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6 Oct 2020
A flea is able to jump about 0.5 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 exported by a muscle is proportional to its cross-sectional area, and the work is done by the muscle in this force times the length of contraction. If we magnified a flea by a factor of 1000, the cross-section of its muscle would increase by 10002 and the length of contraction would increase by 1000. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well."
A flea is able to jump about 0.5 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 exported by a muscle is proportional to its cross-sectional area, and the work is done by the muscle in this force times the length of contraction. If we magnified a flea by a factor of 1000, the cross-section of its muscle would increase by 10002 and the length of contraction would increase by 1000. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well."
KathLv10
11 Nov 2020
