Newtonian Physics, by Benjamin Crowell - Science, Tutorial, and textbook (pdf document) free file download at fliiby.com

"Book 1 in the Light and Matter series of free introductory physics textbooks www.lightandmatter.com The Light and Matter series of introductory physics textbooks: 1 2 3 4 5 6 Newtonian Physics Conservation Laws Vibrations and Waves Electricity and Magnetism Optics The Modern Revolution in Physics Benjamin Crowell www.lightandmatter.com Fullerton, California www.lightandmatter.com copyright 1998-2005 Benjamin Crowell edition 2.3 rev. August 11, 2007 This book is licensed under the Creative Commons Attribution-ShareAlike license, version 1.0, http://creativecommons.org/licenses/by-sa/1.0/, except for those photographs and drawings of which I am not the author, as listed in the photo credits. If you agree to the license, it grants you certain privileges that you would not otherwise have, such as the right to copy the book, or download the digital version free of charge from www.lightandmatter.com. At your option, you may also copy this book under the GNU Free Documentation License version 1.2, http://www.gnu.org/licenses/fdl.txt, with no invariant sections, no front-cover texts, and no back-cover texts. ISBN 0-9704670-1-X To Paul Herrschaft and Rich Muller. Brief Contents 0 Introduction and Review 19 1 Scaling and Order-of-Magnitude Estimates 43 Motion in One Dimension 2 3 4 5 6 7 8 9 10 Velocity and Relative Motion 69 Acceleration and Free Fall 91 Force and Motion 121 Analysis of Forces 141 Motion in Three Dimensions Newton’s Laws in Three Dimensions Vectors 183 Vectors and Motion 193 Circular Motion 207 Gravity 221 171 Contents Preface . . . . . . . . . . . . . . 15 date changes in size, 56. 0 Introduction and Review 0.1 The Scientiﬁc Method . . . . . . 0.2 What Is Physics? . . . . . . . . Isolated systems and reductionism, 24. 19 22 25 27 28 1.4 Order-of-Magnitude Estimates. . . Summary . . . . . . . . . . . . . Problems . . . . . . . . . . . . . 57 60 61 0.3 How to Learn Physics . . . . . . 0.4 Self-Evaluation . . . . . . . . . 0.5 Basics of the Metric System. . . . The metric system, 28.—The second, 29.— The meter, 30.—The kilogram, 30.— Combinations of metric units, 30. 0.6 0.7 0.8 0.9 The Newton, the Metric Unit of Force Less Common Metric Preﬁxes . . . Scientiﬁc Notation . . . . . . . . Conversions . . . . . . . . . . Should that exponent be positive or negative?, 35. 31 32 32 34 0.10 Signiﬁcant Figures . . . . . . . Summary . . . . . . . . . . . . . Problems . . . . . . . . . . . . . 36 38 40 I Motion in One Dimension 2 Velocity and Relative Motion 2.1 Types of Motion . . . . . . . . . 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. 69 1 Scaling and Order-ofMagnitude Estimates 1.1 Introduction . . . . . . . . . . Area and volume, 43. 2.2 Describing Distance and Time. . . 43 45 A point in time as opposed to duration, 74.—Position as opposed to change in position, 75.—Frames of reference, 75. 73 1.2 Scaling of Area and Volume. . . . Galileo on the behavior of nature on large and small scales, 46.—Scaling of area and volume for irregularly shaped objects, 49. 2.3 Graphs of Motion; Velocity . . . . Motion with constant velocity, Motion with changing velocity, Conventions about graphing, 78. 76.— 77.— 76 1.3 Scaling Applied to Biology. . . . Organisms of diﬀerent sizes with the same shape, 54.—Changes in shape to accommo- 54 2.4 The Principle of Inertia . . . . . . Physical eﬀects relate only to a change in 80 10 velocity, 80.—Motion is relative, 81. 2.5 Addition of Velocities. . . . . . . Addition of velocities to describe relative motion, 83.—Negative velocities in relative motion, 83. 83 2.6 Graphs of Velocity Versus Time 2.7 Applications of Calculus . . Summary . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . 85 86 87 89 3 Acceleration and Free Fall 3.1 The Motion of Falling Objects . . . How the speed of a falling object increases with time, 93.—A contradiction in Aristotle’s reasoning, 94.—What is gravity?, 94. 91 3.2 Acceleration . . . . . . . . . . Deﬁnition of acceleration for linear v − t graphs, 95.—The acceleration of gravity is diﬀerent in diﬀerent locations., 96. 95 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. 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. 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. 3.8 Applications of Calculus . . . . 111 Summary . . . . . . . . . . . . . 113 Problems . . . . . . . . . . . . . 114 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 Reference . Summary . Problems . and .. .. .. Noninertial ..... ..... ..... Frames .... .... .... of . 134 . 137 . 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, 153. Problems . . . . . . . . . . . . . 180 5.3 Analysis of Forces. . . . . . . . 154 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 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 II Motion in Three Dimensions 6 Newton’s Laws Dimensions in Three Addition of vectors given their components, 188.—Addition of vectors given their magnitudes and directions, 188.—Graphical addition of vectors, 188. 6.1 Forces Have No Perpendicular Effects . . . . . . . . . . . . . . 171 Relationship to relative motion, 173. 7.4 Unit Vector Notation . 7.5 Rotational Invariance . Summary . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 189 191 192 8 Vectors and Motion 8.1 The Velocity Vector . . . . 8.2 The Acceleration Vector . . 