Final answer:
The elevator generates 34.496 kilowatts of power by lifting a total mass of 1100 kg at a distance of 40.0 meters in 12.5 seconds. This calculation is based on the work done against gravity and the time taken to perform that work.
Step-by-step explanation:
To calculate the power generated by the elevator, we need to determine the work done and then divide it by the time in which the work was done. Work done (W) in lifting the elevator against gravity is given by the formula W = m * g * h, where m is the mass raised, g is the acceleration due to gravity (9.8 m/s2), and h is the height.
For an elevator lifting a total mass of 1100 kg at a distance of 40.0 meters:
- Work done W = 1100 kg * 9.8 m/s2 * 40.0 m
- W = 1100 * 9.8 * 40
- W = 431200 J (joules)
Power is the rate at which work is done, so Power (P) = Work done (W) / Time (t).
Taking the time as 12.5 seconds:
- Power P = 431200 J / 12.5 s
- P = 34496 W
- P = 34.496 kW (since 1 kW = 1000 W)
The elevator generates 34.496 kilowatts of power.