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College Physics (Urone)
Found in: Page 264
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

Consider humans generating electricity by pedaling a device similar to a stationary bicycle. Construct a problem in which you determine the number of people it would take to replace a large electrical generation facility. Among the things to consider are the power output that is reasonable using the legs, rest time, and the need for electricity 24 hours per day. Discuss the practical implications of your results.

The number of people required to replace electric power plant that generates \(10{\rm{ MW}}\) is \(50000\). The coal or petroleum power plant that satisfy the energy requirements can replaced by \(50000\) people.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Definition of Concepts 

Power: Power is a scalar quantity defined as the amount of energy consumed per unit time.

Mathematically,

\(P = \frac{E}{T}\)

Here, \(P\) is the power, \(E\) is the energy consumed or generated, \(T\) is the time.

As a result, the expression of the energy consumed is,

\(E = PT\)

Step 2: Construction of problem

A person in good physical condition can pedal bicycle at \(13 - 18{\rm{ km}}/{\rm{h}}\) for \(12{\rm{ hrs}}\) a day (\(12{\rm{ hrs}}\) of resting period is given per day). Neglecting any problems of generator efficiency. Determine the number of people it would take to replace an electric power plant that generates \(10{\rm{ MW}}\).

Step 3: Find the number of people required to replace the electric power plant

The energy generated by a person pedaling bicycle is,

\(E = PT\)

Here, \(P\) is the power generated by a person good physical by pedaling bicycle at \(13 - 18{\rm{ km}}/{\rm{h}}\) \(\left( {P = 400{\rm{ W}}} \right)\), and \(T\) is the time of pedaling bicycle \(\left( {T = 12{\rm{ hr}}} \right)\).

Putting all known values,

\(\begin{array}{c}E = \left( {400{\rm{ W}}} \right) \times \left( {12{\rm{ hrs}}} \right)\\ = 4800{\rm{ W}} \cdot {\rm{h}}\end{array}\)

The energy generated by electric power plant is,

\(E' = P'T'\)

Here, \(P'\) is the power generated by the electric power plant \(\left( {P' = 10{\rm{ MW}}} \right)\), and \(T'\) is the time \(\left( {T' = 1{\rm{ day}}} \right)\).

Putting all known values,

\(\begin{array}{c}E' = \left( {10{\rm{ MW}}} \right) \times \left( {1{\rm{ day}}} \right)\\ = \left( {10{\rm{ MW}}} \right) \times \left( {\frac{{{{10}^6}{\rm{ W}}}}{{1{\rm{ MW}}}}} \right) \times \left( {1{\rm{ day}}} \right) \times \left( {\frac{{24{\rm{ hrs}}}}{{1{\rm{ day}}}}} \right)\\ = 2.4 \times {10^8}{\rm{ W}} \cdot {\rm{h}}\end{array}\)

The number of people required to replace the electric power plant is,

\(N = \frac{{E'}}{E}\)

Here, \(E'\) is the energy generated by the electric power plant \(\left( {E' = 2.4 \times {{10}^8}{\rm{ W}} \cdot {\rm{h}}} \right)\) and \(E\) is the energy generated by a person by pedaling bicycle \(\left( {E = 4800{\rm{ W}} \cdot {\rm{h}}} \right)\).

Putting all known values,

\(\begin{array}{c}N = \frac{{2.4 \times {{10}^8}{\rm{ W}} \cdot {\rm{h}}}}{{4800{\rm{ W}} \cdot {\rm{h}}}}\\ = 50000\end{array}\)

Therefore, the number of people required to replace electric power plant that generates \(10{\rm{ MW}}\) is \(50000\). Hence, \(50000\) people can replace the coal or petroleum power plant which generates the same energy.

Most popular questions for Physics Textbooks

A car advertisement claims that its \(900 - {\rm{kg}}\) car accelerated from rest to \(30.0{\rm{ m}}/{\rm{s}}\) and drove \(100{\rm{ km}}\), gaining \(3.00{\rm{ km}}\) in altitude, on \(1.0{\rm{ gal}}\) of gasoline. The average force of friction including air resistance was \(700{\rm{ N}}\). Assume all values are known to three significant figures.

(a) Calculate the car’s efficiency.

(b) What is unreasonable about the result?

(c) Which premise is unreasonable, or which premises are inconsistent?

Consider a person climbing and descending stairs. Construct a problem in which you calculate the long-term rate at which stairs can be climbed considering the mass of the person, his ability to generate power with his legs, and the height of a single stair step. Also consider why the same person can descend stairs at a faster rate for a nearly unlimited time in spite of the fact that very similar forces are exerted going down as going up. (This points to a fundamentally different process for descending versus climbing stairs.)

(a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s?

(b) Discuss how the larger energies needed for the movement of larger animals would relate to metabolic rates.

What is conservative force?

(a) What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months?

(b) How long can a battery that can supply 8.00×104 J run a pocket calculator that consumes energy at the rate of 1.00×10−3 W?
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