The mass of a steel wrecking ball is 1.50 x 10^3 kg. What power is used to raise it to a height of 45.0 m if the work is done in 15.0 seconds?
I calculate:
Work done = potential energy = mgh
Power = mgh/t
Gravity = 9.8 m/s^2
M = 1.5 x 10^3 kg = (1500 kg)
Height – 45 meters
Time – 15 seconds
P = (1500 kg)(9.8 m/s^2)(45 meters) / (15 seconds) W
P = 44100 W or 4.4 x 10^4
Rearranging the formula, we get:
F=dmgh
The force applied to the wrecking ball is equal to the weight of the ball, which is given by:
F=mg
Substituting the given values, we get:
F = (1500 kg)(9.81 m/s^2) = 1.47 x 10^4 N
Therefore, the power used to raise the steel wrecking ball to a height of 45.0 m in 15.0 seconds is:
P = W/t = Fdh/dt = (1.47 x 10^4 N)(45.0 m) / 15.0 s = 4.41 x 10^4 W