Question

Ball 1, with a mass of 140 g and traveling at 13 m/s , collides head on with ball 2, which has a mass of 330 g and is initially at rest.

1. What is the final velocity of the ball 1 if the collision is perfectly elastic?

2. What is the final velocity of the ball 2 if the collision is perfectly elastic?

3. What is the final velocity of the ball 1 if the collision is perfectly inelastic?

4. What is the final velocity of the ball 2 if the collision is perfectly inelastic?

Answer 1

IF the collision is elastic

let the velocity of ball 1 be v1 and ball2 be v2 after the collision

by the conservation of momentum we have

m1u1 + m2u2 = m1v1 + m2v2

140*13 + 330*0 = 140v1 + 330v2

1.4v1 + 3.3v2 = 18.2 --------(1)

velocity of approach = velocity of recess

v2 - v1 = u1 - u2

v2 - v1 = 13 - 0

v2 - v1 = 13 --------(2)

multiplying (2) by 1.4 and adding to (1) we have

4.7v2 = 36.4

v2 = 7.74 m/s

v1 = 7.74 - 13 = -5.25 m/s

1) 5.25 m/s

2) 7.74 m/s

when there is inelastic collision , the balls will stick and move with common velocity

by the conservation of momentum we have

m1u1 + m2u2 = (m1 + m2) V

140*13 + 330*0 = (140+330)*V

V = 3.87 m/s

3) 3.87 m/s

4) 3.87 m/s