The motion of jumping insects is of interest not only to biologists, but also to

Question

The motion of jumping insects is of interest not only to biologists, but also to those who design robots. (Figure 1) shows the speed-versus-time graph for two different takeoff jumps of a 19-mg green leafhopper, as determined from high-speed videos. What is the magnitude of the average net force acting on the leafhopper's body during jump 1? Express your answer to two significant figures and include appropriate units. What is the ratio of the force found in part A to the leafhopper's weight? Express your answer to two significant figures and include appropriate units. Is the average force during jump 2 greater than, less than, or equal to the average force during jump 1? Greater than Less than Equal to

Explanation / Answer

Part a) Force, F = m(dv/dt) = 0.019 x (0.8/0.006) = 2.53 N

Part b) for jump 2

slope = a = 0.8/3 = 266.67 m/s2

Force, F = 0.019 x 266.67 = 5.06 N

for jump 1

F = 2.53 N

weight, w = mg = 0.019 x 9.81 = 0.186 N

ratio for jump 1 = 2.53/0.186 = 13.60

ratio for jume 2 = 5.06/0.186 = 27.20

c) greater than the jump 1

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