Question

3) On a squash court on planet Omicron Persei 8, a 0.25 kg squash ball is released from a 10 m height. After the first bounce, the ball reaches a maximum height of 6 m. Ignore air resistance. If the ball loses 8 J of energy during impact with the ground, calculate the acceleration due to gravity (in ?/?2) on Omicron Persei 8. Assume the ball fell initially from rest. Express your answer with two significant figures.

Answer 1

Gravitational acceleration on Omicron Persei 8 = g

Mass of the squash ball = m = 0.25 kg

Initial height from which the squash ball is released = h₁ = 10 m

Height to which the squash ball rebounds = h₂ = 6 m

Energy lost during the impact with the ground = E_loss = 8 J

By conservation of energy the initial potential energy of the ball is equal to the energy lost during the impact of the ground plus the final potential energy of the ball.

mgh₁ = E_loss + mgh₂

mg(h₁ - h₂) = 8

g(0.25)(10 - 6) = 8

g = 8 m/s²

Gravitational acceleration on Omicron Persei 8 = 8 m/s²