题目内容
如图10所示,一个与平台连接的足够长斜坡倾角
,一辆卡车的质量为
。关闭发动机,卡车从静止开始沿斜坡滑下,最大速度可达
,已知卡车运动过程中所受空气阻力和地面阻力与速度成正比,即
。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400566921314.png)
(1)求出比例系数k;
(2)现使卡车以恒定功率P沿斜坡向上行驶,达到的最大速度为54
,求功率P;
(3)当卡车开上平台后,继续保持此恒定功率行驶40s,重新匀速行驶,求卡车开上平台后到匀速行驶的过程中克服阻力所做的功。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056520742.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056552296.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056598691.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056645453.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400566921314.png)
(1)求出比例系数k;
(2)现使卡车以恒定功率P沿斜坡向上行驶,达到的最大速度为54
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056754545.png)
(3)当卡车开上平台后,继续保持此恒定功率行驶40s,重新匀速行驶,求卡车开上平台后到匀速行驶的过程中克服阻力所做的功。
(1)10Ns/m(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400570511397.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056973682.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400570511397.png)
(1)
……………………2分
……………………1分
(2)因为
,牵引力
……………………1分
当卡车向上匀速行驶时:
,由此可得:
……………………2分
……………………1分
(3)卡车开上平台后,先加速后匀速,匀速行驶的最大速度为
。
……………………2分
得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057987549.png)
根据动能定理:
……………………2分
……………1分
本题考查机车启动的两种形式,当牵引力等于阻力时速度最大,当汽车以恒定功率行驶时应用W=Pt求牵引力做功
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057098940.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400571441962.png)
(2)因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057222493.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057285534.png)
当卡车向上匀速行驶时:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057363947.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057519904.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140056973682.png)
(3)卡车开上平台后,先加速后匀速,匀速行驶的最大速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057815330.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057893659.png)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140057987549.png)
根据动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400580651084.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241400581121420.png)
本题考查机车启动的两种形式,当牵引力等于阻力时速度最大,当汽车以恒定功率行驶时应用W=Pt求牵引力做功
![](http://thumb2018.1010pic.com/images/loading.gif)
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