题目内容
(16分)一个质量m=1kg物体,以初速度v0=4m/s从斜面上A点沿斜面向上运动,物体沿斜面向上运动的最大距离L=1.2m,经过一段时间后物体再返回到A点,此时物体速率vt=2m/s,且返回到A点之前物体已做匀速运动.设斜面的倾角
,物体与斜面间的动摩擦因数
,物体在运动过程中受到的空气阻力大小与其速率成正比.试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219091253162.jpg)
(1)物体在运动过程中受到的空气阻力与速率的比例系数
;
(2)物体刚沿斜面向上运动时的瞬间加速度大小;
(3)物体从开始沿斜面向上运动到返回出发点所用的时间.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909110367.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909110269.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219091253162.jpg)
(1)物体在运动过程中受到的空气阻力与速率的比例系数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909141199.gif)
(2)物体刚沿斜面向上运动时的瞬间加速度大小;
(3)物体从开始沿斜面向上运动到返回出发点所用的时间.
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219092501508.gif)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219092662174.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909235980.gif)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219092501508.gif)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219092662174.gif)
(16分)解析:(1)设空气阻力为:
(2分)
(2分)
(1分)
(2)设刚抛出时物体的加速度为a0,
则:
(2分)
(2分)
(3)设物体沿斜面向上运动时的加速度为a,以沿斜面向上为正方向
则:
(1分)
取对物体取极短
时间有:
即:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909578971.gif)
得:
(1分)
对物体沿斜面向上运动的全过程累加求和有:
(1分)
即:
得:
(1分)
同理对物体沿斜面向下运动的全过程有:
(1分)
有:
(1分)
得:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219097032185.gif)
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909391270.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909422737.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909235980.gif)
(2)设刚抛出时物体的加速度为a0,
则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909484839.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219095001504.gif)
(3)设物体沿斜面向上运动时的加速度为a,以沿斜面向上为正方向
则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909531784.gif)
取对物体取极短
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909547214.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909562835.gif)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909578971.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909593963.gif)
对物体沿斜面向上运动的全过程累加求和有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219096251683.gif)
即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909640935.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219096561321.gif)
同理对物体沿斜面向下运动的全过程有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909671916.gif)
有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121909687801.gif)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241219097032185.gif)
(1分)
![](http://thumb2018.1010pic.com/images/loading.gif)
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