An escalator in a shopping center is designed to move 30 people, 75 kg each, at a constant speed of 0.8 m/s at 45° AP needed to drive this escalator. What would your answer be if the escalator velocity were to be doubled? Clue: You can start with the first law and cancel out terms. You can consider this a closed System. 5 kPa Pump slope. Determine the minimum power input

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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An escalator in a shopping center is designed to move 30 people, 75 kg each, at a constant
speed of 0.8 m/s at 45° AP = 5 kPa Pump slope. Determine the minimum power input
needed to drive this escalator. What would your answer be if the escalator velocity were to
be doubled? Clue: You can start with the first law and cancel out terms. You can consider this a closed
System.
Transcribed Image Text:An escalator in a shopping center is designed to move 30 people, 75 kg each, at a constant speed of 0.8 m/s at 45° AP = 5 kPa Pump slope. Determine the minimum power input needed to drive this escalator. What would your answer be if the escalator velocity were to be doubled? Clue: You can start with the first law and cancel out terms. You can consider this a closed System.
Expert Solution
Step 1

Assumptions:

  1. Air drag and friction are negligible.
  2. The average mass of each person is 75 kg.
  3. The escalator operates steadily, with no acceleration or breaking.
  4. The mass of escalator itself is negligible. 

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 45o = (0.8 m/s) sin 45o

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 

E˙in - E˙outRate of net energy transfer by heat, work and mass = dEsystemdtRate of change in internal, kinetic,potential etc. energies=0

E˙in = dEsystemdt = Esystemt

W˙in = PEt = mgzt = mgVvert

 

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