Conceptual Physics

760 Pages·2008·14.6 MB·English

by  Kinetic Books

Table of Contents
0 Introduction.............................................................................................................................1
Mechanics
1 Measurement and Mathematics.............................................................................................7
2 Motion in One Dimension.....................................................................................................24
3 Vectors..................................................................................................................................52
4 Motion in Two and Three Dimensions..................................................................................65
5 Force and Newton's Laws....................................................................................................88
6 Work, Energy, and Power...................................................................................................121
7 Momentum..........................................................................................................................145
8 Uniform Circular Motion......................................................................................................166
9 Rotational Kinematics.........................................................................................................175
10 Rotational Dynamics...........................................................................................................198
11 Static Equilibrium and Elasticity..........................................................................................205
12 Gravity and Orbits...............................................................................................................220
13 Fluid Mechanics..................................................................................................................247
Mechanical Waves
14 Oscillations and Harmonic Motion......................................................................................275
15 Wave Motion.......................................................................................................................294
16 Sound.................................................................................................................................308
17 Wave Superposition and Interference................................................................................322
Thermodynamics
18 Temperature and Heat.......................................................................................................335
19 Kinetic Theory of Gases.....................................................................................................360
20 First Law of Thermodynamics, Gases, and Engines..........................................................373
21 Second Law of Thermodynamics, Efficiency, and Entropy................................................383
Electricity and Magnetism
22 Electric Charge and Coulomb's Law..................................................................................400
23 Electric Fields.....................................................................................................................419
24 Electric Potential.................................................................................................................436
25 Electric Current and Resistance.........................................................................................457
26 Capacitors...........................................................................................................................476
27 Direct Current Circuits........................................................................................................489
28 Magnetic Fields...................................................................................................................505
29 Electromagnetic Induction..................................................................................................539
30 Electromagnetic Radiation..................................................................................................557
Light and Optics
31 Reflection............................................................................................................................574
32 Refraction...........................................................................................................................596
33 Lenses................................................................................................................................607
34 Interference.........................................................................................................................627
Modern Physics
35 Special Relativity................................................................................................................638
36 Quantum Physics Part One................................................................................................659
37 Quantum Physics Part Two................................................................................................688
38 Nuclear Physics..................................................................................................................698
Answers to selected problems.............................................................................................721
Copyright 2000-2007 © Kinetic Books Company
All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or
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For additional information on the product(s) and purchasing, please contact Kinetic Books Company.
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0.0 - Welcome to an electronic physics textbook!
Textbooks, like this one, contain words and illustrations. In an ordinary textbook, the
words are printed and the illustrations are static, but in this book, many of the
illustrations are animations and many words are spoken. Altogether, this textbook
contains more than 600,000 words, 150 simulations, 1000 animations, 5000
illustrations, 15 hours of audio narration, and 35,000 lines of Java and JavaScript
code.
All this is designed so that you will experience more physics. You will race cars
around curves, see the forces between charged particles, dock a space craft,
generate electricity by moving a wire through a magnetic field, control waves in a
string to “make music”, measure the force exerted by an electric field, and much
more. These simulations and animations are designed to allow you to “see” more
physics and make it easier for you to assess your learning, since many of them
pose problems for you to solve.
The foundation of this textbook is the same as a traditional textbook: text like this
and illustrations. Concepts like “velocity” or “Newton’s second law” are explained as
they are in traditional textbooks. From there we go a step further, taking advantage
of the computer and giving you additional ways to learn about physics. The textbook
has many features: simulations; problems where the computer checks your answers
and then works with you step by step; animations that are narrated; search
capability; and much more. We will start with some simulations. In subsequent
sections, we will show you how we use animations and narration to teach physics,
and how a computer will help you solve problems.
At the right are three examples of how we take advantage of an interactive
simulation engine. Click on any of the illustrations to start an interactive simulation; it
will open a separate window. When you are done, you can close the window. The
window that contains this text will remain open.
