A flea is able to jump straight up about 0.38 m. It has been said that if a flea

Question

A flea is able to jump straight up about 0.38 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 850, the cross section of its musclewould increase by 8502 and thelength of contraction would increase by 850. How high would this "superflea" be able to jump?(Don't forget that the mass of the "superflea" increases as well.)

Explanation / Answer

The above response is mostly correct... except for the lastline. Her answer is incorrect. . The whole point of this problem is to illustrate that thejumping height is NOT greater! Here's why: .    The work done is simply force timesdistance. The force applied by the muscles is proportional toarea of the muscles. .    The work done is equal to   mgh, the increase in potential energy (where h is the height theflea jumps to). . So now... .              force of muscles * length of contraction =   mass * g * h . When the flea becomes   850 times larger in eachdimension, the area increases by 8502  and the length increases by 850 times. So the work, on the left side, increases by : .      8502 * force of muscles *850* length of contraction =    ??? . THE PROBLEM EXPLICITY STATES "Don't forget that the mass ofthe flea increases as well". The mass is proportional to VOLUME, sothe mass increases by a factor of   8503 !!!    So now... .      8502 * force of muscles *850* length of contraction =   8503 * mass * g * h . And notice that the factors of   850 on bothsides cancel out. So what are we left with? . Same height. Even ifthe flea is 850 larger in each dimension, it can still only jump toa height of 0.38 meters

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