A flea is able to jump straight up about 0.51 m. It has been said that if a flea

Question

A flea is able to jump straight up about 0.51 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 a 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 1060, the cross section of its muscle would increase by 1060^2 and the length of contraction would increase by 1060. How high would this "super flea" be able to jump? (Don't forget that the mass of the "super flea" increase as well.) m

Explanation / Answer

The work done by the muscle increases by a factor 10602 x1060. But the mass also increases by the same factor.

Hence m'gh' = 10603 mgh

h'=10603x 0.51/10603 =0.51 m

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