In the first simulation, you aim the monkey’s banana bazooka so that the banana
will reach the professor. The instant the banana is fired, the professor lets go of the
tree and falls toward the ground. You aim the banana bazooka by dragging the
head of the arrow shown on the right. Aim the bazooka and then press GO. Press
RESET to try again. (And do not worry: We, too, value physics professors, so the
professor will emerge unscathed.)
This is an animated version of a classic physics problem and appears about halfway
through a chapter of the textbook. The majority of our simulations require the
calculation of precise answers, but like this one, they are all great ways to see a
concept at work.
In the second simulation, you can extend a simple circuit. The initial circuit shown
on the right contains a battery and a light bulb. You can add light bulbs or more wire
segments by dragging them near the desired location. Once there, they will snap
into place. You can also use an ammeter to measure the amount of current flowing
through a section of a wire, and a voltmeter to measure the potential difference
across a light bulb or the battery.
There are many experiments you can conduct with these simple tools. For instance,
place a light bulb in the horizontal segment above the one which already contains
the light bulb and connect it to the circuit with two additional vertical wire segments.
Does this alter the power flowing through the first light bulb? The brightness of each
light bulb is roughly proportional to the power the circuit supplies to it.
How do the potential differences across the light bulbs compare to one another? To the potential difference across the battery? Measure the
current flowing through a piece of wire immediately adjacent to the battery, and through each of the wire segments that contains a light bulb.
Do you see a mathematical relationship between these three values?
You will be asked to make observations in many simulations like this, and as you learn physics, to apply what you have learned to answer
problems posed by the simulations. You will use your knowledge to do everything from juggle to dock a spaceship!
In the third simulation, you experiment with a simple electric generator. When the crank is turned, the rectangular wire loop shown in the
illustration turns in a magnetic field. The straight lines you see are called magnetic field lines. Turning the handle of the generator creates an
electric current and what is called an emf. The emf is measured in volts.
After you launch the simulation, you can change your point-of-view with a slider. The illustration you see to the right provides a conceptual
overview of what a generator is. If you change the viewing angle, you can better see the angle between the wire and the field, and how that
affects the current. A device called an oscilloscope is used to measure the emf created by the generator.
Copyright 2000-2007 Kinetic Books Co. Chapter 00 1
The electric generator is an advanced topic, and if you are just beginning your study of physics, it presents you with many unfamiliar concepts.
However, the simulation shows how we can take advantage of software to allow you to change the viewing angle and to view processes that
change over time.
If you want to see more simulations we enjoyed creating: “dragging” a ball to match a graph, sliding a block up a plane, electromagnetic
induction, electric potential, space docking mission and wave interference. You can click on any of these topics and the link will take you to that
section. There are many simulations; to see even more of them, you can click on the table of contents, pick a chapter, and then click on any
section whose name starts with “interactive problem.”
To move to the next section, click on the right arrow in the black bar above or below, the arrow to the right of 0.0.
0.1 - Whiteboards
Right now, you are reading the text of this textbook. Its design is similar to that found in
traditional textbooks. By “text,” we mean the words you are reading and the illustrations
and writing you see to the right.
As you read the words, study the illustrations and work the problems, you may feel as
though you are using a traditional textbook. (We like to think it is well-conceived and
well-written, but that is for you to judge.) You can print out this textbook and use it as
you would a traditional print textbook.
When you use the electronic version of this book, however, you have access to an
entirely different way of learning the material. It starts with what we call the whiteboards.
You launch the whiteboards by clicking on the illustrations to the right. They present the
same material discussed in the text, but do so using a sequence of narrated animations.
Whiteboards
The text and the whiteboards cover essentially the same material. You could learn
physics exclusively through the whiteboards, or you could learn it all via the words and Illustrate physics concepts
pictures you now see. The text sometimes contains additional material: the history of Explain with narration
the topic, an application of a principle and so on. Everything found in the whiteboards is
always found in the text, so you do not have to click through them unless you find them
a useful way to learn. The point is: You have a choice. You may also find a combination
of the two particularly useful, especially for topics you find challenging.
