题目内容
(14分)据报道:2012年10月14日,奥地利男子费利克斯·鲍姆加特纳在美国新墨西哥州东南部罗斯韦尔地区成功完成高空极限跳伞,从3.9万米高度起自由落体,创下纪录;时速达到约1342公里,成为不乘坐喷气式飞机或航天飞行器而超音速飞行的世界第一人.
(1)设定鲍姆加特纳连同装备总质量为
,从距地高H处由静止开始竖直下落
时达到最大速度
,打开降落伞后,到达地面时速度可忽略不计,设定他下落整个过程中各处重力加速度都为
.求:
①鲍姆加特纳连同装备从开始下落至到达地面的过程中,损失的机械能;
②由静止开始下落
达到最大速度
的过程中,克服阻力所做的功.
(2)实际上重力加速度与距地面高度有关,设定地面重力加速度数值为
,地球半径R="6400" km,求距地高度
处的重力加速度数值.(保留三位有效数字,不考虑地球自转影响)
(1)设定鲍姆加特纳连同装备总质量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203215399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203230313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203262265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203277273.png)
①鲍姆加特纳连同装备从开始下落至到达地面的过程中,损失的机械能;
②由静止开始下落
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203230313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203262265.png)
(2)实际上重力加速度与距地面高度有关,设定地面重力加速度数值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203324760.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203340710.png)
(1)①
②
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203386753.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203355837.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012033711051.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203386753.png)
试题分析: (1)①由题意知,由能量守恒定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203402948.png)
解得:损失的机械能
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203355837.png)
②对人下落
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203230313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012034491076.png)
可得克服阻力所做的功
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012033711051.png)
(2)设距地
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203480303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203496313.png)
对地表的物体有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012035111043.png)
对
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203480303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250012035581230.png)
联立解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001203386753.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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