Question

Consider the following special cases of collisions. In all cases, a cart of m1m1 comes in with a velocity vv and hits a cart m2m2 at rest. Most of these are answerable with either intuition or with mathematics. What are the final velocities of both carts if:

a. The collision is elastic, and both carts are the same mass? (First collision playing marbles or pool)

b. The collision is inelastic, and both carts are the same mass? (Young child tackles identical twin sibling)

c. The collision is elastic, and the mass of the first cart is very small compared to the mass of the second cart? (Rubber ball hits wall)

Answer 1

a) when the cart of mass m hits another cart of mass m, than the cart initially in motion stops and the cart at rest starts to move with the velocity with which the other cart was moving, so in this case, the second cart will start moving with velocity v.

b) here the collision is inelastic

m1*v1 = (m1+m2)*v2

because now m1 and m2 will move together,

so, m*v = 2m*v2, v2 = v/2, so they will have velocity v/2

c) In this case since m2 is very large and collision is elastic, velocity of second cart will be zero

and m1 will move with velocity v after the collision but in opposite direction.