Question

You are playing croquet with some friends. Assume the mass of the mallet is 3m and the mass of the ball is m. The time of impact between the mallet and the ball is 1.00ms. You give your mallet head an initial velocity of 2.00 m/s.

A. With what velocity does your ball roll away after you hit it if the collision is elastic? Assume the final velocity of the mallet head is 1.00m/s.

B. If m=0.454kg, what force did the mallet head exert on the ball?

C. If the mallet stuck to the ball, what is the final velocity of the mallet-ball combination?

Answer 1

Answer:

a) 3 m/s b) 1362 N c) 1.5 m/s

Explanation:

Using conversation law of momentum

M₁U₁ + M₂U₂ = M₁ V₁ + M₂V₂ where M₁ =3m, M₂ = m, time of impact t = 1 ms = 1 / 1000 in s = 0.001 s

substitute the values

a) 3m × 2 + 0 = 3m × 1 + m × V₁

6 = 3 + V₁

V₁ = 3 m/s

b) force of impact = ma = m × Δv / t = (0.454 × 3 ) / 0.001 = 1362 N where m = 0.454 kg

c) 3m× 2 + 0 = V (3m + m)

6m = 4mV

V = 6m / 4m = 1.50 m/s