If you are reading this on a computer, try clicking on the illustration titled “Concept 1” to
the right. This will open the whiteboard in a separate window. Each whiteboard is
equipped with animations, audio and its own set of controls. Both this textbook and the
whiteboards can be used simultaneously. If you do not have headphones or
speakers, click on the “show text” button after you open the whiteboard.This will
allow you to read the whiteboard narration.
The electronic format provides a visually compelling way for you to learn what can be
complex concepts and formulas. For instance, instead of a static diagram that
represents a car rounding a curve, our format allows us to actually show the car moving
Whiteboard components
and turning. We can also show you a greater amount of information (cid:237) for example, how
the horizontal and vertical velocities of the car change over time. Concept slides explain idea
Typical sections throughout the book feature three graphic elements on the right side of
the page, corresponding to three parts of the whiteboard. The first introduces the
concept: For instance, what does the term “displacement” mean? The second contains
the equation: How is displacement calculated? The third, located at the bottom right,
then works an example problem to test your understanding of the concept and the
equation.
The textbook contains hundreds of these whiteboards. If you would like to view some
more to get a sense of how animation and audio play together, you can browse any
chapter. You can explore topics like displacement, graphing simple harmonic motion,
hitting a baseball, electric field diagrams, determining the type of image produced by a
mirror and the force of a magnetic field on a moving charged particle.
To move to the next section, click on the right-arrow in the black bar above or below,
the arrow to the right of 0.1. Equations provide formula(s)
2 Copyright 2000-2007 Kinetic Books Co. Chapter 00
Examples work basic problems
0.2 - Interactive problems
In the first section of this chapter, we encouraged you to try various simulations. We
call simulations where you set values and watch the results interactive problems. In
this section, we explain in more detail how they work.
A sample interactive problem can be launched by clicking on the graphic on the
right. When the correct x (horizontal) and y (vertical) velocities are supplied, the
juggler will juggle the three balls. Before you proceed, you may wish to read the
instructions below for using these interactive simulations.
As mentioned, you launch the simulations by clicking on the graphic. Typically, you
will be asked to enter a value in the simulation. Sometimes you fill in a value in a
text entry box, and other times you select a value using spin dials that have up and
down arrow buttons.
Then, you typically push the GO button and the simulation begins (cid:237) things begin to
move. Most simulations have a RESET button that allows you to start again. Many
have a PAUSE button that makes things go three times faster (just kidding (cid:237) they
pause the simulation so you can record data).
Many simulations, especially those at the beginning of the chapters, just ask you to observe how entering different values changes the results.
Simulations often come with gauges that display variables as they change, such as a speedometer to keep track of a car’s speed as it goes
around a track. You may observe the relationship between mass and the amount of gravitational force, for instance. Other simulations provide
direct feedback if you succeed: the juggler juggles, you beat another racecar, and so forth.
Simulations later in the chapter often ask you to perform calculations in order to achieve a particular goal. These simulations are designed to
make trial-and-error an ineffective tactic since they require a great amount of precision in the answer.
Enough preamble: Try the juggling simulation to the right. Enter any values you like for the initial y and x velocities, using the spin dials. Then
press GO and watch as the juggler begins to juggle. Press RESET to enter a different set of values. A hint: One pair of values that will enable
you to juggle is 6.0 m/s (meters per second) for the y velocity and 0.6 m/s for the x velocity.
0.3 - Sample problems and derivations
The mouse goes 11.8 meters in 3.14
seconds at a constant acceleration of
1.21 m/s2.
What is its velocity at the beginning
and end of the 11.8 meters?
In addition to text and interactive problem sections, this textbook contains sections with sample problems and derivations of equations.
Sample problems often demonstrate a useful problem-solving technique. You see a typical sample problem above. Derivations show how
an equation new to you can be created from equations you have already learned.
