You drop a ball, mass 117.1 grams from a height of 68.9 cm. It bounces back to a height of 48.1 from the floor. What is the change in gravitational potential energy from the moment it is dropped, to the moment it reaches the maximum height from the bounce?
To find the change in gravitational potential energy, we need to determine the initial gravitational potential energy and the final gravitational potential energy.
The gravitational potential energy is given by the equation:
PE = m * g * h
Where:
PE is the gravitational potential energy,
m is the mass of the object,
g is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
h is the height.
Step 1: Calculate the initial gravitational potential energy:
m = 117.1 grams = 0.1171 kg
h = 68.9 cm = 0.689 m
PE_initial = m * g * h
PE_initial = 0.1171 kg * 9.8 m/s² * 0.689 m
PE_initial ≈ 0.825 J
Step 2: Calculate the final gravitational potential energy:
h = 48.1 cm = 0.481 m
PE_final = m * g * h
PE_final = 0.1171 kg * 9.8 m/s² * 0.481 m
PE_final ≈ 0.553 J
Step 3: Calculate the change in gravitational potential energy:
ΔPE = PE_final - PE_initial
ΔPE = 0.553 J - 0.825 J
ΔPE ≈ -0.272 J
The change in gravitational potential energy from the moment the ball is dropped to the moment it reaches the maximum height from the bounce is approximately -0.272 Joules. The negative sign indicates a decrease in potential energy due to loss during the bounce.