A flea is able to jump straight up about 0.54 m. It has been said that if a flea
ID: 1788931 • Letter: A
Question
A flea is able to jump straight up about 0.54 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 its cross-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 1070, the cross section of its muscle would increase by 10702 and the length of contraction would increase by 1070. How high would this "super flea" be able to jump? (Don't forget that the mass of the "super flea" increases as well.
Explanation / Answer
As maximum force exerted by muscle is proportional to cross section area so force also increased by 10702 times.
Lets consider the mass of flea is m, length of contraction l , force exerted by flea is f then
Workdone= gravitational potential energy
W= fl =mgh
Now., M= 1070m, L= 1070l, F= 10702f
So, FL=MgH
10702×1070fl= 1070m ×g H
Substituting fl from above mentioned
10702×mgh=m gH
10702×.54 = H= 5779.08 m
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