A flea is able to jump straight up about 0.47 m. It has been said that if a flea

Question

A flea is able to jump straight up about 0.47 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100-story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle is proportional to itscross-sectional area, and the work done by the muscle is this force times the length of contraction. If we magnified a flea by a factor of 1005, the cross section of its muscle would increase by 10052 and the length of contraction would increase by 1005. How high would this "super flea" be able to jump? (Don't forget that the mass of the "super flea" increases as well.)

m

Explanation / Answer

Let old mass be m
new mass, m' = 1005 m

New area , A' = 10052 A

New force applied,F' = 10052 F

ne contraction, d' = 1005 d
Work done, W' = F'*d'
= 10052 F * 1005 d
= 10052*1005 w

this work done increases potential energy:
initially:
W = m*g*h ...eqn 1

now:
W' = m'*g*h' ..eqn 2

divide eqn 2 by eqn 1
W'/W = (m'/m)*(h'/h)
10052*1005 = 1005*(h'/0.47)
h'=10052*0.47
=4724.44 m
Answer: 4724.44 m

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