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An elevator has mass 600 kg, not including passengers. The elevator is designed to ascend, at...

An elevator has mass 600 kg, not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 20.0 m (five floors) in 16.0 s, and it is driven by a motor that can provide up to 40 hp to the elevator.

A. What is the maximum number of passengers that can ride in the elevator? Assume that an average passenger has mass 65.0 kg.

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Answer #1

n, the no. of people

The elevator ascends at constant speed, i.e. a=0

? F = F-(Wele - Wn) --> F = Wele - Wn

v = 20/16 = 1.25 m/s

power = 40 hp = 40*745.6998 = 29827.99 W

P = F.v = (Wele -Wn)*1.25

29827.99= (600*9.8+65*n*9.8)*1.25

n = 28.2 --> 28 people

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Answer #2

28 people

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Answer #3

Assume the elevator does not have a counterweight. Also assume that the acceleration and deceleration effects are negligible.

m g h / t = power

(600 + n*65) g 20 / 16 = 40 * 746 watts/hp

600 * 9.8 * 20/16 + n * 65 * 9.8 * 20/16 = 29840

7350 + 1991 n = 29840

n = (29840 - 7350 ) / 1991 = 11.3 or 11 people

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Answer #4

Power of motor in Watts = 30*745.7 = 22,371 watts,
Watts * time = energy or work done
22,371 * 15 = 335,565J

Work done = mass * gravity acceleration * height
335,565 = mass * 9.8*16
Mass = 335,565/(9.8*16)
Mass = 2,140kg

Mass of empty elevator = 600kg
Mass of passenger load = 2140-600 = 1540kg
Ave mass of passenger = 65kg
Number of passengers = 1540/65 = 23.7

Elevator can take 23 passengers.

OR

P = 30 * 750 (2 sig fig)
Weight of lift and n passengers = 6000 + n*650 N

Constant speed = 16/15 m/s

Increase in potential energy = (6000 + n*650) * 16/15 each second

ie power = (6000 + n*650) * 16/15 watt
= 30 * 750


find n

The question is rubbish of course since the force to accelerate the lift from 0 to 16/15 m/s is much higher and is occurring at a time when the motor has just started and hence has a lower power.

This is why lifts do not lift a dead weight. As the lift goes up a counter-weight goes down so that the motor only needs to apply a foce to overcome friction once constant speed is reached.

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