## Three Balls in Successive Collisions

When three balls lie on a table and undergo collisions with each other we can apply Newton's Law of Restitution and the Law of Conservation of Momentum to each collision, obtaining simultaneous equations and solving them.

Suppose three balls, A, B and C, are on a table. All the balls have massand the coefficient of restitution between any two balls isBall A moves towards ball B, and on colliding with it, ball B moves towards ball C.

The Law of Conservation of Momentum for the first collision gives

(1)

Newton's Law of Restitution applied to the first collision gives

(2)

(1) + (2) gives

(1)-(2) gives

The Law of Conservation of Momentum for the second collision collision gives

(3)

Newton's Law of Restitution applied to the second collision gives

(4)

(3) + (4) gives

(1)-(2) gives