题目内容
一
辆质量为2.0×103
的汽车以额定功率为
6.0×104
在水平公路上行驶,汽车受到的阻力为一定值,在某时刻汽车的速度为
,加速度为
,求(g取
):
(1)汽车所能达到的最大速度
是多大?
(2)若汽车从静止开始做匀加速直线运动(不是额定功率行驶),加速度的大小为
,则这一过程能保持多长时间?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373661885.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736634234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736680237.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736696326.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736712459.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736727526.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736743411.gif)
(1)汽车所能达到的最大速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736758309.gif)
(2)若汽车从静止开始做匀加速直线运动(不是额定功率行驶),加速度的大小为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736774494.gif)
(1) 在速度为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736712459.gif)
的时刻,由
1
2
联立得
3
当牵引力与摩擦力平衡时,速度达到最大,此时
4
代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737117473.gif)
(2)随速度增加,牵引力
的功率逐渐变大
,当功率达到额定功率时,机车达到匀加速直线运动所能达到的最大速度
,设此时机车的牵引力为
,则由牛
顿第二定律,有
5
又
6
联立解得
时间![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737429501.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736712459.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373680572.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736836457.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123736852419.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373686872.gif)
联立得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737070547.gif)
当牵引力与摩擦力平衡时,速度达到最大,此时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737086440.gif)
代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737102514.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737117473.gif)
(2)随速度增加,牵引力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373680572.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373714872.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737273205.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737289215.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373730465.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737320453.gif)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737336421.gif)
联立解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737398445.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412373739865.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123737429501.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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