Problem 8.15 A peacock mantis shrimp smashes its prey with a hammer-like appenda

Question

Problem 8.15 A peacock mantis shrimp smashes its prey with a hammer-like appendage by storing energy in a springlike section of exoskeleton on its appendage. The spring has a force constant of 5.9×104N/m.

Part A If the spring stores 0.0106 J of energy, over what distance must the shrimp compress it? Express your answer to two significant figures and include appropriate units.

Part B

What power does the shrimp generate if it unleashes the energy in 0.0016 s? (The power per mass of the shrimp appendage is more than 20 times greater than that generated by muscle alone, showcasing the shrimp's ability to harness the potential energy of its spring.)

Express your answer to two significant figures and include appropriate units.

Explanation / Answer

A)

k = spring constant = 59000 N

U = energy stored = 0.0106 J

x = ?

using the formula

U = (0.5) k x2

0.0106 = (0.5) (59000) x2

x = 0.0006 m

part B)

P = power = U/t = 0.0106 /0.0016 = 6.625 J

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