题目内容
(18分)如图所示,长为L的不可伸长的绳子一端固定在O点,另一端系质量为m的小球,小球静止在光滑水平面上。现用大小为F水平恒力作用在另一质量为2m的物块上,使其从静止开始向右运动,一段时间后撤去该力,物块与小球发生正碰后速度大小变为原来的一半而速度方向不变,小球恰好能在竖直平面内做圆周运动。已知重力加速度为g,小球和物体均可视为质点,试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242335203973502.jpg)
(1)小物块碰撞前速度V0的大小;
(2)碰撞过程中系统损失的机械能;
(3)恒力F作用时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242335203973502.jpg)
(1)小物块碰撞前速度V0的大小;
(2)碰撞过程中系统损失的机械能;
(3)恒力F作用时间。
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233522800762.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233520881599.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233521489610.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233522800762.png)
试题分析:(1) 小球恰好能在竖直平面内做圆周运动,即通过最高点对轨道压力为0,此时设最高点速度为V,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233523720690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233524703489.png)
小球从最低点摆到最高点过程,根据动能定理有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233525155978.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233525623560.png)
小物块和小球碰撞过程中,动量守恒定律 有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233526606966.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233520881599.png)
(2)二者碰撞前的系统总动能为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242335284631076.png)
碰撞后的动能为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242335298511410.png)
碰撞前后只有动能发生了变化,因此损失的机械能
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242335307251001.png)
(3)物块在光滑的水平桌面上,有拉力F作用时做匀加速运动,加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233531380633.png)
力F撤去后在光滑的水平面做匀速运动,设加速时间为t则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824233532628468.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242335334861163.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目