Question

1. Two identical carts are moving on a frictionless surface with constant velocity v (cart 1 v cart 2 -v). After they collide elastically what is their final velocities?

2. Two identical carts are moving on a frictionless surface with constant velocity v (cart 1 v cart 2 -v). After they collide inelastically they stick together. What are their final velocities?

Please explain.

Answer 1

1) Let the final velocities be v1 and v2

By the coservation of momentum we have

m1u1 + m2u2 = m1v1 + m2v2

mv - mv = mv1 + mv2

v1 + v2 = 0 -------(1)

Velocity of approach = velocity of recess

v2 - v1 = u1 - u2

v2 - v1 = v - (-v)

v2 - v1 = 2v ------(2)

adding both equation we have

v2 = v

v1 = -v

cart 1 -v Cart 2 v

2) during inelastic collision , Both the carts will stick

Let the final velocities of the block be V

conserving the momnetum we have

m1u1 + m2u2 = (m1 + m2)V

V = (m1u1 + m2u2 ) / (m1 + m2)

= mv - mv / m + m = 0