To calculate the potential energy lost and regained by the basketball, we need to use the formula for gravitational potential energy:
Potential energy = mass * acceleration due to gravity * height
Given: Mass of the basketball, m = 0.0400 kg Height when dropped, h1 = 5.00 m Height when it bounces back, h2 = 3.00 m Acceleration due to gravity, g ≈ 9.8 m/s² (approximate value on Earth)
a) Potential energy lost on the way down: The potential energy lost is equal to the initial potential energy minus the final potential energy.
Initial potential energy = m * g * h1 Final potential energy = m * g * h2
Potential energy lost = Initial potential energy - Final potential energy
Potential energy lost = m * g * h1 - m * g * h2
Substituting the given values: Potential energy lost = 0.0400 kg * 9.8 m/s² * 5.00 m - 0.0400 kg * 9.8 m/s² * 3.00 m
b) Potential energy regained on the way back: The potential energy regained is the difference between the initial potential energy when the ball reaches its lowest point and the potential energy when it reaches the maximum height on the way back.
Initial potential energy (at the lowest point) = m * g * h2 Final potential energy (at the maximum height on the way back) = m * g * h1
Potential energy regained = Final potential energy - Initial potential energy
Potential energy regained = m * g * h1 - m * g * h2
Substituting the given values: Potential energy regained = 0.0400 kg * 9.8 m/s² * 5.00 m - 0.0400 kg * 9.8 m/s² * 3.00 m
Note: The potential energy lost on the way down is equal to the potential energy regained on the way back, as long as there are no energy losses due to other factors like air resistance or friction.