Question

Ball 1, with a mass of 130 g and traveling at 13 m/s , collides head on with ball 2, which has a mass of 310 g and is initially at rest. A)What is the final velocity of the ball 1 if the collision is perfectly elastic. B)What is the final velocity of the ball 2 if the collision is perfectly elastic. C)What is the final velocity of the ball 1 if the collision is perfectly inelastic. D)What is the final velocity of the ball 2 if the collision is perfectly inelastic?

Answer 1

Let m1 = 130g = 0.130kg and m2 = 310g = 0.310kg. The initial velocity of m1 is u1 = 13ms and that of m2 is u2 = 0m/s.

(A) Let v1 and v2 be the final velocity of m1 and m2 after collision, if the collision is perfectly elastic. Then the velocity of m1 after perfectly elastic collision is given by,

So the magnitude of velocity of m1 after collision is 5.32m/s and since its value is negative, the direction of m1 is opposite to its initial direction before collision.

(B) The velocity of m2 after perfectly elastic collision is,

So the magnitude of velocity of m2 after collision is 7.68m/s and since its value is positive, the direction of m2 after collision is same as the initial direction of m1 before collision.

(C) If the collision is pwefectly inelastic, after collision the two masses stick together and move as a single system after collision. Let v be their common velocity after collision. Applying law of conservation of momentum, we get,

So the magnitude of velocity of m1 after collision is 3.84m/s and since its value is positive, the direction of m1 after collision is same as its intial direction.

(D) Since the collision is perfectly inelastic, the magnitude of velocity of m2 after collision is also 3.84m/s and the direction of m2 after collision is same as the initial direction of m1 before collision.