PHYSICS: The Nature Of Things

Preface

Our book's title is taken from De Rerum Natura, a work by Lucretius,
a roman writer of the first century AD who tried to persuade his readers
by using logical arguments based on observation and experience. This approach
is still in style - modern physicists employ the same methods. Like Lucretius,
both research physicists and physics students struggle to understand *the
nature of things*.

The goal of this book is to help science students develop the kinds of logical thinking that they will need to understand physics. These skills are useful in physics and other disciplines as well. Students often find physics the most difficult of the sciences because, even in the introductory courses, it demands much more than the memorization of facts. To study physics successfully, students need to learn to think like physicists. Students must move beyond being hunters and gatherers of formulae to solve problems - they must become, like physicists, creative problem solvers. In this book we have tried to help students develop the logical reasoning and analytical skills that enable a physicist to practice his or her art.

Citizens in a modern technological society need to be scientifically literate. That only a small, elite group of bright students survives introductory physics and goes on to become aerodynamic engineers or physics professors is no longer acceptable. We hope to make physics accessible to all those who choose to take a physics course. We make it accessible not by watering it down, but by giving students the tools they need to grab hold of the subject and make it their own. Physics is fascinating and fun - at least we think so - and we have tried to convey some of our own enthusiasm for the subject. Examples such as the motion of a hot-dog skier ( Example 3.5, Exercise 3.2) are intended to show the power of physics as a tool for understanding the world and, at the same time, spark students' interest.

Intended for a course that requires calculus as a prerequisite or co-requisite. this text uses calculus throughout, in derivations, examples, and problems. In the first few chapters calculus is used sparingly, mostly in optional sections, so that those students who are just starting calculus will not be overwhelmed. Later in the book, more familiarity is assumed. An interlude following Chapter 7 discusses the use of integration in physics, and presents a five-step plan for setting up integrals. Basic knowledge of algebra, geometry, and trigonometry is assumed. Appendix I includes some basic relations from these disciplines as a reminder and reference for students.

The order of topics in the book is largely traditional, but is organized to allow a large range of sequencing options. For example, introducing angular momentum of a particle in Part II offers the option of foregoing rigid body dynamics in favor of a faster move to the twentieth century. Chapter 14 on oscillatory motion could be used any time after the discussion of energy (Chapter 8). We have included optics in the section on wave motion, to stress the unity of such wave phenomena as interference. However, Chapters 16-18 could easily be covered after E&M if desired. The part on thermodynamics is self contained and could be studied any time after basic mechanics. The first three sections of Chapter 34 (relativity) could be covered after Chapter 3, and section 34.4 could be introduced after Chapter 8. The sections on modern physics tend to be more qualitative, because of the level of mathematical sophistication required for a detailed treatment. They are designed to serve as the culmination of a two or three-semester survey or as an impedance-matching introduction to a standard course on modern physics. These chapters emphasize the conservation principles developed in Part II.

Throughout the book we stress two major themes: conceptual understanding and a consistent approach to problem solving. The material in the book is divided into eight parts, each introducing a unified body of concepts: Newtonian Mechanics; Conservation Laws; Continuous systems; Oscillations and Waves; Thermodynamics; Electromagnetic fields; Electrodynamics; and Twentieth Century Physics. This division helps the students organize their knowledge. The introduction to each part explains the theme to be covered and provides some historical perspective. We begin each chapter with a discussion of the opening photograph, frequently raising a question that we answer within the chapter. Just as each chapter begins with a physical situation to introduce the concepts of the chapter, each topic within the chapter is introduced with a conceptual discussion before the mathematics is presented. In this way we emphasize that working with the concepts is the first essential step in solving a problem. Then the mathematics is used to complete the solution. Similarly, we place a great deal of emphasis on using diagrams to help conceptualize problems and plan their solution. We encourage students to use diagrams as graphical tools to aid their understanding and to help make the transition from a verbal presentation to a mathematical model. Unlike many texts, we not only tell students to use diagrams, we always do it ourselves.

