Ball 1, with a mass of 120g and traveling at 11m/s , collides head on with ball

Question

Ball 1, with a mass of 120g and traveling at 11m/s , collides head on with ball 2, which has a mass of 310g 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?

Express your answer using two significant figures.

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

Express your answer using two significant figures.

Explanation / Answer

Let u be the initial velocity of ball 1 and 0 be the initial velocity of ball 2.

Conservation of Momentum: m1u + 0 = m1V1 + m2V2
rearrange to solve for V2. V2 = (m1u - m1v1)/m2

Kinetic energy is conserved, and it is elastic so...
.5*m1u^2 = .5*m1V1^2 + .5*m2V2^2
Multiply by 2, solve for V1, and plug in the momentum equation for V2:
V1 = u * ((m1-m2)/(m1+m2))

V1 = 11*((.12-.31)/(.12+.31)) = -4.86 m/s

(going back to the first equation) V2 = ((.12*11) - (.12* -4.86))/ .31 = 6.14 m/s


For Inelastic:
V1 = V2 = m1*u/ (m1+m2)
(.12*11)/(.12+.31) = 3.07 m/s

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