High-speed motion pictures ( 3500 f r a m e s / s e c o n d ) of a jumping 300 ?

Question

High-speed motion pictures (3500frames/second) of a jumping 300?g flea yielded the data to plot the flea's acceleration as a function of time as shown in the figure(Figure 1) . (See "The Flying Leap of the Flea," by M. Rothschild et al. in the November 1973 Scientific American.) This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Use the measurements shown on the graph to answer the questions.

Find the initial net external force on the flea. How does it compare to the flea's weight? Find the maximum net external force on this jumping flea. When does this maximum force occur? Express your answer using two significant figures. Use the graph to find the flea's maximum speed. Express your answer using two significant figures.

Explanation / Answer

a)

at t = 0, a/g = 62.5

a = 62.5*9.8 = 612.5 m/s^2

F = m*a = 300*10^-6*612.5 = 0.183750 N

b)

F = m*a/(m*g) = a/g = 62.5*w


c)

a_max/g = 137.5 m/s^2

a_max = 137.5*9.8

a_max = 1347.5 m/s^2

Fmax = m*a_max = 300*10^-6*1347.5 = 0.404250 N


d)

t = 1 + (0.25/2)

= 1.125 s

e)

impulse = 300*10^-6*[ 62.5*9.8*1.25 + 0.5*1.25*(137.5-62.5)*9.8) ]

       = 0.367500 N.s

impulse = chnage in momentum

m*v = 0.367500

v = 0.367500/(300*10^-6)

v = 1225 m/s

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