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Energy -- Power

Module by: R.G. (Dick) Baldwin. E-mail the author

Summary: This module explains power in a format that is accessible to blind students.

Preface

General

This module is part of a collection (see http://cnx.org/content/col11294/latest/ ) of modules designed to make physics concepts accessible to blind students. The collection is intended to supplement but not to replace the textbook in an introductory course in high school or college physics.

This module explains power in a format that is accessible to blind students.

Prerequisites

In addition to an Internet connection and a browser, you will need the following tools (as a minimum) to work through the exercises in these modules:

The minimum prerequisites for understanding the material in these modules include:

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

General background information

What is work?

You learned in an earlier module that work occurs when a force causes a mass to be displaced by some distance. You learned that the equation for the quantity of work done is equal to

W = (f*newton)*(d*meter) = f*d*N*m

You also learned that work is measured in joules, where one joule is equal to one newton multiplied by one meter.

1 joule = 1 N * 1 m, or

1 joule = (1 kg * m/s^2) * m, or

1 joule = 1 kg*m^2/s^2

Paste the right-hand expression into the Google search box and press Enter just to be sure.

What about time?

Note that the equation for work says nothing about time. The same amount of work is done if it takes one second or one month for the object to which the force is applied to move by the same distance.

That doesn't sound right!

This goes against our normal concept of work. If Joe spreads one cubic yard of topsoil on the lawn in one hour and Bill requires three hours to do the same job, we might say that Joe is working harder than Bill.

Power

To be correct from a physics viewpoint, we would need to say that Joe is delivering more power than Bill. In other words, power is a measure of the rate at which work is done. They both do the same amount of work, but Joe does it more quickly than Bill. Hence Joe delivers more power than Bill.

Power in equation form

Power is the ratio of work to time. In equation form,

Power = Work/time

The SI unit for power

The SI unit for power is the watt . One watt of power is being delivered when one joule of work or energy is being delivered each second.

An electric heater

In other words, if you have an electric heater that is properly rated at 60 watts, it will deliver 60 joules of energy per second when it is turned on.

This means that somewhere in the world, someone or something must be doing work at a rate of 60 joules per second in order to insert the energy into the electrical grid that your heater will be taking out of the grid and turning into heat energy.

Horsepower

For historical reasons, particularly in the U.S., we also use the term horsepower to describe the power delivered by a machine. This is particularly true in the automotive industry, but it applies to other kinds of machines as well. We might speak of a car with a 300 horsepower engine, or a clothes washing machine with a quarter-horsepower motor.

One horsepower is equal to approximately 750 watts.

Most machines do work

Most machines are designed to consume electrical or chemical energy and do work on an object. Some machines, such as the treadmill at the health center, are designed to consume human energy in order to do work.

In order for a machine to do work, it must consume energy in some form.

Power ratings for machines

Machines are often described by a power rating. The power rating indicates the rate at which that machine can do work on objects.

When I was in the military many years ago, there were potato peeling machines in kitchens in the mess halls. Their purpose was to do work on potatoes by removing the peel. Presumably a machine with a high power rating could peel more potatoes per hour than one with a lower power rating.

Automobile engines and horsepower

Automobile engines are often rated in terms of power using horsepower as the units. At the drag-race track, contests are held to determine which vehicle can move from point A to point B in the shortest amount of time.

Since work is measured as force multiplied by distance, and power is measured as the work done per unit of time, everything else being equal, one would expect that the vehicle with the highest power rating would be the winner in moving a given distance in the shortest amount of time.

What about the units?

What are the units of power? We know that

Power = force * distance/seconds

We know that the units of force are

f = m*a = kg*m/s^2

We know that the units of time are seconds, and the units of distance are meters. Therefore,

Power = f*d/time = (kg*m/s^2)*(m/s) = (kg*m^2)/(s^3), or

Power = kg*(m^2)*(s^(-3))

Plug the right-hand expression into the Google search box and you will learn that

1 watt = 1 kg*(m^2)*(s^(-3)), or

1 watt = 1 N*m/s

Another viewpoint

As explained above,

Power = force*distance/time

We learned in earlier modules that velocity is equal to the ratio of displacement and time. Therefore,

Power = force * velocity

Therefore, power is proportional to both force and velocity. A truck in a load-pulling contest that moves rather slowly but with great force is powerful.

Similarly, a racing motorcycle that moves very fast with relatively little force is also powerful.

And the great granddaddy of them all, a huge boulder that plows through a house at great speed during a landslide is very powerful.

Sample calculations

A story of two cranes

One crane named A lifts a 1000 kg object to a height of 100 meters in 10 seconds. Another crane named B requires 100 seconds to do the same thing.

Which crane does the most work?

Which crane delivers the most power?

Solution:

Both cranes do the same amount of work by displacing the same object the same distance against the force of gravity. The work done is equal to

(1000kg*9.8m/s^2)*100m = 980000 joules

Crane A delivers 980000 joules in 10 seconds. Therefore, crane A delivers

(980000 joules) / (10 seconds) = 98000 watts

Crane B delivers

(980000 joules) / (100 seconds) = 9800 watts

Therefore, crane A delivers the most power.

Another story about cranes

One crane named A lifts a 1000 kg object to a height of 100 meters in 10 seconds. Another crane named B lifts a 500 kg object to a height of 100 meters in 5 seconds.

Which crane does the most work?

Which crane delivers the most power?

Solution:

The work done by crane A is

(1000 kg) * (9.8 (m / (s^2))) * (100 m) = 980000 joules

The work done by crane B is

(500 kg) * (9.8 (m / (s^2))) * (100 m) = 490000 joules

Therefore crane A does the most work.

Crane A delivers 980000 joules in 10 seconds. Therefore, crane A delivers

(980000 joules) / (10 seconds) = 98000 watts

Crane B delivers

(490000 joules) / (5 seconds) = 98000 watts

Therefore, both cranes deliver the same amount of power.

Your electric bill

An electric bill is often expressed in terms of kilowatt-hours (kwh). One kilowatt-hour represents a power expenditure of 1000 watts in one hour.

How many joules of energy are represented by 100 kwh?

Solution:

1 kwh = 1000 watt * 1 hour * 3600 s/hour, or

1 kwh = 3.6*10^6 watt*s

1 watt = 1 N*m/s, therefore

1 kwh = 3.6*10^6 *(N*m/s) * s = 3.6*10^6 N*m

1 joule = 1 N*m, therefore

1 kwh = 3.6*10^6 joules, and

100 kwh = 3.6*10^8 joules

Do the calculations

I encourage you to repeat the calculations that I have presented in this lesson to confirm that you get the same results. Experiment with the scenarios, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modules in this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

Note:

Housekeeping material
  • Module name: Energy -- Power for Blind Students
  • File: Phy1200.htm
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • potential energy
    • work
    • gravitational potential energy
    • elastic potential energy
    • kinetic energy
    • mechanical energy
    • total mechanical energy
    • power
    • watt

Note:

Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDF file for this module at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should be aware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

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A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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