You drop a ball, mass 127.5 grams from a height of 83.0 cm. It bounces back to a height of 50.5 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?
PE=orig-final
= mg(.83-.505)
To calculate the change in gravitational potential energy, we need to find the difference in height between the initial drop and the maximum height after the bounce.
The change in gravitational potential energy (ΔPE) can be determined using the formula:
ΔPE = m * g * Δh
Where:
m is the mass of the ball (127.5 grams or 0.1275 kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
Δh is the change in height (initial height - final height).
First, let's convert the mass of the ball to kilograms:
Mass (m) = 127.5 grams ÷ 1000 = 0.1275 kg
The initial height is 83.0 cm, which is 0.83 meters, and the final height is 50.5 cm, which is 0.505 meters.
Now we can calculate the change in height:
Δh = 0.83 m - 0.505 m = 0.325 m
Next, we can calculate the change in gravitational potential energy:
ΔPE = 0.1275 kg * 9.8 m/s^2 * 0.325 m
Finally, we can solve for the change in gravitational potential energy:
ΔPE ≈ 0.128 J
Therefore, the change in gravitational potential energy from the moment it is dropped to the moment it reaches the maximum height from the bounce is approximately 0.128 Joules.