题目内容
(10分)如图所示,在倾角为
的足够长的斜面上,有一质量
的物体,物体与斜面之间的动摩擦因数为
,物体受到沿斜面向上的拉力
的作用,并从静止开始运动,作用
撤去力F,试求:撤去力F后多长时间物体的速度大小达到
?(g=10m/s2,
,结果保留三位有效数字)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218186753110.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818566248.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818581439.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818597295.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818612410.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818628295.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818644387.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818659452.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218186753110.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818690289.gif)
在最初的
内,物体在
的拉力作用下,从静止开始沿斜面做匀加速直线运动,据受力分析如图,根据牛顿第二定律和物体的平衡条件可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218187534615.jpg)
(1分)
(1分)
且
(1分)
由以上三式可得
(1分)
末断绳,物体的瞬时速度达到
(1分)
从绳子断开,物体继续沿斜面向上运动达到最高点速度为零的过程,设加速度为a2,经过的时间为t2,则
(1分)
(1分)
再设物体从最高点沿斜面下滑过程中加速度为
,到物体的速度大小达到
所用时间为
,则由牛顿第二定律和运动学的基本公式,得
(1分)
(1分)
综上所述,从断绳到物体速度达到
所经历的总时间为
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818722194.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818737395.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218187534615.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818768545.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818768461.gif)
且
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818784381.gif)
由以上三式可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818800849.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818815200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818862447.gif)
从绳子断开,物体继续沿斜面向上运动达到最高点速度为零的过程,设加速度为a2,经过的时间为t2,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818878893.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818893535.gif)
再设物体从最高点沿斜面下滑过程中加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818909199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818924364.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818971189.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818971662.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121818987481.gif)
综上所述,从断绳到物体速度达到
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121819002361.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121819018427.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目