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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 \(800 \mathrm{MW}\) ?

Short Answer

Expert verified
(a) It would take \(40\) people to run a \(4.00\text{-kW}\) electric clothes dryer. (b) It would take \(8,000,000\) people to replace an \(800\text{ MW}\) electric power plant.

Step by step solution

01

Part (a): Calculate the number of people needed to run a 4.00-kW electric clothes dryer

First, we need to convert the power from kW to W by multiplying by 1000: Power_needed = 4.00 kW * 1000 = 4000 W Now, we can find the number of people needed as: Number_of_people = Power_needed / Power_generated_by_one_person where Power_generated_by_one_person = 100 W. Number_of_people = 4000 W / 100 W = 40 people So, it would take 40 people to run a 4.00-kW electric clothes dryer.
02

Part (b): Calculate the number of people needed to replace an 800 MW electric power plant

First, we need to convert the power from MW to W by multiplying by 1,000,000: Power_needed = 800 MW * 1,000,000 = 800,000,000 W Now, we can find the number of people needed as: Number_of_people = Power_needed / Power_generated_by_one_person where Power_generated_by_one_person = 100 W. Number_of_people = 800,000,000 W / 100 W = 8,000,000 people So, it would take 8,000,000 people to replace an 800 MW electric power plant.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Power Generation
Electric power generation is a fundamental aspect of modern civilization. It's the process by which electrical energy is generated from other types of energy sources. In many cases, this involves the conversion of mechanical energy into electric energy, like in power plants.
At the core of electric power generation is the generator. A basic generator works by converting kinetic energy (from sources like wind, water, or steam) into electrical energy through electromagnetic induction. The generator has a magnetic field that changes relative to the windings inside, which produces electricity.
  • Fossil fuel plants burn coal, oil, or gas to heat water into steam, which then drives turbines connected to generators.
  • Nuclear power plants use nuclear reactions to create heat for steam production and turbine movement.
  • Renewable sources such as hydropower, wind, and solar directly convert natural energy forms into electricity.
Understanding the basics of electric power generation helps explain how different energy forms are converted with maximum efficiency, crucial for meeting our daily power needs.
Human Power Output
Humans can be seen as engines, converting food into mechanical work, which can be harnessed to create electric power. The average person in good physical shape can produce about 100 watts of power over a period of time.
This might not sound like a lot when compared to machines, but it is significant. Human-powered mechanisms have been used throughout history to perform tasks from grinding grain to powering small gadgets. Today, there are even bikes and other devices designed to convert human-generated mechanical energy into electricity.
While human power output is limited and varies from person to person, it's an interesting concept that highlights human physical capability. It's crucial for understanding how humans have historically contributed to energy processes and how they could sustainably generate power on a small scale for specific applications.
Conversion of Units
Understanding energy and power often involves converting units to see how different scales compare. In electricity, energy is often measured in watts (W), kilowatts (kW), and megawatts (MW), among other units.
A watt is a basic unit of power, representing the rate of energy transfer equivalent to one joule per second. When dealing with large quantities of power, such as those generated by power plants or used by heavy appliances, kilowatts and megawatts are more practical.
  • 1 kW = 1,000 W
  • 1 MW = 1,000,000 W
In practical terms, this conversion is essential for calculating how many resources are needed for different applications, like determining how much human power would be needed to replace electric power generation in appliances or plants.
Electricity Usage
Electricity usage is a crucial consideration for both individuals and society at large. It's important to understand how much electricity various devices consume. This knowledge helps in managing energy costs and being more energy-efficient.
Electric clothes dryers, for instance, typically require around 4 kW to operate, which means they consume 4,000 watts continuously while running. This is a significant amount for a single household appliance.
Understanding the electricity needs of large operations, like power plants, further broadens our understanding. For instance, a large power plant might generate about 800 MW, which translates into 800,000,000 watts. This scale is necessary to meet the electricity demands of cities and industrial complexes.
  • Knowing the power rating of appliances can help in calculating their energy consumption.
  • It is important for planning electricity sources, ensuring supply meets demand.

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Most popular questions from this chapter

An electron in a television tube is accelerated uniformly from rest to a speed of \(8.4 \times 10^{7} \mathrm{m} / \mathrm{s}\) over a distance of \(2.5 \mathrm{cm} .\) What is the power delivered to the electron at the instant that its displacement is \(1.0 \mathrm{cm} ?\)

A 7.0-kg box slides along a horizontal frictionless floor at \(1.7 \mathrm{m} / \mathrm{s}\) and collides with a relatively massless spring that compresses \(23 \mathrm{cm}\) before the box comes to a stop. (a) How much kinetic energy does the box have before it collides with the spring? (b) Calculate the work done by the spring. (c) Determine the spring constant of the spring.

Suppose the ski patrol lowers a rescue sled and victim, having a total mass of \(90.0 \mathrm{kg}\), down a \(60.0^{\circ}\) slope at constant speed, as shown below. The coefficient of friction between the sled and the snow is 0.100 . (a) How much work is done by friction as the sled moves \(30.0 \mathrm{m}\) along the hill? (b) How much work is done by the rope on the sled in this distance? (c) What is the work done by the gravitational force on the sled? (d) What is the total work done?

Consider a linear spring, as in Figure \(7.7(\) a), with mass \(M\) uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position \(x=0, \quad\) is moving with speed \(v\) in the \(x\) -direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring \(d m\) in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)

A spark of static electricity, such as that you might receive from a doorknob on a cold dry day, may carry a few hundred watts of power. Explain why you are not injured by such a spark.

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