A person in good physical condition can provide 1.00 times 10 to the two watts of useful electrical power by doing mechanical work, neglecting any problems of generator efficiency and practical considerations such as resting time. How many people would it take to run a 4.00-kilowatt electric clothes dryer? How many people would it take to replace a large electric power plant that generates 800 megawatts?
Let’s start by highlighting some of the vital information given. We’re told that someone in good physical condition can provide 1.00 times 10 to the two watts of useful electrical power. We want to know how many such people it would take to run a 4.00-kilowatt clothes dryer.
And in part two, we want to find how many people it would take to replace a generator that generates 800 megawatts of electricity.
Let’s call the number of people it would take to run the clothes dryer 𝑁 sub 𝑑 and the number of people it would take to replace the generator as 𝑁 sub 𝑔. Solving for these values will involve converting units.
Let’s call the power one fit person can provide 𝑃 sub 𝑝; that’s 1.00 times 10 to the two watts. The power required to run the dryer, 𝑃 sub 𝑑, is equal to 4.00 kilowatts. And the power generated by the generator, 𝑃 sub 𝑔, is equal to 800 megawatts.
As we start by solving for 𝑁 sub 𝑑, we can see that the number of people needed to run the clothes dryer equals the power required to run the clothes dryer divided by the power supplied by an average person. That equals 4.00 kilowatts divided by 1.00 times 10 to the two watts.
Before we perform this division, we need both our numbers to be in the same units. The prefix kilo means thousand, so one kilowatt is equal to a thousand watts.
That means we can modify the numerator of this fraction to go from 4.00 kilowatts to 4.00 times ten to the third watts.
Now that our numerator and denominator have the same set of units, we can divide these two numbers, and the result is 4.00 times 10 to the one or forty. That’s the number of people it would take to power an electric clothes dryer requiring 4.00 kilowatts of power.
Now that we’ve solved for part one, the number of people required to run the clothes dryer, let’s solve for part two, the number of people it would take to replace the energy generated by our electrical generator, 800 megawatts.
The number of people required, 𝑁 sub 𝑔, is equal to 𝑃 sub 𝑔, the power generated by this generator, divided by 𝑃 sub 𝑝, the power generated by one person. That’s equal to 800 megawatts divided by 1.00 times 10 to the two watts.
The prefix mega means million, so that one megawatt equals one times 10 to the sixth watts. That means that 800 megawatts equals 8.00 times 10 to the eighth watts. We replaced 800 megawatts with that term in watts in our numerator.
Now our numerator and denominator have the same units, and we can perform our division. We find a result of 8.00 times 10 to the sixth. That’s eight million people; that’s how many people would be needed to replace the power generated by this generator.