A 10.0g marble slides to the left with a speed of 0.400m/s on a frictionless hor

Question

A 10.0g marble slides to the left with a speed of 0.400m/s on a frictionless horizontal surface on an icy New York sidewalk and has a head-on, elastic collision with a larger 30.0g marble sliding to the right. with a speed of 0.200m/s. Find the velocity of the smaller marble after collision. Enter for moving the right and negative for motion to the left. Find the velocity of the larger marble after collision. Enter for moving the right and negative for motion to the left. What is the smaller marble's change in momentum with the same sign convention? What is the larger marble's change in momentum with the same sign convention? What is the smaller marble's change in kinetic energy? What is the larger marble's change in kinetic energy?

Explanation / Answer

Given that

m1 =10*10-3kg

m2 =30*10-3kg

u1 =0.400m/s

u2 =0.200m/s

The velocity of the first body after collision is

v1 =(m1-m2)u1/(m1+m2)+(2m2u2/m1+m2)

The velocity of the second body after collision is

v2 =(2m1/m1+m2)u1+(m2-m1)u2/(m1+m2)

Now the change in momentum is given by for the first body =m1(v1-u1) =.........

Now the change in momentum is given by for the second body =m2(v2-u2) =.........

The change in kinetic energy is given by

KE1 =(1/2)m1(v12-u12)

and KE2 =(1/2)m2(v22-u22)

Now substitute all the above values to get the required answers

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