Newtonian Physics By Benjamin Crowell free download

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Preface . . . . . . . . . . . . . . 15
0 Introduction and Review
0.1 The Scientific Method . . . . . . 19
0.2 What Is Physics? . . . . . . . . 22
Isolated systems and reductionism, 24.
0.3 How to Learn Physics . . . . . . 25
0.4 Self-Evaluation . . . . . . . . . 27
0.5 Basics of the Metric System. . . . 28
The metric system, 28.—The second, 29.—
The meter, 30.—The kilogram, 30.—
Combinations of metric units, 30.
0.6 The Newton, the Metric Unit of Force 31
0.7 Less Common Metric Prefixes. . . 32
0.8 Scientific Notation . . . . . . . . 32
0.9 Conversions . . . . . . . . . . 34
Should that exponent be positive or
negative?, 35.
0.10 Significant Figures . . . . . . . 36
Summary . . . . . . . . . . . . . 38
Problems . . . . . . . . . . . . . 40
1 Scaling and Order-of-
Magnitude Estimates
1.1 Introduction . . . . . . . . . . 43
Area and volume, 43.
1.2 Scaling of Area and Volume. . . . 45
Galileo on the behavior of nature on large
and small scales, 46.—Scaling of area and
volume for irregularly shaped objects, 49.
1.3 ? Scaling Applied to Biology. . . . 54
Organisms of different sizes with the same
shape, 54.—Changes in shape to accommodate
changes in size, 56.
1.4 Order-of-Magnitude Estimates. . . 57
Summary . . . . . . . . . . . . . 60
Problems . . . . . . . . . . . . . 61
I Motion in One Dimension
2 Velocity and Relative Motion
2.1 Types of Motion . . . . . . . . . 69
Rigid-body motion distinguished from motion
that changes an object’s shape,
69.—Center-of-mass motion as opposed to
rotation, 69.—Center-of-mass motion in
one dimension, 73.
2.2 Describing Distance and Time. . . 73
A point in time as opposed to duration,
74.—Position as opposed to change in
position, 75.—Frames of reference, 75.
2.3 Graphs of Motion; Velocity . . . . 76
Motion with constant velocity, 76.—
Motion with changing velocity, 77.—
Conventions about graphing, 78.
2.4 The Principle of Inertia . . . . . . 80
Physical effects relate only to a change in
10
velocity, 80.—Motion is relative, 81.
2.5 Addition of Velocities. . . . . . . 83
Addition of velocities to describe relative
motion, 83.—Negative velocities in relative
motion, 83.
2.6 Graphs of Velocity Versus Time . . 85
2.7
R
Applications of Calculus . . . . 86
Summary . . . . . . . . . . . . . 87
Problems . . . . . . . . . . . . . 89
3 Acceleration and Free Fall
3.1 The Motion of Falling Objects . . . 91
How the speed of a falling object increases
with time, 93.—A contradiction in Aristotle’s
reasoning, 94.—What is gravity?, 94.
3.2 Acceleration . . . . . . . . . . 95
Definition of acceleration for linear v − t
graphs, 95.—The acceleration of gravity is
different in different locations., 96.
3.3 Positive and Negative Acceleration . 98
3.4 Varying Acceleration . . . . . . . 101
3.5 The Area Under the Velocity-Time
Graph. . . . . . . . . . . . . . . 104
3.6 Algebraic Results for Constant
Acceleration . . . . . . . . . . . . 107
3.7 ? Biological Effects of Weightlessness109
Space sickness, 109.—Effects of long space
missions, 110.—Reproduction in space,
110.—Simulated gravity, 111.
3.8
R
Applications of Calculus . . . . 111
Summary . . . . . . . . . . . . . 113
Problems . . . . . . . . . . . . . 114
4 Force and Motion
4.1 Force . . . . . . . . . . . . . 122
We need only explain changes in motion,
not motion itself., 122.—Motion changes
due to an interaction between two objects.,
123.—Forces can all be measured on the
same numerical scale., 123.—More than
one force on an object, 124.—Objects can
exert forces on each other at a distance.,
124.—Weight, 124.—Positive and negative
signs of force, 125.
4.2 Newton’s First Law . . . . . . . 125
More general combinations of forces, 127.
4.3 Newton’s Second Law . . . . . . 129
A generalization, 130.—The relationship
between mass and weight, 130.
