Final answer:
The useful power output of an elevator motor can be determined by calculating the work done against gravity and the work required to accelerate the system. By combining these values and factoring in the time over which work is done, you can calculate the power in watts and subsequently estimate the energy cost using the given electricity price.
Step-by-step explanation:
To find the useful power output of an elevator motor, you will need to consider both the work done against gravity to lift the load and the work done to accelerate the entire system. Let's tackle this two-part problem.
Useful Power Output Calculation
Firstly, consider the work against gravity, which is work = force × distance. The force here is the weight of the 2500-kg load, and the distance is the height of 35.0 meters. The weight of the load can be calculated by weight = mass × gravitational acceleration (g), with g being approximately 9.8 m/s². So, the work done against gravity is weight × height.
Next, calculate the kinetic energy required to accelerate the 10,000-kg system to 4.00 m/s from rest. The kinetic energy (KE) is given by KE = ½ × mass × velocity².
The total work done is the sum of the work against gravity and the kinetic energy. Since power is work done per time, we divide the total work by the time taken, which is 12.0 seconds, to find the power output.