We follow the same sequence of steps in sample problems and derivations. (You will also follow this same sequence when you work through
problems called interactive checkpoints; more on this type of problem in the next section.) Sample problems, derivations and interactive
checkpoints all have some or all of the following: a diagram, a table of variables, a statement of the problem-solving strategy, the principles and
equations used, and a step-by-step solution.
To show how these are organized, we work through a sample problem from the study of linear motion. The problem is stated above.
Draw a diagram
Copyright 2000-2007 Kinetic Books Co. Chapter 00 3
It is often helpful to draw a diagram of the problem, with important values labeled. Although almost every problem is stated using an illustration,
we sometimes find it useful to draw an additional diagram.
Variables
We summarize the variables relating to the problem in a table. Some of these have values given in the problem statement or illustration. If we
do not know the value of a variable, we enter the variable symbol. A variable table for the problem stated above is shown.
displacement (cid:507)x = 11.8 m
acceleration a = 1.21 m/s2
elapsed time t = 3.14 s
initial velocity v
i
final velocity v
f
There are two reasons we write the variables. One is so that if you see a variable with which you are unfamiliar, you can quickly see what it
represents. The other is that it is another useful problem-solving technique: Write down everything you know. Sometimes you know more than
you think you know! Some variables may also prompt you to think of ways to solve the problem.
After these two steps, we move to strategy.
What is the strategy?
The strategy is a summary of the sequence of steps we will follow in solving the problem. Some students who used this book early in its
development called the strategy section “the hints,” which is another way to think of the strategy. There are typically many ways to solve a
problem; our strategy is the one we chose to employ. (As we point out in the text when we actually solve this problem, there is another efficient
manner in which to solve it.)
For the problem above, our strategy was:
1. There are two unknowns, the initial and final velocities, so choose two equations that include these two unknowns and the values you
do know.
2. Substitute known values and use algebra to reduce the two equations to one equation with a single unknown value.
Principles and equations
Principles and equations from physics and mathematics are often used to solve a problem. For the problem above, for example, these two
linear motion equations that apply when acceleration is constant are useful:
v = v + at
f i
(cid:507)x = ½(v + v)t
i f
The physics principles are the crucial points that the problems are attempting to reinforce. If they look quite familiar to you at some point: Great!
Step-by-step solution
We solve the problem (or work through the derivation) in a series of steps. We provide a reason for each step. If you want a more detailed
explanation, you can click on a step, which causes a more detailed text explanation to appear on the right. Some students find the additional
information quite helpful; others prefer the very brief explanation. It also varies depending on the difficulty of the problem (cid:237) everyone can use a
little help sometimes.
Here are the first three steps that we used to solve the problem above.
Step Reason
1. v = v + at first motion equation
f i
2. v = v + (1.21 m/s2) (3.14 s) substitute values
f i
3. v = v + 3.80 m/s multiply
f i
0.4 - Interactive checkpoints
The great pyramid of Cheops has a
square base with edges that are
almost exactly 230 m long. The side
faces of the pyramid make an angle
of 51.8° with the ground.
The apex of the pyramid is directly
above the center of the base. Find its
height.
4 Copyright 2000-2007 Kinetic Books Co. Chapter 00
This section shows you an example of an interactive checkpoint. We chose a problem that uses mathematics you may be familiar with in case
you would like to solve the problem yourself.
In interactive checkpoints, all of the problem-solving elements are initially hidden. You can open any element by clicking [Show] below.
You can check your answer at any time by entering it at the top and pressing [Check] to see if you are right. You will find this is far more
efficient than keying all the information into the computer, which provides a good motivation for you to solve the problem yourself. However, if
you are stuck, you can always have the computer help you.
In the parts called Variables, Strategy, and Physics principles and equations, the computer will show you the information you need when you
ask. In the Physics principles and equations section, we show you the principles and equations you need to solve the problem, as well as some
that do not apply directly to the problem.
In the Step-by-step solution, you choose from the equations by clicking on the one you think you need to use. You must enter the correct
values in each Step-by-step part of the solution to proceed to the next step.
