flea is able to jump straight up about 0.37 m. It has been said that if a flea w

Question

flea is able to jump straight up about 0.37 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 900, the cross section of its musclewould increase by 9002 and thelength of contraction would increase by 900. How high would this "superflea" be able to jump?(Don't forget that the mass of the "superflea" increases as well.)

Explanation / Answer

given the maximum force applied is praportionalto cross sectional area of muscle                                   F A and                         F l                                   l = length of contraction                   potential energy achived by the flea on jumping to a height h willbe                          U = mgh = k*A*l                      k = force constant which has the pressure untis          since theflea mgnified by a factor 900 , mass of the flea m'= 900m
              m = intial mass of flea           if h' height reached by flea after mgnifuication                             k=    m*h / A* l = m' * h' /A'*l'                        m' = 900m                        A' = 900A                        l' = 900l                                        pluggingin the above equation                              h' = 900h                            given h = 0.37m                                                                                     

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