物体的质量都为m,拉A物体的细线与水平方向的夹角为30°时处于静止状态,不考虑摩擦力,设弹簧的劲度系数为k.若悬线突然断开后,A在水平面上做周期为T的简谐运动,当B落地时,A恰好将弹簧压缩到最短,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415359253600.jpg)
(1)A振动时的振幅;
(2)B落地时的速度.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415359253600.jpg)
(1)A振动时的振幅;
(2)B落地时的速度.
(1)
(2)
gT (n=0,1,2…)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141535941709.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141536034621.png)
(1)线断前,线的拉力F=mg,
设此时弹簧伸长为x0,
Fcos30°=kx0,得x0=
.
线断后,在弹力作用下,A做简谐运动的振幅为
A=x0=
.
(2)A将弹簧压缩到最短经历的时间为
t=(
+n)T(n=0,1,2…),
在t时间末B落地,速度v为
v=gt=
gT(n=0,1,2…).
设此时弹簧伸长为x0,
Fcos30°=kx0,得x0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141535941709.png)
线断后,在弹力作用下,A做简谐运动的振幅为
A=x0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141535941709.png)
(2)A将弹簧压缩到最短经历的时间为
t=(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141536456338.png)
在t时间末B落地,速度v为
v=gt=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141536034621.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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