Answer:
h = m
0.5 - Quizboards
Each chapter has a quizboard containing several multiple-choice conceptual and
quantitative problems. There are over 250 quizboard problems throughout the textbook.
Quizboards allow you to test your understanding of a chapter. You see a quizboard on
the right.
Quizboards appear between the summary section and the problems section in every
chapter. The quizboard for a chapter can be launched from the quizboard section by
clicking on the image on the right side of the page. The quizboards are designed to
enable you to review many of the crucial ideas in a chapter.
Each problem in a quizboard consists of four parts: the question, the answer choices,
the hints, and the solution. If you think you know the answer to the problem, choose it
and click the “Check answer” button. A message will appear telling you whether you are
correct. You can keep trying until you get the problem right. If you are having trouble,
click “Give me a hint”. Every time you click this button, a new hint appears until there
are no more hints available. You can always click “Show solution” if you find yourself
completely stuck.
Use the “next” and “previous” buttons on the gray bar at the bottom of the window to navigate between problems. You do not have to answer a
problem correctly before moving on, so you can skip problems and come back to them later. If you use the “previous” button to go back to a
problem, it will appear unanswered (even if you answered it before) so that you can try the problem again.
Click on the image to the right to use a sample quizboard. You do not need to know any physics to answer these questions. Good luck!
Copyright 2000-2007 Kinetic Books Co. Chapter 00 5
0.6 - Highlighting and notes
You can add notes or highlight text on most sections of the textbook. Notes always appear at the top of the section. You can use a note to write
short messages about key elements of a section, or to remind yourself not to forget the extra soccer practice or to pick up the groceries.
As the note above says, you insert notes by pressing Add Note at the bottom of the page. You remove a note by clicking on the Delete button
located next to the note. Modify a note by pressing the Edit button.
The text you are reading now is highlighted. To highlight text, click the Highlight button at the bottom of the page to switch it from “Off” to “On”.
When it is “On”, any text you select (by clicking on your mouse and dragging) will be highlighted. You can remove all highlighting from a section
by pressing the “Clear” button.
If the text above is not highlighted, your operating system or browser does not enable us to offer this feature. For instance, the feature is not
available on the Macintosh operating system 0S X 10.2.
If you use a shared computer, the highlighting and notes features may be turned off. The preferences page allows you to enable or disable
either of these features. You will find the preferences page by clicking on the Preferences button at the bottom of the page.
Notes and highlighting are not supported on our Web Access option or the trial version of the product on our web site.
0.7 - Online Homework
This textbook was designed to support online assessment of homework. Instructors can assign specific problems online, and you submit your
responses over the Internet to a central computer. You can work offline and submit the answers when you are ready.
The computer checks the answers, and sends a report about your efforts, and the efforts of your peers, to your instructor. Your instructor can
configure this service in a variety of fashions. For instance, they can set deadlines for homework assignments or decide if you are allowed to
try answering a question a few times.
Online Homework is an optional feature; not all instructors will use it. If your instructor has supplied you with a login ID or told you to sign up for
Online Homework, please log in now. If you are unsure, please check with your instructor.
If you want to learn more about on-line assessment in general, click here.
0.8 - Finding what you need in this book
You can navigate through the book using the Table of Contents button. When you roll your mouse over it, you will see three links.
The Chapter TOC link takes you to the table of contents for the chapter you are currently in. You will see more sections than you might see in a
typical physics textbook table of contents. We chose to make it very easy to navigate to each element of the textbook by listing sample
problems, derivations and other elements discretely.
The Main TOC link takes you to the list of all the chapters in the textbook. Clicking on the third link, Physics Factbook, opens a reference tool
containing useful information including mathematics review topics and formulas, unit conversion factors, fundamental physical constants,
properties of the elements, astronomical data, and physics equations. The Factbook also has a built-in search feature to help you find
information quickly.
This textbook has no index, but likely you will find that entering text in the “search box” is more useful. Search is located at the bottom of each
Web page. Search performs its task by looking at the name of each section, at the first (or essential) time any term is defined, and at some
other types of text. Typing in a phrase like “kinetic energy” will produce a number of useful results.
