Question

On a smooth surface, a soft 100-grams ball A at the velocity of 10 meters per second collides with another 700-grams ball B initially at rest. After collision, the two balls stick together and keep moving in the same direction as ball A. What is the velocity of the two balls after collision?

Answer 1

Let p1 be the momentum of the two balls before collision.

Momentum of ball A: pA = mass × velocity = 0.1 × 10 = 1 Kg.m/s

Momentum of ball B: pB = mass × velocity = 0.7 × 0 = 0 Kg.m/s

p1 = pA + pB = 1 Kg.m/s

After collision the two balls make one ball of mass 0.1 Kg + 0.6 Kg = 0.8 Kg. Let v be the velocity of the balls after collision. p2 the momentum of the two balls after collision is given by

p2 = 0.8 × v

Momenta are conserved, hence p1 = p2 gives

1 = 0.8 v

v = 1.25 m/s