Problem 9) Using Conservation of Momentum and Conservation of Energy: In a broad

Question

Problem 9) Using Conservation of Momentum and Conservation of Energy: In a broadway performance, an 80.0 kg actor swings from a 3.75 m long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0 kg costar in a perfectly inelastic collision. Your goal is to predict how high (relative to the bottom of the arc) the actor and his co-star will go after he catches her. Use the following steps to help you! Use conservation of energy to determine the speed of the actor just before he collides with his costar. a) b) During the instant of the collision, is there a net force acting on the system of the star+costar? What does this tell you about the total momentum of the system? Find the speed of the system (star+costar) just after the collision. c) d) Use conservation of energy to determine the maximum height to which the star+costar rise in their swing after the collision. Problem 9 (a) 8.57 m/s (c) 5.08 m/s (d) 1.32 m

Explanation / Answer

(A) PEi + KEi = PEf + KEf

m g L + 0 = 0 + m v^2 /2

v = sqrt(2 x 9.81 x 3.75)

v = 8.58 m/s

(B) Net force is zero.

that tells us that total momentum of system will be conserved(Or will not change)

(C) Pi = Pf

(80 x 8.58) + (55 x 0) = (80 + 55) v

v = 5.08 m/s

(D)energy conservation,

m v^2 / 2 + 0 = 0 + m g h

h = 5.08^2 / (2 x 9.81) = 1.32 m

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