When you use search, you do not have to worry about sequence: You do not have to guess whether we listed something under, say, “average
velocity” or “velocity average.” Search looks for the terms and presents them to you along with some of their context.
That is it for logistics. The people who worked on this textbook (cid:237) about 50 of us (cid:237) hope you enjoy it. We have a passion for physics, and we
hope some of that carries on to you.
To explore the rest of the book, move your mouse over a Table of Contents button at the top or bottom of this page, and select the Main TOC.
6 Copyright 2000-2007 Kinetic Books Co. Chapter 00
1.0 - Introduction
Heavyweight, lightweight, overweight, slender. Small,
tall, vertically impaired, “how’s the weather up there?”
Gifted, average, 700 math/600 verbal, rocket
scientist. Gorgeous, handsome, hunk, babe.
Humans like to measure things. Whether it is our
body size, height, IQ or looks, everything seems to be
fair game.
Physics will teach you to measure even more things.
For example, quantities such as displacement,
velocity and acceleration are crucial to understanding
motion. Other topics have yet more things to quantify:
Mass and period are concepts required to understand the movement of planets; resistance and current are used for analyzing electric circuits.
Just as you have developed a vocabulary for the things you measure, so have physicists.
There are many different units for measuring different properties. It is possible to go all the way from A through Z in units: amperes, bars,
centimeters, dynes, ergs, farads, grams, hertz, inches, joules, kilograms, liters, meters, newtons, ohms, pascals, quintals, rydbergs, slugs,
teslas, unit magnetic poles, volts, webers, x units, years, and zettabars. (OK, we had to stretch for X, but it is a real unit.)
Physicists have so many units of measure at their disposal because they have plenty to measure. Physicists use amperes to tell how much
electric current flows through a wire, “pascals” quantify pressure, and “teslas” are used to measure the strength of a magnetic field. If you so
desired, you could become a units expert and impress (or worry) your classmates by casually noting that the U.S. tablespoon equals 1.04
Canadian tablespoons, or deftly differentiating between the barrel, U.K. Wine, versus the barrel, U.S. federal spirits, or the barrel, U.S. federal,
all of which define slightly different volumes. Or you could become an international sophisticate, telling friends that one Germandoppelzentner
equals about 77,162 U.K. scruples, which of course equals approximately 101.97 metric glugs, which comes out to3120 ukies, a Libyan unit
used for the sole purpose of measuring ostrich feathers and wool.
Fortunately, you do not need to learn units such as the ones mentioned immediately above, and you will learn the others over time. Textbooks
like this one provide tables that specify the relationships between commonly used units and you will use these tables to convert between units.
1.1 - The metric system and the Système International d’Unités
Metric system: The dominant system of
measurement in science and the world.
Historically, people chose units of measure related to everyday life (the “foot” is one
example). Scientists continued this tradition, developing units such as “horsepower” to
measure power.
The French challenged this philosophy of measurement during their Revolution, when
they decided to give measurement a more scientific foundation. Instead of basing their
system on things that change (cid:237) the length of a person’s foot changes during her
lifetime, for example (cid:237) the French based their system on what they viewed as constant.
Metric system and the Système
To accomplish this, they created units such as the meter, which they defined as a
International
certain fraction of the Earth’s circumference. (To be specific: one ten-millionth of the
meridian passing through Paris from the equator to the North Pole. It turns out that the System defines fundamental units
distance from the equator to the North Pole does vary, but the metric system’s intent of
Larger/smaller units based on powers of
consistency and measurability was exactly on target.)
10
The metric system is also based on another inspired idea: units of measurement should
be based on powers of 10. This differs from the British system, which provides more variety: 12 inches in a foot, 5280 feet to a mile and so
forth.
The metric system makes conversions much simpler to perform. For example, in order to calculate the number of inches in a mile, you would
typically multiply by 5280 (for feet in a mile) and then by 12 (for inches in a foot). However, in the metric system, to convert between units, you
typically multiply by a power of 10. For instance, to convert from kilometers to meters, you multiply by 1000. The prefix “kilo” means 1000.
