题目内容
(12分)如图,水平地面上的矩形箱子内有一倾角为
的固定斜面,斜面上放一质量为m的光滑球。静止时,箱子顶部与球接触但无压力。箱子由静止开始向右做匀加速运动,然后改做加速度大小为a的匀减速运动直至静止,经过的总路程为s,运动过程中的最大速度为v。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049544542568.jpg)
(1)求箱子加速阶段的加速度大小a'。
(2)若a>g tan
,求减速阶段球受到箱子左壁和顶部的作用力。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954423297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049544542568.jpg)
(1)求箱子加速阶段的加速度大小a'。
(2)若a>g tan
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954423297.png)
(1)
(2)左壁作用力为0,顶部作用力![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954516772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954501742.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954516772.png)
试题分析:(1)匀加速阶段,运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954548526.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954579456.png)
匀减速阶段,运动时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954594530.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954579456.png)
全程则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954626597.png)
整理可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954501742.png)
(2)光滑球不受车厢作用力时,只有自身重力和斜面支持力,水平方向加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954657621.png)
加速度所需要的合力由斜面弹力在水平方向的分力提供,若加速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954672643.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954704643.png)
所以当
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954704643.png)
对小球受力分析如下图
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500495473513783.png)
水平竖直方向正交分解可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954750869.png)
水平方向
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954766719.png)
整理可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954797826.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004954516772.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目