Two friends, Al and Jo, have a combined mass of 194 kg. At the ice skating rink,

Question

Two friends, Al and Jo, have a combined mass of 194 kg. At the ice skating rink, they stand close together on skates, at rest and facing each other. Using their arms, they push on each other for 1 second and move off in opposite directions. Al moves off with a speed of 7.9 m/sec in one direction and Jo moves off with a speed of 6.7 m/sec in the other. You can assume friction is negligible. What is Al's mass? 110.58 What is Jo's mass? If you assume the force is constant during the 1 second they are pushing on each other, what is the magnitude of the force of Al on Jo? If you assume the force is constant during the 1 second they are pushing on each other, what is the magnitude of the force of Jo on Al?

Explanation / Answer

Let Al mass is m1

Jo mass is m2

Given m1 + m2 = 194 kg

initial velocities u1 = u2 = 0 m/s

final velocities v1 = 7.9 m/s

v2 = - 6.7 m/s

from conservation of momentum

(m1 * u1) + (m2 * u2) = (m1 * v1) + (m2 * v2)

0 = (m1 * 7.9) - ((194-m1) * 6.7)

m1 = 89.03 kg

1) Al's mass is 89.03 kg

2) Jo's mass is 194-89.03 = 104.97 kg

3) from impulse momentum theorem

F * t = change in momentum

F * t = (m1 * v1) - (m2 * v2)

F * 1 = (104.97 * 7.9) - (89.03 * (-6.7))

F = 1425.76 N

4)

The force of Al on Jo and the force on Jo on Al is same so

F = 1425.76 N

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