At the roller rink, two 20-kg girls accelerate toward each other until they are

Question

At the roller rink, two 20-kg girls accelerate toward each other until they are each moving at 1.0 m/sin the Earth reference frame. They then collide stomach-to-stomach, grab on to each other, and fall to the floor.

Calculate the magnitudes of the momentum of each girl before the collision and after the collision in the Earth reference frame

Calculate the magnitudes of the momentum of each girl before the collision in the reference frame of a mother who started skating with one of the girls and then continued on after the collision without changing speed. Denote the momentum of the girl that moves with the mother as p1 and the momentum of other girl as p2

Calculate the magnitudes of the momentum of each girl after the collision in the reference frame described in part B.

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Explanation / Answer

Mass of each girl = 20 kg

Let velocity of girl 1 (with respect to earth reference) be 1 m/s

then velocity of other (with respect to earth) = -1 m/s

Magnitude of Momentum of girl 1 before collision (with respect to earth)= mv = 20 * 1 = 20 Kg m/s

Magnitude of Momentum of girl 2 before collision (with respect to earth) = mv = 20*1 = 20 Kg m/s

Let velocity of girls after collision be v

By Conservation of momentum

20*1 + 20 *(-1) = (20+20)*v

=> v = 0

So momentum of each girl after collision with respect to earth's reference = 0 kg m/s

With respect to mother's reference frame

velocity of girl 1 (with respect to mother's reference) = 0 m/s

then velocity of other (with respect to mother's reference ) = -2 m/s

Magnitude of Momentum of girl 1 before collision (with respect to mother's reference), p1= mv = 20 * 0 = 0 Kg m/s

Magnitude of Momentum of girl 2 before collision (with respect to mother's reference), p2= mv = 20*2 = 40 Kg m/s

Let velocity of girls after collision be v

By Conservation of momentum

20*0 + 20 *(-2) = (20+20)*v

=> v = -1

So momentum of each girl after collision (with respect to mother's reference, that is as described in part B) = 20*1 = 20 kg m/s

So momentum of each girl after the collision in the reference frame described in part B = 20 kg m/s

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