Find how much work ∆W is done by the motor in lifting the elevator:
P = ∆W / ∆t
where
• P = 45.0 kW = power provided by the motor
• ∆W = work done
• ∆t = 20.0 s = duration of time
Solve for ∆W :
∆W = P ∆t = (45.0 kW) (20.0 s) = 900 kJ
In other words, it requires 900 kJ of energy to lift the elevator and its passengers. The combined mass of the system is M = (m + 490.0) kg, where m is the mass of the elevator alone. Then
∆W = M g h
where
• g = 9.80 m/s² = acceleration due to gravity
• h = 35.0 m = distance covered by the elevator
Solve for M, then for m :
M = ∆W / (g h) = (900 kJ) / ((9.80 m/s²) (35.0 m)) ≈ 2623.91 kg
m = M - 490.0 kg ≈ 2133.91 kg ≈ 2130 kg