Two interludes in the early parts of the text help lay the groundwork
for a systematic approach to problem solving. In the first interlude, following
Chapter 3, we lay out our basic problem-solving strategy.
The major stages of each problem solution -- model, setup, solve, and analyze
-- are identified and discussed at this point. These steps are used and
*labelled* in every example throughout the book. Seeing the method
at work in each example better enables students to apply a similar approach
in their own solutions. Throughout the book we lay out problem-solving
plans that show the logical steps necessary in certain specific classes
of problems. Each plan is explicity laid out in flow-diagram form. The
method for analyzing dynamical systems with Newton's laws (Chapter
5) provides a good example of a problem-solving plan. A table in the appendix
lists all the plans for easy reference. These solution plans will help
the students develop the skills they need to solve problems in physics,
and help them to go beyond that hunter-gatherer, "find the right equation
and stuff in", stage. As students become more proficient they will
be able to adapt the problem-solving plans to their personal style. While
we have attempted to keep the introductory examples straightforward, and
to assure that they demonstrate a steady gradual increase in difficulty
throughout a chapter or part, twenty study problems,
spread throughout the book, emphasize the use of the problem-solving method
in detail with interesting and sometimes intricate problems. The inclusion
of these problems should help to alleviate the complaint that the "examples
didn't prepare me to do the problems".

The solution plans can also be valuable teaching tools, allowing you to identify precisely where students have difficulties. For example, using the plan in Chapter 5, we found that an astonishingly large number of students are convinced that they can't analyze a system with strings unless they know the value of the tension before carrying out the algebra. Once these difficulties have been identified, it is much easier to confront them and, ultimately, eliminate them.

The second interlude, follwing Chapter 7, shows students how to set up problem solutions using integration. The method involves five steps. The first four steps are a procedure for describing a physical process or system in terms of differential elements and transforming a sum over such elements to a standard mathematical form. Only at the final step does the actual evaluation of an integral occur. This final step is the one that students learn in their calculus classes. In each example requiring integration we use this method, with the steps clearly labelled.

Important mathematical tools are introduced as they are needed, and grouped into Math Toolboxes for easy reference. Examples of this feature include dot and cross product of vectors (Chapters 7 and 9) and harmonic functions (Chapter 14).

The careful use of vectors is stressed throughout. In particular we
introduce vectors as the primary descriptive tool in kinematics, using
geometrical addition (sections 1.4-1.6), and then solve one-dimensional
problems as as a special case of one-component vectors (section 2.3). Not
only does this approach stress the importance of vectors from the beginning,
but it makes the meaning of signs in one-dimensional motion obvious. In
addition to boldface type, we have used the arrow-over
notation so that equations in the book will look the same as the equations
you write on the blackboard, or the students write in their notes. We have
avoided the use of *magic* minus signs (as in the spring force) that
are not explicitly tied to a coordinate choice or stated sign convention.

Beginning students often focus on finding the answer without first framing
any expectation of what the magnitude, units or other characteristics of
the answer might be. As scientists, instructors know the importance of
estimation as a problem-solving strategy. It can be difficult to integrate
this strategy into teaching, however, especially if students don't see
it used regularly in their text. We introduce students to these valuable
skills by using back-of-the-envelope calculations
to estimate results, or to decide what is or is not important in a given
situation. These methods are also used to estimate the reasonableness of
an answer or to figure out the basic physics behind a complicated event
like a thunderstorm. The envelope symbol alerts the students whenever we
use these techniques in examples or discussions. Some
problems show this symbol to indicate that the students should use
these techniques in their solution, and that an *exact* answer is
not expected.

The text offers many opportunities for students to test their knowledge and their ability to use the material. Within each chapter, Exercises allow students to practice with ideas they have just learned. Abbreviated solutions --not just answers -- are given at the end of each chapter, so students can get real feedback after they work an exercise. The end-of-chapter material includes the following: Review Questions emphasize conceptual understanding and can be answered by a quote or paraphrase of material from the chapter; Basic Skill Drill is a set of problems that test students' knowledge of fundamental mathematical relations and the meaning of terms introduced in the chapter; an extensive set of Questions and Problems include practical applications and conceptual questions as well as the usual textbook exercises. Symbols preceding each problem identify the level of difficulty, and also indicate the conceptual problems. Many of the problems are sorted by chapter sections, but numerous Additional Problems are included that may require use of material from several sections, or even from previous chapters. Computer problems give the students an opportunity to hone their computer skills --an increasingly important component of education. Most of these problems can be solved using a spreadsheet program, or one of the simple programs on the supplementary computer disk available with the text. Students with more advanced computer skills will have an opportunity to incorporate these skills into their physics problem solving. Challenge problems introduce the more capable students to interesting and stimulating exercises that require advanced problem-solving skills. Part Problems, found at the end of each of the eight parts of the text, give students an opportunity to synthesize their understanding and to see how each topic builds on and enhances what went before.

