An elevator of a 6-story house has a mass of 600 kg, not including passengers. T

Question

An elevator of a 6-story house has a mass of 600 kg, not including passengers. The elevator

is designed to ascend, at constant speed, to the top floor (a vertical distance of 24.0m) in 18.0 s,

and it is driven by a motor that can provide up to 40 hp (1 hp = 746 W) to the elevator. a) What

is the maximum number of passengers that can ride the elevator? Assume that an average

passenger has a mass of 70 kg. b) If the elevator had a counterweight (as described here:

http://science.howstuffworks.com/transport/engines-equipment/elevator3.htm) of 600 kg what

would be the maximum number of passengers

Explanation / Answer

m = 600 kg, h = 24.0 m, t = 18.0 s, P = 40 hp (1 hp = 746 W).

a) What is the maximum number N of passengers that can ride the elevator? Assume that an average
passenger has a mass of M = 70 kg.

speed v = h/t, F = P/v = (m + MN)g

N = (Pt/gh - m)/M = 24

b) m ' = 600 kg,

P/v + m'g = (m + MN')g

N' = 32

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