It takes a flea 1.0x10–3 s to reach a peak speed of 0.74 m/s.
(a) If the mass of the flea is 0.45x10–6 kg, what is the average power required?
(b) Insect muscle has a maximum output of 60 W/kg. If 20% of the flea’s weight is muscle, can the muscle provide the power needed?
(c) The flea has a resilin pad at the base of the hind leg that compresses when the flea bends its leg to jump. Assume that the uncompressed resilin pad is a cube with a side length of 6.0x10–5 m, and that the compressed pad’s thickness is so small as to be negligible. What is the energy stored in the compression of the pads of the two hind legs? The Young’s modulus for resilin is 1.7x106 N/m2.
(d) Does this provide enough power for the jump?
I'm having trouble with part c. I'm thinking I need to use the equation F/A=Y(deltaL/L), but since the compressed thickness is negligible, do I just use L=1, so that the right side of the equation reads YdeltaL?
Thanks
To solve part (c), you are correct in using the equation F/A = Y(deltaL/L). However, since the compressed thickness is negligible, you can assume that the change in length (deltaL) is equal to the uncompressed side length of the cube (6.0x10^-5 m).
Given that the Young's modulus (Y) for resilin is 1.7x10^6 N/m^2 and the area of the cube's face (A) is the square of the side length, you can calculate the force (F) exerted on the resilin pad as F = A * Y * (deltaL / L).
Since the flea has two hind legs, each with a resilin pad, you can multiply the force by 2 to get the total force exerted on both pads.
Finally, to find the energy stored in the compression of the pads, you can use the equation for elastic potential energy:
Elastic Potential Energy = (1/2) * F * deltaL
By plugging in values for F and deltaL, you can calculate the energy stored in the compression of the pads.
I hope this explanation helps clarify the approach to solving part (c). Let me know if you have any further questions!