How long will it take a 1920 W motor to lift a 285 kg piano to a sixth-story window 16.0 m above?
Divide change in potential energy by the power of the motor.
change in potential energy divided by the power. ( 1 W = 1 J/s)
Initial potential energy= mass* g* height
= mass * g*0
= 0
Final potential energy = mass* g* 16.0
finf diffence between final and initial and divide by Power. Answer will be in seconds(s)
3.945 secomds
To calculate the time it would take for a motor to lift a piano to a sixth-story window, we need to use the work-energy principle. The work done by the motor is equal to the change in potential energy of the piano.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy and/or potential energy. In this case, we are only concerned with the change in potential energy, as the piano is being lifted vertically.
The potential energy (PE) of an object is given by the formula: PE = mgh, where m is the mass of the object (in kg), g is the acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth), and h is the height (in meters) of the object above a reference point.
In this scenario, the piano has a mass of 285 kg and is being lifted 16.0 m above its starting position. Plugging these values into the formula, we have:
PE = mgh
PE = 285 kg * 9.8 m/s^2 * 16.0 m
PE = 447360 J (joules)
The work done by the motor (W) is equal to the change in potential energy, which is given by:
W = ΔPE = PE_final - PE_initial
W = PE_final - 0 (as the initial potential energy is zero)
W = PE_final
W = 447360 J (joules)
The power (P) of the motor is given by the formula: P = W/t, where P is power (in watts), W is work (in joules), and t is time (in seconds).
We are given that the motor has a power of 1920 W. Plugging these values into the formula, we have:
P = W/t
1920 W = 447360 J / t
To solve for time (t), we rearrange the equation:
t = 447360 J / 1920 W
t ≈ 233.0 seconds (approximately)
Therefore, it would take approximately 233.0 seconds (or about 3 minutes and 53 seconds) for the 1920 W motor to lift the 285 kg piano to a sixth-story window 16.0 m above.