4.4 What Force Is Not . . . . . . . . 132
Force is not a property of one object.,
132.—Force is not a measure of an object’s
motion., 132.—Force is not energy., 133.—
Force is not stored or used up., 133.—
Forces need not be exerted by living things
or machines., 133.—A force is the direct
cause of a change in motion., 133.
4.5 Inertial and Noninertial Frames of
Reference . . . . . . . . . . . . . 134
Summary . . . . . . . . . . . . . 137
Problems . . . . . . . . . . . . . 138
5 Analysis of Forces
5.1 Newton’s Third Law . . . . . . . 141
A mnemonic for using Newton’s third law
correctly, 143.
11
5.2 Classification and Behavior of Forces146
Normal forces, 149.—Gravitational forces,
149.—Static and kinetic friction, 149.—
Fluid friction, 152.
5.3 Analysis of Forces. . . . . . . . 153
5.4 Transmission of Forces by Low-Mass
Objects . . . . . . . . . . . . . . 156
5.5 Objects Under Strain . . . . . . 158
5.6 Simple Machines: The Pulley . . . 159
Summary . . . . . . . . . . . . . 161
Problems . . . . . . . . . . . . . 163
II Motion in Three Dimensions
6 Newton’s Laws in Three
Dimensions
6.1 Forces Have No Perpendicular
Effects . . . . . . . . . . . . . . 171
Relationship to relative motion, 173.
6.2 Coordinates and Components. . . 175
Projectiles move along parabolas., 176.
6.3 Newton’s Laws in Three Dimensions 177
Summary . . . . . . . . . . . . . 179
Problems . . . . . . . . . . . . . 180
7 Vectors
7.1 Vector Notation . . . . . . . . . 183
Drawing vectors as arrows, 185.
7.2 Calculations with Magnitude and
Direction . . . . . . . . . . . . . 186
7.3 Techniques for Adding Vectors . . 188
Addition of vectors given their
components, 188.—Addition of vectors
given their magnitudes and directions,
188.—Graphical addition of vectors, 188.
7.4 ? Unit Vector Notation . . . . . . 189
7.5 ? Rotational Invariance . . . . . . 189
Summary . . . . . . . . . . . . . 191
Problems . . . . . . . . . . . . . 192
8 Vectors and Motion
8.1 The Velocity Vector . . . . . . . 194
8.2 The Acceleration Vector . . . . . 195
8.3 The Force Vector and Simple
Machines . . . . . . . . . . . . . 198
8.4
R
Calculus With Vectors . . . . . 199
Summary . . . . . . . . . . . . . 203
Problems . . . . . . . . . . . . . 204
12
9 Circular Motion
9.1 Conceptual Framework for Circular
Motion . . . . . . . . . . . . . . 207
Circular motion does not produce an outward
force, 207.—Circular motion does not
persist without a force, 208.—Uniform and
nonuniform circular motion, 209.—Only an
inward force is required for uniform circular
motion., 209.—In uniform circular motion,
the acceleration vector is inward, 210.
9.2 Uniform Circular Motion . . . . . 212
9.3 Nonuniform Circular Motion . . . . 215
Summary . . . . . . . . . . . . . 216
Problems . . . . . . . . . . . . . 217
10 Gravity
10.1 Kepler’s Laws . . . . . . . . . 222
10.2 Newton’s Law of Gravity . . . . . 224
The sun’s force on the planets obeys an
inverse square law., 224.—The forces between
heavenly bodies are the same type of
force as terrestrial gravity., 225.—Newton’s
law of gravity, 226.
10.3 Apparent Weightlessness . . . . 229
10.4 Vector Addition of Gravitational
Forces . . . . . . . . . . . . . . 230
10.5 Weighing the Earth . . . . . . . 232
10.6 ? Evidence for Repulsive Gravity . 235
Summary . . . . . . . . . . . . . 237
Problems . . . . . . . . . . . . . 239

Preface
Why a New Physics Textbook?
We Americans assume that our economic system will always scamper
to provide us with the products we want. Special orders don’t
upset us! I want my MTV! The truth is more complicated, especially
in our education system, which is paid for by the students
but controlled by the professoriate. Witness the perverse success
of the bloated science textbook. The newspapers continue to compare
our system unfavorably to Japanese and European education,
where depth is emphasized over breadth, but we can’t seem to create
a physics textbook that covers a manageable number of topics
for a one-year course and gives honest explanations of everything it
touches on.
