A flea (mass 0.5 milligrams) can jump about 15 cm straight up in the air. a) Wha

Question

A flea (mass 0.5 milligrams) can jump about 15 cm straight up in the air.

a) What initial velocity is required for the flea to reach that height? Neglect air resistance.

b) If the flea accelerates from rest to the initial velocity you calculated in part (a) over a period of about 1 millisecond, what mechanical power is produced by the flea during that period of time?

c) Given that one kilogram of muscle can produce about 100 watts of power, is it possible that a muscular contraction could propel the flea into the air?

e) If a baby fly (mass 10 milligrams) is hovering (stationary) right above the flea when it jumps, so the flea jumps vertically into the bottom of the fly with the initial velocity calculated in part (a), what are the final velocities of both flea and fly, right after their (elastic) collision?

Explanation / Answer

(a)

initial velocity = voy

height y = 15 cm = 0.15 m

at the maximum height final velocity vf = 0

from equations of motion

vf^2 - vi^2 = 2*ay*y

0^2 - voy^2 = -2*9.8*0.15

voy = 1.71 m/s

(b)

power = W/t = KE/t = 0.5*m*voy^2/t

power = (0.5*0.5*10^-6*1.71^2)/(1*10^-3)

power = 0.000731 W <<---answer

(c)

YES

(d)

m1 = 0.5 mg (flea)            m2 = 10 mg (fly)

u1 = 1.71 m/s          u2 = 0

after collision

v1 = ?      v2 = ?

in elestic collision both momentum and energy is conserved

m1*u1 + m2*u2 = m1*v1 + m2*v2

0.5*1.71 + 10*0 = 0.5*v1 + 10*v2

0.5*m1*v1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2

0.5*1.71^2 + 10*0 = 0.5*v1^2 + 10*v2^2

v1( flea) = -1.54 m/s

v2(fly) = 0.163 m/s

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