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 2.0 m/s in 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.

Explanation / Answer

a)

Initial Momentum of girls before collsion

Pbefore =mv =20*2=40 kg-m/s

By Conservation of momentum

20*(2)+20(-2)=(20+20)V

V=0

Final momentumof girls after collision

Pafter =0 Kg-m/s

b)

For the mother reference frame

P1,before =mv1=20*0=0 Kg-m/s

P2,before =mv2=20(2-(-2))=80 Kg-m/s

c)

By Conservation of momentum

20*0+20(4)=(20+20)V

V=2 m/s

Momentum of each girl after collision

Pafter =20*2=40 Kg-m/s

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