A team of piano movers are lifting a grand piano from the ground to the third floor of a building, 30 m above the ground. The mass of the piano is 1000 kg, and it accelerates at 2 m/s². It takes the team 600 seconds (10 minutes) to lift the piano.
To calculate the work done by the team of movers to lift the piano, we can use the work-energy principle:
Work = Change in kinetic energy + Change in potential energy
Since the piano starts from rest on the ground, its initial kinetic energy is zero. Therefore, the work done by the team is equal to the change in potential energy:
Work = mgh
where:
m = mass of the piano (1000 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height lifted (30 m)
Work = (1000 kg)(9.8 m/s²)(30 m)
Work = 294,000 Joules
Next, we can calculate the total amount of work done by the team of movers:
Work = Force x distance
294,000 Joules = Force x distance
The force required to lift the piano can be calculated using Newton's second law:
F = ma
F = (1000 kg)(2 m/s²)
F = 2000 N
Therefore, the distance that the movers lifted the piano is:
294,000 Joules = (2000 N) x distance
distance = 147 meters
Since it took the team of movers 600 seconds to lift the piano a distance of 147 meters, their average power output can be calculated as follows:
Power = Work / Time
Power = 294,000 Joules / 600 seconds
Power = 490 W
Therefore, the team of piano movers exerted an average power of 490 Watts to lift the grand piano to the third floor of the building over a period of 600 seconds.