A flea is able to jump straight up about 0.50 m. It has been said that if a flea

Question

A flea is able to jump straight up about 0.50 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 800, the cross section of its muscle would increase by 8002 and the length of contraction would increase by 800. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well.)

Explanation / Answer

given A flea is able to jump a height h1 = 0.50m work done in contraction of muscle is W = Fx = KAx this work done in contraction is equal to energy to jump to aheight h then KAx = mgh orA1x1/A2x2 =h1m1/h2m2 here A2 =800A1 h1 = 0.50 m m2 = 800m1 then h2=(A2x2h1/A1x1)*m1/m2    =(m1/800m1)(800A1/A1)(800x1/x1)*h1    = 800*0.50 h2 = 400 m here A2 =800A1 h1 = 0.50 m m2 = 800m1 then h2=(A2x2h1/A1x1)*m1/m2    =(m1/800m1)(800A1/A1)(800x1/x1)*h1    = 800*0.50 h2 = 400 m

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