题目内容
在一次国际城市运动会中,要求运动员从高为H的平台上A点由静止出发,沿着动摩擦因数为μ的滑道向下运动到B点后水平滑出,最后落在水池中.设滑道的水平距离为L,B点的高度h可由运动员自由调节(取
).求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242140162152564.jpg)
(1)运动员到达B点的速度与高度h的关系;
(2)运动员要达到最大水平运动距离,B点的高度h应调为多大?对应的最大水平距离xm为多少?
(3)若图中H=4 m,L=5 m,动摩擦因数μ=0.2,则水平运动距离要达到7 m,h值应为多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214015310625.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242140162152564.jpg)
(1)运动员到达B点的速度与高度h的关系;
(2)运动员要达到最大水平运动距离,B点的高度h应调为多大?对应的最大水平距离xm为多少?
(3)若图中H=4 m,L=5 m,动摩擦因数μ=0.2,则水平运动距离要达到7 m,h值应为多少?
(1
(2)
(3)2.62 m 0.38 m
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214017011940.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214017713739.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214018789588.png)
试题分析:(1)设斜面长度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214019897263.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242140207391291.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408242140216911024.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214017011940.png)
(2)根据平抛运动公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214023376445.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214024717602.png)
由③~⑤式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214025482884.png)
由⑥式可得,当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214017713739.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214018789588.png)
(3)在⑥式中令x=2 m,H=4 m,L=5 m,μ=0.2,则可得到:
-h2+3h-1=0
求出
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214028898860.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824214030052882.png)
点评:第一问中也可以用牛顿第二定律结合运动学公式求解,哪个简便你可以去尝试比较.
求一个物理量的极值,常见的方法是把这个物理量先表示出来,通过数学知识(可以配方)求极值.
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目