Understanding Physics Text
Understanding Physics is built on the foundations of the 6th Edition of Halliday, Resnick, and Walker's Fundamentals of Physics which we often refer to as HRW 6th. The Following Description is Exerpted from the Preface:
Why a Revised Text?
A physics major recently remarked that after struggling through the first half of his junior level mechanics course, he felt that the course was now going much better. What had changed? Did he have a better background in the material they were covering now? "No," he responded. "I started reading the book before every class. That helps me a lot. I wish I had done it in Physics One and Two." Clearly, this student learned something very important. It is something most physics instructors wish they could teach all of their students as soon as possible. Namely, no matter how smart your students are, no matter how well your introductory courses are designed and taught, your students will master more physics if they learn how to read an "understandable" textbook carefully.
We know from surveys that the vast majority of introductory physics students do not read their textbook carefully.We think there are two major reasons why: (1) many students complain that physics textbooks are impossible to understand and too abstract, and (2) students are extremely busy juggling their academic work, jobs, personal obligations, social lives and interests. So, they develop strategies for passing physics without spending time on careful reading.We address both of these reasons by making our revision to the sixth edition of Fundamentals of Physics easier for students to understand and by providing you as an instructor with more Reading Exercises (formerly known as Checkpoints) and additional strategies for encouraging students to read the text carefully. Fortunately, we are attempting to improve a fine textbook whose active author, Jearl Walker, has worked diligently to make each new edition more engaging and understandable.
In the next few sections we provide a summary of how we are building upon HRW 6th and shaping it into this new textbook.
A Narrative That Supports Student Learning
One of our primary goals is to help students make sense of the physics they are learning. We cannot achieve this goal if students see physics as a set of disconnected mathematical equations that each describe only to a small number of specific situations.We stress conceptual and qualitative understanding and continually make connections between mathematical equations and conceptual ideas.We also try to build on ideas that student can be expected to already understand, based on the resources they bring from their everyday experiences.
In Understanding Physics we have tried to tell a story that flows from one chapter to the next. Each chapter begins with an introductory section that discusses why new topics introduced in the chapter are important and explains how the chapter builds on previous chapters and prepares students for those that follow. We place explicit emphasis on basic concepts that recur throughout the book.We use extensive forward and backward referencing to reinforce connections between topics. For example, in the introduction of Chapter 16 on Oscillations we state: "Although your study of simple harmonic motion will enhance your understanding of mechanical systems it is also vital to understanding the topics in electricity, magnetism, and light encountered in Chapters 30-37. Finally, a knowledge of SHM provides a basis for understanding the wave nature of light and how atoms and nuclei absorb and emit energy."
Emphasis on Observation and Experimentation
Observations and concrete, everyday experiences are the starting points for development of mathematical expressions. Experiment-based theory building is a major feature of the book.We build ideas on experience that students either already have or can easily gain through careful observation.
Whenever possible, the physical concepts and theories developed in Understanding Physics grow out of simple observations or experimental data that can be obtained in typical introductory physics laboratories. We want our readers to develop the habit of asking themselves:What do our observations, experiences and data imply about the natural laws of physics? How do we know a given statement is true? Why do we believe we have developed correct models for the world?
Toward this end, the text often starts a chapter by describing everyday observations that students are familiar with. This makes Understanding Physics a text that is both relevant to student's everyday lives and draws on existing student knowledge. We try to follow Arnold Arons' principle "idea first, name after." That is, we make every attempt to begin a discussion by using everyday language to describe common experiences. Only then do we introduce formal physics terminology to represent the concepts being discussed. For example, everyday pushes, pulls, and their impact on the motion of an object are discussed before introducing the term "force" or Newton's second law.We discuss how a balloon shrivels when placed in a cold environment and how a pail of water cools to room temperature before introducing the ideal gas law or the concept of thermal energy transfer.
The "idea first, name after" philosophy helps build patterns of association between concepts students are trying to learn and knowledge they already have. It also helps students reinterpret their experiences in a way that is consistent with physical laws.
Examples and illustrations in Understanding Physics often present data from modern computer based laboratory tools. These tools include computer-assisted data acquisition systems and digital video analysis software.We introduce students to these tools at the end of Chapter 1. Examples of these techniques are shown in Figs. P-1 and P-2 at the right and Fig. P-3 below. Since many instructors use these computer tools in the laboratory or in lecture demonstrations, they are part of the introductory physics experience for more and more of our students. The use of real data has a number of advantages. It connects the text to the students' experience in other parts of the course and it connects the text directly to real world experience. Regardless of whether data acquisition and analysis tools are used in the student's own laboratory, our use of realistic rather that idealized data helps students develop an appreciation of the role that data evaluation and analysis plays in supporting theory.
FIGURE P-1 A video analysis shows that the center of mass of a two-puck system moves at a constant velocity.
FIGURE P-2 Electronic temperature sensors reveal that if equal amounts of hot and cold water mix the final temperature is the average of the initial temperatures.