The revolutionaries were a little extreme (as revolutionaries tend to be) and they held onto their position of power for only a decade or so. While
some of their legacy (including their political art, rather mediocre as is much political art) has been forgotten, their clever and sensible metric
system endures. Most scientists, and most countries, use the metric system today.
Scientists continue to update and refine the metric system. This expanded and updated system of measurement used today is called the
Système International d’Unités, or SI. We typically use SI units in this textbook; several times, though, we refer to different units that may be
better known to you or are commonly used in the sciences. We will discuss some of the SI units further in this chapter.
Over the years, scientists have refined measurement systems, making the definition of units ever more precise. For example, instead of being
Copyright 2000-2007 Kinetic Books Co. Chapter 01 7
based on the Earth’s circumference, the meter is now defined as the distance light travels in a vacuum during the time interval of
1/299,792,458 of a second. Although perhaps not as memorable as the initial standard, this definition is important because it is constant,
precise, indestructible, and can be reproduced in laboratories around the world.
In addition to using meters for length, the Système International uses seconds (time), kilograms (mass), amperes (electric current), kelvins
(temperature), moles (amount of substance) and candelas (luminous intensity). Many other derived units are based on these fundamental
units. For instance, a newton measures force and is equal to kilograms times meters per second squared. On Earth, the force of gravity on a
small apple is about one newton.
At the risk of drowning you in terminology, we should point out that you might also encounter references to the MKS (meter/kilogram/second)
and CGS (centimeter/gram/second) systems. These systems are named for the units they use for length, mass and time.
1.2 - Prefixes
Metric units often have prefixes. Kilometers and centimeters both have prefixes before
the word “meter.” The prefixes instruct you to multiply or divide by a power of 10: kilo
means multiply by 1000, so a kilometer equals 1000 meters. Centi means divide by
100, so a centimeter is one one-hundredth of a meter. In other words, there are
100 centimeters in a meter. The table in Equation 1 on the right lists the values for the
most common prefixes.
Prefixes allow you to describe the unimaginably vast and small and everything in
between. To illustrate, every day the City of New York produces 10 gigagrams of
garbage. The distance between transistors in a microprocessor is less than a
micrometer. The power of the Sun is 400 yottawatts (a yotta corresponds to the factor of
1024). It takes 3.34 nanoseconds for light to travel one meter. The electric potential
difference across a nerve cell is about 70 millivolts.
Prefixes
These prefixes can apply to any unit. You can use gigameters to conveniently quantify a
Create larger, smaller units
vast distance, gigagrams to measure the mass of a huge object, or gigavolts to describe
a large electrical potential difference.
Some of the most common prefixes (cid:237) kilo, mega, and giga (cid:237) are commonly used to
describe the specifications of computers. The speed of a computer microprocessor is
measured by how many computational cycles per second it can perform.
Microprocessor speeds used to be specified in megahertz (one million cycles per
second) but are now specified in gigahertz (one billion cycles per second). Modem
speeds have increased from kilobits to megabits per second. (Although bits are not part
of the metric system, computer scientists use the same prefixes.)
The units of measurement you use are a matter of both convenience and convention.
For example, snow skis are typically measured in centimeters; a ski labeled “170” is 170
centimeters long. However, it could also be called a 1.7-meter ski or a 1700-millimeter
ski. The ski industry has decided that centimeters are reasonable units and has settled
on their use as a convention. Common prefixes for powers of 10
In this textbook, you are most likely to encounter kilo, mega and giga on the large side
of things and centi, milli, micro and nano on the small. Some other prefixes are not as
common because they just do not seem that useful. Is it easier to say “a decameter”
than the more straightforward 10 meters? And, for the extremely large and small,
scientists often use another technique called scientific notation rather than prefixes.
What is the distance between the
towns in kilometers?
1000 m = 1 km
8 Copyright 2000-2007 Kinetic Books Co. Chapter 01