The muscle cross section increases by 500^2 = 250,000, not 5002. The energy stored in the muscle increases by area x length = 500^3 = 125,000,000. The flea's mass increases by the cube of length, or the same ratio, 125,000,000.
M g H = stored muscle energy.
H, the jumping height, is proportional to
(stored muscle energy/M)
and this ratio does not change. Neither does the height that it can jump.
A flea is able to jump straight up about 0.49 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 500, the cross section of its muscle would increase by 5002 and the length of contraction would increase by 500. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well.)
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knln
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