This book can be used by students with widely varying levels of ability. Each chapter stresses the basic concepts first. By including or excluding the Digging Deeper boxes, the optional Math Topic boxes, optional sections (marked with an *), and the Advanced and Challenge problems, the instructor can tailor the text to her or his own students. Instructor marginal notes (in cyan) indicate which optional topics are used later in the book, and also explain the reasons for some of our choices of topic and organization. We have also given references for some of our sources.

Essays, some by guest authors, address interesting sidelights or more advanced topics. We happily remember the student who suddenly remarked "I get it!" after reading the bicycle essay. By applying Newton's laws to a subject he enjoyed, he finally made sense of it all.

Definitions and equations are color-coded to help students recognize their level of importance. Despite the emphasis throughout the text on problem-solving as a reasoning process, some things must be memorized to be used efficiently. Anything in a gold box is fundamental and should be memorized!!! Level 2 equations, in olive boxes, are important and will often be useful in solving problems. Level 3 equations, unboxed and unnumbered, are intermediate or less important results that need not be memorized. Occasionally we need to refer to intermediate results in order to guide students through a problem solution or derivation. Such results are given lower case roman numerals. Any reference to these equations is local (within a page or so of the original statement).

Marginal notes (in black) alert the students to common errors, point out important features and special cases, give additional references, refer to previously discussed, related issues, and add clarifying commentary.

Because students remember best what they learned first, we have taken pains to keep the discussions accurate. Even if topics must be expanded on later, students should never have to unlearn anything. Extensive review of the manuscript by dozens of teaching colleagues and consultations with several authorities on specific topics have helped to ensure that all concepts are correctly presented. If you find any errors we would certainly appreciate hearing about them.

In writing this book we have been guided by our students. We have listened
to their complaints, watched how they work and noted where they have difficulties.
We have also been cognizant of recent research on physics education, which,
for the most part, supports our own observations. Thus, this book is written
*for the student*. No book can make physics easy for everyone, but
we can show students an approach that works. Our problem-solving strategy
has been tested and approved by hundreds of our students, and it has increased
their exam scores dramatically. We are confident it can work for your students
as well.

The authors and publisher recognize that errors in quantitative material can undermine the effectiveness of a text. A great deal of attention and effort has been invested to assure that all of the quantitative material in the text (and the solutions manuals) is correct and accurate. Accuracy checking went on throughout preparation of the manuscript, as well as during production of the textbook.

During the years that manuscript was being written and developed, many people were involved in assuring accuracy.

- Dozens of physics professors reviewed numerous drafts of the manuscript. All were asked to review the examples, exercises and problems. Many reviewers focused specifically on this quantitative material, at the publisher's request.
- The authors solved every end-of-chapter problem and checked each to be sure that it did not make unstated assumptions or rely upon unstated information.
- Jon Celesia of San Francisco State University carefully reviewed the final manuscript, checking for unstated assumptions, unclear explanations, and any possible inaccuracies.

During the year-long process of drawing all the art and setting all the type, numerous checks were performed.

- The authors proofread every syllable and symbol through two (in some cases three) stages of proof.
- One independent proofreader was hired to read the entire first stage of proof. Another professional proofreader checked both stages of proof, and all subsequent revisions.
- Barbara Uchida of the College of San Mateo checked every one of the in-chapter Examples and Exercises for accuracy and clarity.
- Every end-of-chapter problem was solved by a team of physics professors and graduate students. These solutions were then reviewed by an independent accuracy checker before going to the authors for final approval.

A final source of quality assurance for both quantitative and non-quantitative material has been students. During the development of the manuscript, many of the Examples, Exercises and end-of-chapter problems were tested with students in class and in homework assignments. The first half of the book has been used by students at San Francisco state University and at the University of California at Davis. The results have been very gratifying, both for the instructors and the students.

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