The publishers try to please everybody by including every imaginable
topic in the book, but end up pleasing nobody. There is wide
agreement among physics teachers that the traditional one-year introductory
textbooks cannot in fact be taught in one year. One
cannot surgically remove enough material and still gracefully navigate
the rest of one of these kitchen-sink textbooks. What is far
worse is that the books are so crammed with topics that nearly all
the explanation is cut out in order to keep the page count below
1100. Vital concepts like energy are introduced abruptly with an
equation, like a first-date kiss that comes before “hello.”
The movement to reform physics texts is steaming ahead, but
despite excellent books such as Hewitt’s Conceptual Physics for nonscience
majors and Knight’s Physics: A Contemporary Perspective
for students who know calculus, there has been a gap in physics
books for life-science majors who haven’t learned calculus or are
learning it concurrently with physics. This book is meant to fill
that gap.
Learning to Hate Physics?
When you read a mystery novel, you know in advance what structure
to expect: a crime, some detective work, and finally the unmasking
of the evildoer. Likewise when Charlie Parker plays a blues, your ear
expects to hear certain landmarks of the form regardless of how wild
some of his notes are. Surveys of physics students usually show that
they have worse attitudes about the subject after instruction than
before, and their comments often boil down to a complaint that the
person who strung the topics together had not learned what Agatha
Christie and Charlie Parker knew intuitively about form and structure:
students become bored and demoralized because the “march
through the topics” lacks a coherent story line. You are reading the
first volume of the Light and Matter series of introductory physics
textbooks, and as implied by its title, the story line of the series
is built around light and matter: how they behave, how they are
Preface 15
different from each other, and, at the end of the story, how they
turn out to be similar in some very bizarre ways. Here is a guide to
the structure of the one-year course presented in this series:
1 Newtonian Physics Matter moves at constant speed in a
straight line unless a force acts on it. (This seems intuitively wrong
only because we tend to forget the role of friction forces.) Material
objects can exert forces on each other, each changing the other’s
motion. A more massive object changes its motion more slowly in
response to a given force.
2 Conservation Laws Newton’s matter-and-forces picture of
the universe is fine as far as it goes, but it doesn’t apply to light,
which is a form of pure energy without mass. A more powerful
world-view, applying equally well to both light and matter, is provided
by the conservation laws, for instance the law of conservation
of energy, which states that energy can never be destroyed or created
but only changed from one form into another.
3 Vibrations and Waves Light is a wave. We learn how waves
travel through space, pass through each other, speed up, slow down,
and are reflected.
4 Electricity and Magnetism Matter is made out of particles
such as electrons and protons, which are held together by electrical
forces. Light is a wave that is made out of patterns of electric and
magnetic force.
5 Optics Devices such as eyeglasses and searchlights use matter
(lenses and mirrors) to manipulate light.
6 The Modern Revolution in Physics Until the twentieth
century, physicists thought that matter was made out of particles
and light was purely a wave phenomenon. We now know that both
light and matter are made of building blocks with a combination of
particle and wave properties. In the process of understanding this
apparent contradiction, we find that the universe is a much stranger
place than Newton had ever imagined, and also learn the basis for
such devices as lasers and computer chips.
A Note to the Student Taking Calculus Concurrently
Learning calculus and physics concurrently is an excellent idea —
it’s not a coincidence that the inventor of calculus, Isaac Newton,
also discovered the laws of motion! If you are worried about taking
these two demanding courses at the same time, let me reassure you.
I think you will find that physics helps you with calculus while calculus
deepens and enhances your experience of physics. This book
is designed to be used in either an algebra-based physics course or
a calculus-based physics course that has calculus as a corequisite.
This note is addressed to students in the latter type of course.
Art critics discuss paintings with each other, but when painters
16
get together, they talk about brushes. Art needs both a “why”
and a “how,” concepts as well as technique. Just as it is easier to
enjoy an oil painting than to produce one, it is easier to understand
the concepts of calculus than to learn the techniques of calculus.
This book will generally teach you the concepts of calculus a few
weeks before you learn them in your math class, but it does not
discuss the techniques of calculus at all. There will thus be a delay
of a few weeks between the time when a calculus application is first
pointed out in this book and the first occurrence of a homework
problem that requires the relevant technique. The following outline
shows a typical first-semester calculus curriculum side-by-side with
the list of topics covered in this book, to give you a rough idea of
what calculus your physics instructor might expect you to know at
a given point in the semester. The sequence of the calculus topics
is the one followed by Calculus of a Single Variable, 2nd ed., by
Swokowski, Olinick, and Pence.