On average, froghopper insects have a mass of 12.6 mg and jump to a height of 43

Question

On average, froghopper insects have a mass of 12.6 mg and jump to a height of 433 mm. The takeoff velocity is achieved as the little critter flexes its legs over a distance of approximately 2.00 mm. Assume a vertical jump with constant acceleration.

1) How long does the jump last (the jump itself, not the time in the air)? (Express your answer to three significant figures.)

2) What is the froghopper’s acceleration during that time? (Express your answer to three significant figures.)

3) What force did the ground exert on the froghopper during the jump? Express your answer in millinewtons. (Express your answer to three significant figures.)

4) What force did the ground exert on the froghopper during the jump? Express your answer as a multiple of the insect’s weight. (Express your answer to three significant figures.)

Explanation / Answer

1) initial jump velocity is v.

at maximum height, speed = 0

using vf^2- vi^2 = 2ad ( when it is in air)

0^2 - v^2 = 2(-9.81) (0.433)

v = 2.91 m/s

this speed achieved in 2 mm = 0.002 m distance from rest.

using vf^2 - v^2 = 2ad

2.91^2 - 0^2 = 2(a)(0.002)

a = 2117.02 m/s^2

using v= u + at

2.91 = 0 + 2117.02t

t = 1.37 x 10^-3 sec

2) a = 2117.02 m/s^2

3) F = ma = 12.6 x 10^-6 x 2117.02 = 0.0267 N or 26.7 mN

4) F = 0.0267 / (12.6 x 10^-6 x 9.81) = 216 times weight

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.