To calculate the work done on the elevator, we need to find the total change in potential energy and the total change in kinetic energy.
Given data:
Initial velocity, u = 0 m/s
Final velocity, v = 2.0 m/s
Mass of the elevator, m = 400 kg
Height, h = 20 m
1. Change in potential energy:
ΔPE = mgh
ΔPE = 400 kg * 9.81 m/s^2 * 20 m
ΔPE = 78,480 J
2. Change in kinetic energy:
Initial kinetic energy, KE1 = 0
Final kinetic energy, KE2 = 0.5mv^2
KE2 = 0.5 * 400 kg * (2.0 m/s)^2
KE2 = 800 J
3. Total work done on the elevator:
Work = ΔPE + ΔKE
Work = 78,480 J + 800 J
Work = 79,280 J
Therefore, the work done on the elevator is 79,280 Joules.