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Applied Physics: Concepts into Practice is intended for students enrolled in engineering technology, engineering, and medical degree programs. Students should have a basic knowledge of algebra, geometry, and trigonometry at the high school level. With this math background, students should be able to understand everything in the book. The text is intended for use in a two-semester sequence. For the first semester, Parts 1 and 2 cover mechanics and thermodynamics. For the second semester, Parts 3, 4, and 5 discuss electromagnetics, optics, and some modern physics.
Physics is the study of the forces in nature and how those forces interact with matter. Because these interactions can often be stated in a precise mathematical form, physics involves much use of mathematical modeling. The formulation of physical laws in a mathematical framework implies that a prerequisite of a serious study of physics is a certain fluency with mathematics. However, it is not necessary that students have such fluency before they begin the study of physics. Rather, the mathematical fluency can be developed along with the physical concepts.
In Applied Physics, mathematics is used as a language to describe the workings of nature, in contrast to being used as a number grinder where raw data are reduced to numerical answers that give no sense of perspective. Often in problem solving, physical concepts are used only to initially set up a problem, and then the problem becomes essentially one of mathematics. However, in this text, the internal consistency of the mathematics takes the problem to its final answer, which has a very real physical significance. Mathematical formalism is minimal, and a common-sense approach to mathematical methods is employed. The mathematics is ''bootstrapped'' along with the physics. By studying the text, students will naturally come to be able to ''speak'' mathematics with a certain degree of fluency.
In this way, I have gone beyond the mathematical limitations that an algebra-based text often imposes upon itself. I wrote Applied Physics because I could not find a textbook that integrated the physics and math well at the applied physics level. The mathematical approach for this kind of text is new. But in giving this book the mathematical continuity such a text so sorely needs, I have remained within the prerequisite student math background of only algebra, trigonometry, and geometry. With this background, many of the basic principles of higher math can be developed in a common sense way: on an as-needed basis when the physical concepts require it. The physics drives the math, not vice versa. A physicist, Sir Isaac Newton, invented the mathematical discipline known as calculus because the deeper mathematical perspective that calculus provided was necessary for a deeper physical understanding of the universe.
Role of Derivations
In my teaching experience, I've noticed that students have the most difficulty with problem solving in properly interpreting a problem. Identifying a problem's context is crucial to its solution. If students know where an equation comes from, they know what situation the equation describes and what the equation is capable of solving. They also know what a particular equation cannot do. Without the proper context, all equations are alike, and the students cannot see the forest for the trees. Therefore, derivations are given for most equations used in this text. By presenting the derivations, the text effectively demonstrates the use of mathematics as a language and modeling tool. Thus, a sense of perspective as to the physical concept can be attained.
My advice to students is to do problems, work problems, and then do some more problems! In doing problems, students must struggle with the theory and in so doing gradually become familiar with it as they set up a problem, review it, and determine how to solve it. Answers are provided for each problem, giving students a goal to reach for. A great deal of material must be included in two semesters, and thus a fast pace is required. Therefore, the problems at the end of each chapter have been kept to a number that could reasonably be attempted during the time period allotted for each chapter. More difficult problems are indicated by an asterisk (*) before the problem number. There are very few ''plug-and-chug'' problems in this text. However, the book is sufficiently complete that students will not have to refer to an outside text to solve any of the problems.
Applied Physics gives students an opportunity to understand physics, in contrast to simply being exposed to it. Obtaining the correct answer for an exercise does not necessarily mean that the solver has any insight into the physical concept being investigated. For example, computers can crank numbers, but computers have absolutely no sense of perspective as to the nature of a given problem. Traveling the path to a correct answer is a significant learning experience for students. Their reward is a correct answer. The answers to the problems in Applied Physics are, in most cases, not nice round numbers because the world seldom operates in nice round numbers (take p, for instance). If the answer that a student obtains for a certain problem is essentially the same one given in the text, then the answer is probably correct. A student's answer may vary from the one given in the text because of round-off errors. Students shouldn't worry if their answers disagree slightly with the answers in the book. The path to an answer is what is important, not the number of decimal places to which the answer is carried out.
Units and Dimensional Analysis
Although I haven't devoted any space specifically to units and dimensional analysis, Appendix C includes a table of common symbols, dimensions, and units. Units are carried along in all of the examples. I feel that dimensional analysis is a contextual subject and thus can be taught most effectively by including appropriate units in each example. An answer for a given problem is usually not just a number, but a number that has some physical meaning associated with it. That physical meaning is usually assigned a name, such as a force in newtons or a mass in kilograms. In solving the problems, students are required to set up their own equations for a solution. The final equation should have the appropriate units. If, for example, the answer is energy in joules, the final equation should have dimensions of energy and not, say, momentum. If the final equation is dimensionally incorrect, then there is something wrong with the derivation.
