Ok I have been working on this problem and have been unable toget it. Can someon

Question

Ok I have been working on this problem and have been unable toget it. Can someone please help me?
A flea is able to jump straight up about 0.47 m. It has been said that if a flea were asbig as a human, it would be able to jump over a 100 story building!When an animal jumps, it converts work done in contracting musclesinto gravitational potential energy (with some steps in between).The maximum 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 factorof1000, the cross section of its musclewould increase by 10002 and the length of contractionwould increase by 1000. How highwould this "superflea" be able to jump? (Don't forget that the massof the "superflea" increases as well.) Ok I have been working on this problem and have been unable toget it. Can someone please help me?

Explanation / Answer

The force the flea could exert is proportional to the crosssection, so the force would increase by 10002 . The length would also increase by 1000. . So the work done would increase by  10003 . So... the work doneis        Work = m gh   . The work increases by a huge factor!! But wait asecond... . The mass also increases proportionally with the volume, whichwould be    10003  bigger... . So you would get: .      original work *10003 =   original mass *10003 * g h . notice the factors of 10003 cancel ...    and you would end up with thesame   h as the original. . Which means that if we made the flea 1000 times taller andwider and longer... it would still only be able to jump to aheightof     0.47m       . So... the work doneis        Work = m gh   . The work increases by a huge factor!! But wait asecond... . The mass also increases proportionally with the volume, whichwould be    10003  bigger... . So you would get: .      original work *10003 =   original mass *10003 * g h . notice the factors of 10003 cancel ...    and you would end up with thesame   h as the original. . Which means that if we made the flea 1000 times taller andwider and longer... it would still only be able to jump to aheightof     0.47m      

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