问题 计算题

如图所示,一位质量m=60 kg、参加“挑战极限运动”的业余选手,要越过一宽为x=2.5 m的水沟后跃上高为h=2.0 m的平台.他采用的方法是:手握一根长L=3.25 m的轻质弹性杆一端,从A点由静止开始匀加速助跑,至B点时杆另一端抵在O点的阻挡物上,接着 杆发生形变,同时人蹬地后被弹起,到达最高点时杆处于竖直状态,人的重心在杆的顶端,此刻人放开杆水平飞出并趴落到平台上,运动过程中空气阻力可忽略不计.    

(1)设人到达B点时速度vB=8 m/s,人匀加速运动的加速度a=2 m/s2,求助跑距离xAB

(2)人要最终到达平台,在最高点飞出时刻的速度应至少多大?(g=10 m/s2)

(3)设人跑动过程中重心离地高度H=0.8 m,在(1)、(2)两问的条件下,在B点人蹬地弹起瞬间应至少再做多少功?

答案

解:(1)由运动学公式vB2=2axAB,可得xAB=16 m

(2)设人在最高点最小速度为v,人做平抛运动过程,有L-h=gt2,x=vt

解得v=x·=5 m/s

(3)人从B点至最高点过程,由动能定理得W-mg(L-H)=mv2mvB2

解之W=mg(L-H)+mv2mvB2=300 J

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Topic
★How to   小题1:your parents to give up smoking
 小题2:
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★You are either worried about their health or   小题4:with smelling their smoke.
Ways
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★Spend   小题9:time with them. For example, go for
a walk, do a puzzle, or listen to music together.
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