For its size, the common flea is one of the most accomplished jumpers in the ani

Question

For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.20 mm -long, 0.480 mg critter can reach a height of 16.0 cm in a single leap. Neglecting air drag, what is the takeoff speed of such a flea? Calculate the kinetic energy of this flea at takeoff and its kinetic energy per kilogram of mass Km = J/kg If a 78.0 kg , 2.00 m -tall human could jump to the same height compared with his length as the flea jumps compared with its length, how high could he jump, and what takeoff speed would he need? In fact, most humans can jump no more than 60.0 cm from a crouched start. What is the kinetic energy per kilogram of mass at takeoff for such a 78.0 kg person? Where does the flea store the energy that allows it to make such a sudden leap?

Explanation / Answer

GPE = mgh = KE = 0.5m*v^2
so flea takeoff speed v = sqrt(2gh) = sqrt(19.6*0.16) = 1.77 m/s (indep of mass)

can use KE of flea = GPE = 0.48*10^-3kg * 9.8m/s^2 * 0.2m = 9.40 *10^-4 J

KE of flea per kg = 1.56 J /kg (Note: this = v^2 / 2 = g*h, indep of mass!)

Human jump relative height = 0.16m * 2000mm/2.20mm = 145 m

Human relative takeoff speed = sqrt(2*g*h) = sqrt(19.6*145) = 53.3 m/s

KE of human per kg = g*h = 9.8m/s^2 * 0.6m m/s = 5.88 J/kg (indep of mass)

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