Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 3, Problem 73RQ

(a)

To determine

The power required when the cabin is fully loaded.

The power required when no counterweight is used.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Counterweight of the elevator cabin that is partially balanced (m) is 400kg.

Constant speed of the elevator cabin (V) is 1.2m/s.

Friction force (Ff) is 800N.

Density of the water (ρ) is 1000kg/m3.

Acceleration due to gravity (g) is 9.81m/s2.

Calculation:

Calculate the power required when the cabin is fully loaded (W˙).

  W˙=mgzΔt=mgV=[(400kg)(9.81m/s2)(1.2m/s)(1N1kgm/s2)(1kW1000Nm/s)]=4.71kW

Thus, the power required when the cabin is fully loaded is 4.71kW_.

When no counterweight is used, then the mass of the elevator cabin would be 800kg.

  m=800kg

Calculate the power required when no counterweight is used (W˙).

  W˙=mgV=[(800kg)(9.81m/s2)(1.2m/s)(1N1kgm/s2)(1kW1000Nm/s)]=9.42kW

Thus, the power required when the cabin is fully loaded is 9.42kW_.

(b)

To determine

The power required when the empty cabin is descending.

The power required when the empty cabin is descending with the friction force.

(b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the weight of the elevator cabin when it is empty.

  m=400kg150kg=250kg

Calculate the power required when the empty cabin is descending (W˙).

  W˙=mgV=[(250kg)(9.81m/s2)(1.2m/s)(1N1kgm/s2)(1kW1000Nm/s)]=2.94kW

Thus, the power required when the empty cabin is descending is 2.94kW_.

Calculate the power developed during the friction between the cabin and the guide rails (W˙friction).

  W˙friction=FfzΔt=FfV=(800N)(1.2m/s)(1kW1000Nm/s)=0.96kW

Calculate the total power required (W˙total).

  W˙total=W˙+W˙friction=2.94kW+0.96kW=3.90kW

Thus, the power required when the empty cabin is descending with the friction force is 3.90kW_.

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Chapter 3 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

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