Question

A 1.0kg object initially moving with a velocity of 3.0m/s to the right makes an elastic head-on collision with a 1.5kg object initially moving to the left at 2.0m/s. a) What are the final velocities of the two objects after the collision? b) Using the given initial data for the two-object system as well as your results, show that the total kinetic energy is conserved for this elastic collision.

Answer 1

taking right side as +ve and left side -ve, velocities of two objects are +3 and -2 respectively. Let these mass have velocities V1 and V2 after collision.
By momentum conservation
1x3 + 1.5x(-2) = 1xV1 + 1.5xV2
V1 + 1.5 V2 = 0 ............1

As collision is elastic, coefficient of restituition is e = 1
e is defined as (V2 - V1)/(U1 - U2)
hence 1 = (V2 - V1)/( 3 - (-2))

V2 - V1 = 5 ..............2
solving equations 1 and 2 we get
V1 = -3 m/s and V2 = 2 m/s
hence two masses are oving with same speeds as before the collision but in opposite direction.
As their speeds are same, their kinetic energy is same or toatal kinetic energy of two masses is conserved in in elastic collision.