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Expert-verified Found in: Page 264 ### College Physics (Urone)

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

See the step by step solution

## 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. ### Want to see more solutions like these? 