Newtonian Physics Benjamin Crowell Book 1 in the Light and Matter series of introductory physics textbooks www.com Newtonian Physics www.com The Light and Matter series of introductory physics textbooks: 1 Newtonian Physics 2 Conservation Laws 3 Vibrations and Waves 4 Electricity and Magnetism 5 Optics 6 The Modern Revolution in Physics www.com Newtonian Physics Benjamin Crowell www.com Light and Matter Fullerton, California www.com © 1998-2002 by Benjamin Crowell All rights reserved.com To Paul Herrschaft and Rich Muller.com Brief Contents 0 Introduction and Review. 15 1 Scaling and Order-of-Magnitude Estimates 35 Motion in One Dimension 2 Velocity and Relative Motion. 54 3 Acceleration and Free Fall. 75 4 Force and Motion.
99 5 Analysis of Forces. 115 Motion in Three Dimensions 6 Newton’s Laws in Three Dimensions. 147 8 Vectors and Motion. 203 Solutions to Selected Problems .com Contents Preface.
13 A Note to the Student Taking Calculus Concurrently. 14 0 Introduction and Review 15 0.1 The Scientific Method .2 What Is Physics? .3 How to Learn Physics .5 Basics of the Metric System .6 The Newton, the Metric Unit of Force .7 Less Common Metric Prefixes. 28 Motion in One 0. 32 Dimension 53 Homework Problems.
33 2 Velocity and Relative Motion 54 2.1 Types of Motion .2 Describing Distance and Time .3 Graphs of Motion; Velocity.4 The Principle of Inertia .5 Addition of Velocities .6 Graphs of Velocity Versus Time .7 ∫ Applications of Calculus. 72 1 Scaling and Order-of- Magnitude Estimates35 3 Acceleration and Free 1.2 Scaling of Area and Volume .1 The Motion of Falling Objects .3 Scaling Applied to Biology .4 Order-of-Magnitude Estimates .3 Positive and Negative Acceleration .5 The Area Under the Velocity-Time Graph87 3.6 Algebraic Results for Constant Acceleration .7* Biological Effects of Weightlessness .8 ∫ Applications of Calculus .com 4 Force and Motion 99 4.2 Newton’s First Law .3 Newton’s Second Law .4 What Force Is Not .5 Inertial and Noninertial Frames of Reference. 113 5 Analysis of Forces 115 5.1 Newton’s Third Law .2 Classification and Behavior of Forces 120 5.3 Analysis of Forces .4 Transmission of Forces by Low-Mass Objects .5 Objects Under Strain .6 Simple Machines: The Pulley .2 Calculations with Magnitude and Direction 150 7.3 Techniques for Adding Vectors .4* Unit Vector Notation. 156 8 Vectors and Motion 157 8.1 The Velocity Vector .2 The Acceleration Vector .3 The Force Vector and Simple Machines 162 8.4 ∫ Calculus With Vectors.
165 Motion in Three Homework Problems. 166 Dimensions 137 6 Newton’s Laws in Three Dimensions 137 6.1 Forces Have No Perpendicular Effects137 6.2 Coordinates and Components .3 Newton’s Laws in Three Dimensions 142 Summary .com 9 Circular Motion 169 9.1 Conceptual Framework for Circular Motion 169 9.2 Uniform Circular Motion .3 Nonuniform Circular Motion .2 Newton’s Law of Gravity .4 Vector Addition of Gravitational Forces .5 Weighing the Earth .6* Evidence for Repulsive Gravity. 198 Exercises 203 Solutions to Selected Problems211 Glossary 217 Mathematical Review 219 Trig Tables 220 Index 221 www.com Preface Why a New Physics Textbook? We 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 Concep- tual Physics for non-science 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. 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 introduc- tory 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 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 re- sponse 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 that have both 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.com 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.
It has been said that critics discuss art with each other, but artists 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 tech- nique. 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. topics typically covered at the same chapters of this book point in a calculus course 0-1 introduction review 2-3 velocity and acceleration limits 4-5 Newton's laws the derivative concept techniques for finding derivatives; 6-8 motion in 3 dimensions derivatives of trigonometric functions 9 circular motion the chain rule 10 gravity local maxima and minima chapters of Conservation Laws 1-3 energy concavity and the second derivative 4 momentum 5 angular momentum the indefinite integral chapters of Vibrations and Waves 1 vibrations the definite integral 2-3 waves the fundamental theorem of calculus 14 www.com 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! 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.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 techniques 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 thick- ness of a penny.