8.3 The Force Vector and Machines . . . . . . . . . . 8.4 Calculus With Vectors . . Summary . . . . . . . . . . Problems . . . . . . . . . . . . . 194 . . . 195 Simple . . . 198 . . . 199 . . . 203 . . . 204 6.2 Coordinates and Components . . . 175 Projectiles move along parabolas., 176. 6.3 Newton’s Laws in Three Dimensions 177 Summary . . . . . . . . . . . . . 179 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. 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. 9.2 Uniform Circular Motion . . 9.3 Nonuniform Circular Motion . Summary . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . 212 215 216 217 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 Appendix 1: Exercises 244 Appendix 2: Photo Credits 256 Appendix 3: Hints and Solutions 257 13 14 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. Newtonian Physics 0-1 introduction 2-3 velocity and acceleration 4-5 Newton’s laws 6-8 motion in 3 dimensions review limits the derivative concept techniques for ﬁnding derivatives; derivatives of trigonometric functions the chain rule local maxima and minima concavity and the second derivative the indeﬁnite integral the deﬁnite integral the fundamental theorem of calculus 9 circular motion 10 gravity Conservation Laws 1-3 energy 4 momentum 5 angular momentum Vibrations and Waves 1-2 vibrations 3-4 waves Preface 17 18 The Mars Climate Orbiter is prepared for its mission. The laws of physics are the same everywhere, even on Mars, so the probe could be designed based on the laws of physics as discovered on earth. There is unfortunately another reason why this spacecraft is relevant to the topics of this chapter: it was destroyed attempting to enter Mars’ atmosphere because engineers at Lockheed Martin forgot to convert data on engine thrusts from pounds into the metric unit of force (newtons) before giving the information to NASA. Conversions are important! Chapter 0 Introduction and Review If you drop your shoe and a coin side by side, they hit the ground at the same time. Why doesn’t the shoe get there ﬁrst, since gravity is pulling harder on it? How does the lens of your eye work, and why do your eye’s muscles need to squash its lens into diﬀerent shapes in order to focus on objects nearby or far away? These are the kinds of questions that physics tries to answer about the behavior of light and matter, the two things that the universe is made of. 0.1 The Scientiﬁc Method Until very recently in history, no progress was made in answering questions like these. Worse than that, the wrong answers written by thinkers like the ancient Greek physicist Aristotle were accepted without question for thousands of years. Why is it that scientiﬁc knowledge has progressed more since the Renaissance than it had in all the preceding millennia since the beginning of recorded history? Undoubtedly the industrial revolution is part of the answer. Building its centerpiece, the steam engine, required improved tech- 19 a / Science is a cycle of theory and experiment. niques for precise construction and measurement. (Early on, it was considered a major advance when English machine shops learned to build pistons and cylinders that ﬁt together with a gap narrower than the thickness of a penny.) But even before the industrial revolution, the pace of discovery had picked up, mainly because of the introduction of the modern scientiﬁc method. Although it evolved over time, most scientists today would agree on something like the following list of the basic principles of the scientiﬁc method: (1) Science is a cycle of theory and experiment. Scientiﬁc theories are created to explain the results of experiments that were created under certain conditions. A successful theory will also make new predictions about new experiments under new conditions. Eventually, though, it always seems to happen that a new experiment comes along, showing that under certain conditions the theory is not a good approximation or is not valid at all. The ball is then back in the theorists’ court. If an experiment disagrees with the current theory, the theory has to be changed, not the experiment. (2) Theories should both predict and explain. The requirement of predictive power means that a theory is only meaningful if it predicts something that can be checked against experimental measurements that the theorist did not already have at hand. That is, a theory should be testable. Explanatory value means that many phenomena should be accounted for with few basic principles. If you answer every “why” question with “because that’s the way it is,” then your theory has no explanatory value. Collecting lots of data without being able to ﬁnd any basic underlying principles is not science. (3) Experiments should be reproducible. An experiment should be treated with suspicion if it only works for one person, or only in one part of the world. Anyone with the necessary skills and equipment should be able to get the same results from the same experiment. This implies that science transcends national and ethnic boundaries; you can be sure that nobody is doing actual science who claims that their work is “Aryan, not Jewish,” “Marxist, not bourgeois,” or “Christian, not atheistic.” An experiment cannot be reproduced if it is secret, so science is necessarily a public enterprise. As an example of the cycle of theory ..."

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