An escalat 0.8 m/ t What wou Analysis: A Mas The V. Under stat- people on E -E Rate of net ener by heat, work 2
An escalat 0.8 m/ t What wou Analysis: A Mas The V. Under stat- people on E -E Rate of net ener by heat, work 2
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Transcribed Image Text:Example 13
An escalator in a shopping center is designed to move 30 people, 75 kg each, at a constant speed of
0.8 m/s t 45 slope. (a) Determine the minimum power input eeded to drive this escalator. (b)
What would your answer be if the escalator velocity were to be doubled?
Analysis: At design conditions, the total mass moved by the escalator at any given time is
Mass = (30 persons)(75 kg/person) = 2250 kg
The vertical component of escalator velocity is
Vvert = V sin 45° =
(0.8 m/s)sin45°
Under stated assumptions, the power supplied is used to increase the potential energy of people. Taking the
people on elevator as the closed system, the energy balance in the rate form can be written as
AE
sys
! dt
system
Ein = dEs/ dt =
= 0
->
%3D
out
SAS
At
Rate of net energy transfer
by heat, work 2nd mass
Rate of change in mternal. kinetac.
potental etc.energies
APE
mgA:
mgVen
%3D
in
%3D
rert
That is, under stated
ions, the power input to the escalator must be equal to the rate of increase of
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