Power - Physics Question

Question

An elevator motor provides 45.0 kW of power while lifting an elevator 35.0 m. If the elevator contains seven passengers each with an average mass of 70.0 kg and it takes 20.0 s to accomplish this task, determine the mass of the elevator.

Answer 1

45,000 watts is the power. Since it took 20s to complete, and since power and work are related by:

P = W/t then 45000 = W/20 or W = 900000 joules.

Since W = Fd and F = mg, we can say that W = mgd and since m = 7•70 + m_elevator we can say that m = 490 + m_elevator or

900000 = (490 + m_elevator)(9.81)(35)

2621.232 = 490 + m_elevator

m_elevator = 2131.232 kg or (using 3 sig figs)

m_elevator = 2130 kg