An elevator has mass 570 kg , not including passengers. The elevator is designed

Question

An elevator has mass 570 kg , not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 19.5 m (five floors) in 15.3 s , and it is driven by a motor that can provide up to 45 hp to the elevator.

Problem 7.59 Part A An elevator has mass 570 kg, not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 19.5 m (five floors) in 15.3 s, and it is driven by a motor that can provide up to 45 hp to the elevator. What is the maximum number of passengers that can ride in the elevator? Assume that an average passenger has mass 65.0kg. Express your answer as an integer. n=

Explanation / Answer

speed of the elevator=distance /time

=19.5/15.3=1.2745 m/s

power provided=45 hp=45*746 W=33570 W

then force applied by the pulling wire=power/speed

=33570/1.2745=26339.74 N

this force should be greater than the weight of the elevator (including passengers)

if maximum number of passengers is n,

then (570+n*65)*9.8 < 26339.74

==>570+n*65 <2687.72

==>n*65 <2117.72

==> n<32.58

hence maximum 32 passengers can ride the elevator.

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