题目内容
(18分)在“极限”运动会中,有一个在钢索桥上的比赛项目.如图所示,总长为
的均匀粗钢丝绳固定在等高的
、
处,钢丝绳最低点与固定点
、
的高度差为
,动滑轮起点在
处,并可沿钢丝绳滑动,钢丝绳最低点距离水面也为
.若质量为
的人抓住滑轮下方的挂钩由
点静止滑下,最远能到达右侧
点,
、
间钢丝绳相距为![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934290169.png)
,高度差为
.若参赛者在运动过程中始终处于竖直状态,抓住滑轮的手与脚底之间的距离也为
,滑轮与钢丝绳间的摩擦力大小视为不变,且摩擦力所做功与滑过的路程成正比,不计参赛者在运动中受到的空气阻力、滑轮(含挂钩)的质量和大小,不考虑钢索桥的摆动及形变.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019343839671.jpg)
(1)滑轮与钢丝绳间的摩擦力是多大?
(2)若参赛者不依靠外界帮助要到达
点,则人在
点处抓住挂钩时至少应该具有多大的初动能?
(3)比赛规定参赛者须在钢丝绳最低点脱钩并到达与钢丝绳最低点水平相距为
、宽度为
,厚度不计的海绵垫子上.若参赛者由
点静止滑下,会落在海绵垫子左侧的水中.为了能落到海绵垫子上,参赛者在
点抓住挂钩时应具有初动能的范围?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009279.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934102309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934102309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934149303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934149303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934196339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934243313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934243313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934102309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934290169.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934321494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934336553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934352313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019343839671.jpg)
(1)滑轮与钢丝绳间的摩擦力是多大?
(2)若参赛者不依靠外界帮助要到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934102309.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
(3)比赛规定参赛者须在钢丝绳最低点脱钩并到达与钢丝绳最低点水平相距为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934430348.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934446278.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934009300.png)
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019346481699.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934617920.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934633927.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019346481699.png)
试题分析: (1)根据动能定理,参赛者在A到C的过程中满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934664917.png)
将
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934321494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934336553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934617920.png)
(2)根据动能定理,参赛者在A到B的过程中满足
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934742690.png)
将①式代入,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934633927.png)
(3)参赛者落到海绵垫的过程是平抛运动。设人脱离钢索时的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934773262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934789250.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934804401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934820829.png)
由题意知,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934867411.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934882930.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934914412.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934929990.png)
设参赛者在A点抓住挂钩的初动能为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001934945384.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019350381144.png)
由此可得,参赛者在A点抓住挂钩的最小和最大初动能分别为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019350541263.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019350701355.png)
即初动能范围为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250019352721726.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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