Using Physics Education Research
In re-writing the text we have taken advantage of two valuable findings of physics education research. One is the identification of concepts that are especially difficult for many students to learn. The other is the identification of active learning strategies to help students develop a more comprehensive understanding of physics concepts.
Addressing Learning Difficulties
Extensive scholarly research exists on the difficulties students have in learning physics.
1 We have made a concerted effort to address these difficulties. In Understanding Physics, issues that are known to confuse students are discussed with care. This is true even for topics like the nature of force and its effect on velocity and velocity changes that may seem trivial to professional physicists. We write about subtle, often counter-intuitive topics with carefully chosen language and examples designed to draw out and remediate common alternative student conceptions. For example, we know that students have trouble understanding passive forces such as normal and friction forces.
2 How can a rigid table exert a force on a book that rests on it? In Section 6-4 we present an idealized model of a solid that is analogous to an inner spring mattress with the repulsion forces between atoms acting as the springs. In addition, we invite our readers to push on a table with a finger and experience the fact that as they push harder on the table the table pushes harder on them in the opposite direction.
Incorporating Active Learning Opportunities
We designed Understanding Physics to be more interactive and to foster thoughtful reading.We have retained a number of the excellent Checkpoint questions found at the end of HRW 6th chapter sections (which we now call Reading Exercises). We have created many new Reading Exercises that require students to reflect on the material in important chapter sections. For example, just after reading Section 6-2 that introduces the two-dimensional free-body diagram, students encounter Reading Exercise 6-1. This multiple-choice exercise requires students to identify the free-body diagram for a helicopter that experiences three non-collinear forces. The distractors were based on common problems student have with the construction of free-body diagrams. When used in "Just-In-Time Teaching" assignments or for in-class group discussion, this type of reading exercise can help students learn a vital problem solving skill as they read.
FIGURE P-3 A video analysis of human motion reveals that in free fall the center of mass of an extended body moves in a parabolic path under the influence of the Earth's gravitational force.
FIGURE P-4 Compressing an innerspring mattress with a force.The mattress exerts an oppositely directed force, with the same magnitude, back on the finger.
We also created a set of Touchstone Examples. These are carefully chosen sample problems that illustrate key problem solving skills and help students learn how to use physical reasoning and concepts as an essential part of problem solving. We selected some of these touchstone examples from the outstanding collection of sample problems in HRW 6th, and we created some new ones. In order to retain the flow of the narrative portions of each chapter, we have reduced the overall number of sample problems to those necessary to exemplify the application of fundamental principles.Also, we chose touchstone examples that require students to combine conceptual reasoning with mathematical problem solving skills. Few, if any, of our touchstone examples are solvable using simple "plug-and-chug" or algorithmic pattern matching techniques.
Alternative problems have been added to the extensive, classroom tested endof- chapter problem sets selected from HRW 6th. The design of these new problems are based on the authors' knowledge of research on student learning difficulties. Many of these new problems require careful qualitative reasoning, that explicitly connect conceptual understanding to quantitative problem solving. In addition, estimation problems, video analysis problems, and "real life" or "context rich" problems have been included. The organization and style of Understanding Physics has been modified so that it can be easily used with other research based curricular materials that make up what we call The Physics Suite. The Suite and its contents are explained at more length at the end of this preface.
Reorganizing for Coherence and Clarity
For the most part we have retained the organization scheme inherited from HRW 6th. Instructors are used to the general organization and topics that are treated in a typical course sequence in calculus-based introductory physics. In fact, ordering of topics and their division into chapters is the same for 27 of the 38 chapters. The order of some topics has been modified to be more pedagogically coherent. Most of the reorganization was done in Chapters 3 through 10 where we adopted a sequence known as New Mechanics. In addition, we decided to move HRW 6th Chapter 25 on capacitors so it becomes the last chapter on electricity. Capacitors are now introduced in Chapter 28 in Understanding Physics.
The New Mechanics Sequence
HRW 6th and most other introductory textbooks use a similar sequence in the treatment of classical mechanics. It starts with the development of the kinematic equations to describe constantly accelerated motion. Then two-dimensional vectors and the kinematics of projectile motion are treated. This is followed by the treatment of dynamics in which Newton's Laws are presented and used to help students understand both one- and two-dimensional motions. Finally energy, momentum conservation, and rotational motion are treated.
About 12 years ago when Priscilla Laws, Ron Thornton, and David Sokoloff were collaborating on the development of research-based curricular materials, they became concerned about the difficulties students had working with two-dimensional vectors and understanding projectile motion before studying dynamics.
At the same time Arnold Arons was advocating the introduction of the concept of momentum before energy.
3 Arons argued that (1) the momentum concept is simpler than the energy concept, in both historical and modern contexts and (2) the study of momentum conservation entails development of the concept of center-of-mass which is needed for a proper development of energy concepts.
