(Physics Question): A motor having a maximum power rating of 8.1 x 10^4 watts is used to operate an elevator. What is the maximum weight….?

What is the maximum weight this motor can lift at an average speed of 3 m/s? (show work on how to get answer)

Power = Work ÷ time
Work = Force * distance
Power = Force * distance ÷ time
Power = Weight * Velocity

Since the elevator is moving upward at a average speed, this equation can be used to determine the maximum weight this motor can lift.

8.1 * 10^4 = Weight * 3
Weight = 8.1 * 10^4 ÷ 3 = 2.7 * 10^4 N

The motor can produce F = P/v = 8.1E4/3 = 2.7E4 Newtons of lifting force. But there will be friction and losses, so the max weight the lift can lift will be something less than that value. ANS.

Power = change in energy / time

The energy changing is PE, m*g*h
Power = m*g*h/t

Separate
Power = (m*g)*(h/t)

Define as follows
M*g = weight
H/t = vertical speed

Sub in and solve for weight
Power = weight*v
Weight = power/v = 81000 W / 3 m/s = 27000 N

Presto!