A mover hoists a 200 kg piano from the ground to a height of 5 m using a single pulley. What was the change in the piano's energy?
Gain in potential energy
=mgh
=200kg*9.81 m/s²*5m
=9810 N-m
equals work done in hoisting the piano.
To calculate the change in the piano's energy, we need to consider the work done by the mover in hoisting the piano.
The work done is given by the equation:
Work = Force × Distance × cos(θ)
In this case, the distance is the height the piano is lifted, which is 5 m. The force required to lift the piano can be calculated using the formula:
Force = mass × gravity
where the mass of the piano is 200 kg, and the acceleration due to gravity is approximately 9.8 m/s².
Therefore, the force required to lift the piano is:
Force = 200 kg × 9.8 m/s² = 1960 N
Now, substituting the values into the work equation:
Work = 1960 N × 5 m × cos(θ)
Since the pulley system only changes the direction of the force and not the magnitude, the angle θ between the force and the direction of displacement is 0°. Therefore, cos(0°) = 1.
Work = 1960 N × 5 m × 1 = 9800 J
The work done by the mover to lift the piano is 9,800 Joules (J). This is also the change in the piano's potential energy because the energy acquired by the piano is equal to the work done on it.
So, the change in the piano's energy is 9,800 J.