In order to address these concerns about the traditional mechanics sequence a small group of physics education researchers and curriculum developers convened in 1992 to discuss the introduction of a new order for mechanics.
4 One result of the conference was that Laws, Sokoloff, and Thornton have successfully incorporated a new sequence of topics in the mechanics portions of various curricular materials that are part of the Physics Suite discussed below.
5 These materials include Workshop Physics, the RealTime Physics Laboratory Module in Mechanics, and the Interactive Lecture Demonstrations.This sequence is incorporated in this book and has required a signifi- cant reorganization and revisions of HRW 6th Chapters 2 through 10.
The New Mechanics sequence incorporated into Chapters 2 through 10 of understanding physics includes:
Chapter 2: One-dimensional kinematics using constant horizontal accelerations and then vertical free fall as applications.
Chapter 3: One-dimensional dynamics begins with the application of Newton's laws of motion starts with a consideration of accelerations associated with horizontal applied forces (pushes or pulls) with little friction present. The treatment begins with single forces along a line and then superposition of forces at a vector sum is introduced. Next, in Section 3-9 vertical free fall is treated. Readers consider observations that lead to the postulation of "gravity" as a constant invisible force acting vertically downward.
Chapter 4: Two-dimensional vectors, vector displacements, unit vectors and the decomposition of vectors into components are treated.
Chapter 5: The study of kinematics and dynamics is extended to two-dimensional motions involving single forces including projectile motion and circular motion.
Chapter 6: The study of kinematics and dynamics is extended to two-dimensional motions involving combined forces including contact forces (normal and friction), gravitational forces, and air drag.
Chapters 7 & 8: Topics in these chapters deal with impulse and momentum change, momentum conservation, particle systems, center of mass, and the motion of the center-of-mass of an isolated system.
Chapters 9 & 10: These chapters introduce kinetic energy, work, potential energy, and energy conservation.
Just-in-Time Mathematics
In general, we introduce mathematical topics in a "just-in-time" fashion. For example, we treat one-dimensional vector concepts in Chapter 2 along with the development of one-dimensional velocity and acceleration concepts.We hold the introduction of twoand three-dimensional vectors, vector addition and decomposition until Chapter 4, immediately before students are introduced to two-dimensional motion and forces in Chapters 5 and 6.We do not present vector products until they are needed.We wait to introduce the dot product until Chapter 9 when concept of physical work is presented. Similarly, the cross product is first presented in Chapter 11 in association with the treatment of torque.
Notation Changes
Mathematical notation is often confusing, and ambiguity in the meaning of a mathematical symbol can prevent a student from understanding an important relationship. It is also difficult to solve problems when the symbols used to represent different quantities are not distinctive. Some key features of the new notation include:
We adhere to recent notation guidelines set by the U.S. National Institute of Standard and Technology Special Publication 811 (SP 811).
We try to balance our desire to use familiar notation and our desire to avoid using the same symbol for different variables. For example, p is often used to denote momentum, pressure, and power.We have chosen to use lower case p for momentum and capital P for pressure since both variables appear in the kinetic theory derivation. But we stick with the convention of using capital P for power since it does not commonly appear side by side with pressure in equations.
We denote vectors by an arrow instead of bolding so the printed equations look like handwritten equations.
We label each vector component with a subscript that explicitly relates it to its coordinate axis.This eliminates the common ambiguity about whether a quantity represents a magnitude which is a scalar or a vector component which is not a scalar.
We often use subscripts to spell out the names of objects that are associated with mathematical variables even though instructors and students will tend to use abbreviations and we also represent the fact that one object is exerting a force on another with an arrow in the subscript. For example, the force exerted by a rope on a block would be denoted as
1 L. C. McDermott and E. F. Redish, "Resource Letter PER-1: Physics Education Research," Am. J. Phys. 67, 755-767 (1999)
2 John J. Clement, "Expert novice similarities and instruction using analogies," Int. J. Sci. Ed. 20, 1271-1286 (1998)
3 Private Communication between Arnold Arons and Priscilla Laws by means of a document entitled "Preliminary Notes and Suggestions,"August 19, 1990; and Arnold Arons, Development of Concepts of Physics (Addison-Wesley, Reading MA, 1965)
4 The New Mechanics Conference was held August 6-7, 1992 at Tufts University. It was attended by Pat Cooney, Dewey Dykstra, David Hammer, David Hestenes, Priscilla Laws, Suzanne Lea, Lillian McDermott, Robert Morse, Hans Pfister, Edward F. Redish, David Sokoloff, and Ronald Thornton.
5 Laws, P.W. "A New Order for Mechanics" pp. 125-136, Proceedings of the Conference on the Introductory Physics Course, Rennselaer Polytechnic Institute, Troy New York, May 20-23, Jack Wilson, Ed. 1993 (John Wiley & Sons, New York 1997)
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Elastic Collision
Inelastic Collision
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