Question

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?

Short answer

(a) Number of people needed to run a $4.00kW$electric clothes dryer if each person can put out a $100W$of useful power are 40.

(b) The number of people required to replace a large electric power plant that generates $800MW$is 8 million.

Step-by-step solution

Power

Power: Power is defined as the rate at which energy is expended. Greater power means a large amount of work or energy developed in a short time.

Number of people needed to run an electric clothes dryer

(a)

The rate of work done per person is,

$P_P=100W$

Power consumption of electric clothes dryer is,

$P_D=4.00kW$

Number of people required to run an electric clothes dryer is,

$n=\frac{P_D}{P_P}$

Putting all known values,

$$\begin{gathered} n=\frac{4.00kW}{100W} \\ =\frac{4.00kW\left({\displaystyle \frac{1000W}{1kW}}\right)}{100W} \\ =40 \end{gathered}$$

Therefore, 40 peoples are required to run an electric clothes dryer.

Number of people needed to replace large electric generator

(b)

The power generated by a large electric power plant generator is,

$P_G=800MW$

Number of people required to replace the large electric power plant generator is,

$N=\frac{P_W}{P_P}$

Putting all known values,

role="math" localid="1668691687774" $$\begin{gathered} N=\frac{800MW}{100W} \\ =\frac{800\times {10}^{6}W}{100W} \\ =8\times {10}^{6}W \end{gathered}$$

Therefore,$8\times {10}^{6}W$ people are required to replace a large electric power plant generator.