A flea is able to jump straight up about 0.54 m. It has been said that if a flea

Question

A flea is able to jump straight up about 0.54 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 1070, the cross section of its muscle would increase by 1070^2 and the length of contraction would increase by 1070. How high would this "super flea" be able to jump? (Don't forget that the mass of the "super flea" increases as well.

Explanation / Answer

The F is proportional to the crossectional area, so it's multiplied by 1000. Since the mass is multiplied by 1000, acceleration remains the same.

The Work will be 1000F * 1000, so it will be 1 million times the original amount of work.

Now, d = vi(t) + 1/2at^2, where vi(t) = 0.

d = 1/2 at^2 - the flea still jumps the same distance, despite it's magnification, because the acceleration remains the same.

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