A penguin (m=15kg) standing on a frictionless sheet of ice catches an octupus(m=

Question

A penguin (m=15kg) standing on a frictionless sheet of ice catches an octupus(m=10kg) thrown at a speed of 4.0m/s. How fast will the penguin holding the octupus move after the collision? How much kinetic energy was lost during this collision? If the penguin slides back onto a spring with a constant of 100N/m, what is the maximum the spring will compress? If the penguin recoils from the spring in an elastic collision, how much total impulse does the penguin transfer to the spring over the course of the collision?

Explanation / Answer

By momentum conservation, we can find final velocity of penguin and octopus which move together.
10kg*4m/s = (10+15)kg v
v = 4*10/25 = 1.6 m/s
KE lost = 0.5*10*4*4 - 0.5*25*1.6*1.6 = 48 J

FOR maximum compression in spring,
0.5*25*1.6*1.6 = 0.5*100*x^2
x = sqrt (0.64)
= 0.8 m
impulse transferred = change in momentum of penguin
= 25*1.6 - -25*1.6
= 80 kg m/s

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