题目内容
如图所示,质量为
=50
的人站在长度为
=4.0
的平板车的左端,平板车始终以
=2.0m/s的速度向右匀速运动,开始人与车保持相对静止。从某一时刻起人以
=2.0m/s2的加速度在平板车上向右跑步,并从平板车的右端水平跳出。求:
(1)人水平跳出平板车时相对于地面的速度为多大?
(2)在此人跑步的全过程中,平板车向他提供了多少能量?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241150436063414.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043325303.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043340232.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043340200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043325303.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043574212.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043590190.gif)
(1)人水平跳出平板车时相对于地面的速度为多大?
(2)在此人跑步的全过程中,平板车向他提供了多少能量?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241150436063414.jpg)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043746355.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043730572.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043746355.gif)
(1)。设人经历时间
水平跳出平板车,则有:
,解得
=2.0![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043793182.gif)
所以,人跳出时的速度为:
(7分)
(2)。人向右跑步时,所受静摩擦力为:
,
所以,人对平板车产生了向左的摩擦力![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043824550.gif)
在人跑步全程中,平板车向右发生的位移为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043840509.gif)
则平板车克服f′做的功为:
,
即平板车向人提供了
的能量。(7分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043746185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043762610.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043746185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043793182.gif)
所以,人跳出时的速度为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043730572.gif)
(2)。人向右跑步时,所受静摩擦力为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043824547.gif)
所以,人对平板车产生了向左的摩擦力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043824550.gif)
在人跑步全程中,平板车向右发生的位移为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043840509.gif)
则平板车克服f′做的功为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043855620.gif)
即平板车向人提供了
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115043746355.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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