Question

At the roller rink, two 20-kg girls accelerate toward each other until they are each moving at 1.8 m/s in the Earth reference frame. They then collide stomach-to-stomach, grab on to each other, and fall to the floor. A- Calculate the magnitudes of the momentum of each girl before the collision and after the collision in the Earth reference frame. Enter your answers numerically separated by a comma. B- 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. Enter your answers numerically separated by a comma. C- Calculate the magnitudes of the momentum of each girl after the collision in the reference frame described in part B. Enter your answers numerically separated by a comma.

Answer 1

a) here,

magnitude of initial momentum of each girl = mass * velocity

magnitude of initial momentum of each girl = 20 * 1.8

magnitude of initial momentum of each girl = 36 Kg.m/s

as the collision , using conservation of momentum

let the final speed is v

v* (20 + 20) = 20 * 1.8 - 10 * 1.8

v = 0

final moemntum = 0 Kg.m/s

the final momentum of each girl = 0 Kg.m/s

b)

for the mother ,

for the girl moving with mother p1 = 0 * 20

p1 = 0 Kg.m/s

for the second girl

p2 = 20 *(1.8 - (-1.8))

p2 = 72 Kg.m/s

the momentum of second girl is 72 Kg.m/s

c)

after the collision ,

as the girls stop moving relative to grond

momentum of both girls is same as seen by mother

momentum of each girl = 20 * 1.8

momentum of each girl = 36 kg.m/s