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 asa human, it would be able to jump over a 100 story building! Whenan animal jumps, it converts work done in contracting muscles intogravitational potential energy (with some steps in between). Themaximum force exerted by a muscle is proportional to itscross-sectional area, and the work done by the muscle is this forcetimes the length of contraction. If we magnified a flea by a factorof 750, the cross section of its musclewould increase by 7502 and thelength of contraction would increase by 750. How high would this "superflea" be able to jump?(Don't forget that the mass of the "superflea" increases aswell.)
1 m

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 =750A1             h1 = 0.50 m             m2 = 750m1         then          h2=(A2x2h1/A1x1)*m1/m2               =m1/750m1)(600A1/A1)(600x1/x1)*h1                = 750*0.50                = 375m       here A2 =750A1             h1 = 0.50 m             m2 = 750m1         then          h2=(A2x2h1/A1x1)*m1/m2               =m1/750m1)(600A1/A1)(600x1/x1)*h1                = 750*0.50                = 375m

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