A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time: (a) How many people would it take to run a 4.00-kW electric clothes dryer? (b) How many people would it take to replace a large electric power plant that generates 800 MW?

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skyluke89 skyluke89 · Answer 1 · 2019-01-24T10:16:28+01:00

(a) 40 people

Explanation:

- The power produced by a single person is [tex]P_1 = 100 W[/tex]

- The total power to run the dryer is [tex]P=4.00 kW=4000 W[/tex]

- So, the number of people needed would be the ratio between the total power needed and the power generated by a single person:

[tex]n=\frac{P}{P_1}=\frac{4000 W}{100 W}=40[/tex]

(b) 8 million people

Explanation:

- The power produced by a single person is [tex]P_1 = 100 W[/tex]

- The total power to replace the electric power plant is [tex]P=800 MW=8 \cdot 10^8 W[/tex]

- So, as before, the number of people needed would be the ratio between the total power needed and the power generated by a single person:

[tex]n=\frac{P}{P_1}=\frac{8 \cdot 10^8 W}{100 W}=8 \cdot 10^6[/tex]

which corresponds to 8 million people.