Final answer:
The work done by the elevator motor to lift a 1000kg elevator a height of 100m is 980,000 joules. The power required to lift the elevator in 54 seconds at constant speed is approximately 18.148 kilowatts.
Step-by-step explanation:
To calculate the work done by the elevator motor to lift a 1000kg elevator a height of 100m, we apply the formula for work, which is Work (W) = force x distance. The force in this case is the gravitational force, which is mass (m) times the acceleration due to gravity (g), so we get W = mgh. Using the mass of the elevator (1000kg), the height (100m), and the acceleration due to gravity (approximately 9.8m/s2), the work done is:
W = 1000kg * 9.8m/s2 * 100m = 980,000 joules (J).
Next, to find the power that the motor must supply to do this in 54 seconds, we use the formula for power (P), which is the work done divided by the time taken (t). Thus, P = W/t. With the work done as 980,000 J and the time as 54s, the power required is:
P = 980,000 J / 54s = approximately 18,148 watts (W), or 18.148 kilowatts (kW).