Dimensional analysis is not a subject in its own right, but rather an aid to obtaining a proper perspective of a physical concept. Dimensional analysis also can be a big help in initially learning the language of mathematics. Often it is the only way that students know, in beginning their study of physics, whether or not the end equation will solve the problem. Dimensional analysis is ever-present in this book, but seldom directly focused upon.
Applying the Approach to the Real-World Classroom
Through several years of teaching at IUPUI, I have successfully taught introductory applied physics students using the approach of integrating physics and math--in both the classroom and the lab. The approach that math and physics go hand in hand is gaining ground. A nationwide workshop, called the CPU (Constructing Physics Understanding) Project, was recently conducted for high school teachers. The workshop was supported by the National Science Foundation and was funded by an Eisenhower Grant. In the workshop, laboratory-based elicitation exercises were used to develop the physical concepts being studied, and direct experience was used to debunk tightly held initial misconceptions about physics. In the force and motion studies, the laboratory equipment included motion carts and inclined planes as well as ultrasonic motion sensors interfaced to computers that, with the appropriate software, gave real-time plots of displacement, velocity, and acceleration versus time. Teachers in the role of students could obtain a direct correlation between the motion studied and the shape of a graph. Later teachers used these same graphs, coupled with the equation of a straight line and the ability to find the area inside simple geometric shapes such as a rectangle or a right triangle, to derive the four equations of motion. They learned that a continuum of ideas leads from the basic concept of motion to the mathematical representation of that motion on a graph to the derivation of equations describing that motion. The integration of math and physics and the continuum between the two is one of the guiding philosophies of this book.
Also in the workshop, the propagation of light was studied in optics. The equipment used was a small flashlight with a grain-of-wheat bulb as a point source of light. The light was shone on a small, solid square template, and the shadow was observed. Up to four flashlights were stacked one upon another, and the shadow went from a dark square through four steps to a fully illuminated screen. Next a bulb with a long vertical filament was substituted for the four stacked flashlights, and the shadow appeared as a dark shadow gradually tapering off to a fully illuminated screen. The student studying light would come to the conclusion that the long vertical filament was just like an infinite number of point sources stacked one on top of another with an infinitesimal space between each point source. The concepts of infinity and infinitesimals arise from purely physical phenomena. The physics forces on us a mathematical way of looking at the world, and without the math, much of the physics is lost. However, the math can be developed in such a way that it is constantly grounded to a real situation and the real utility of the mathematical method shown. This common sense approach works and can serve to defuse the math phobia that many students have.
Applying the Approach in the Laboratory
I have used this approach in student laboratories to good effect. I first give a short talk on the theory of the phenomenon or phenomena the students are going to explore, and I develop the equations they will use to describe the physical case under study. I then show how certain parameters in these equations (such as instantaneous velocity or force) can be gathered as data by the equipment, and I explain the equipment in terms of the concept under study. The data are then gathered and plotted (usually as a straight line) to show relationships visually. I am also able to show how the real world differs from the ideal by, for instance, pointing out that the graph the students actually obtained has a force of friction because of a nonzero y intercept. In the laboratory the physical concepts, the equipment, and the math all act together as an indivisible whole.
Reviewers highlighted the writing style, examples, and problems sets as strengths of this text. The examples and exercises illustrate the application of physics theory.
StudyWizard e-tutorial CD-ROM--Packaged at the back of the text, this CD gives students another medium with which to learn physics. It includes review questions and vocabulary practice for each chapter and for Appendix A: Mathematics.
Writing Style--A friendly, casual writing style engages introductory physics students and makes physics less threatening for them.
Examples--Students will relate to and find interesting the real-world examples taken from everyday life.
Conceptual Problems--Multiple-choice and essay questions develop a mental feel for physics concepts without a focus on the math.
Exercises--Conveniently divided by chapter section for easy assignment of problems. An asterisk identifies more comprehensive exercises (solving these exercises requires an understanding of earlier material in the book).
Objectives--Along with the chapter-opening outline, these provide students with an overview of the chapter. Objectives are performance-based so that instructors can use them in curriculum development of activities and assessment materials. Questions in the Test Item File that accompanies the Romine text are tied to specific objectives to help instructors target their testing.
Key Concepts--These are bolded within the text, highlighted in the margin with their definition, and summarized at the end of the chapter.
Important Formulas--Formulas are highlighted within the chapter. End results of the derivations are summarized as numbered equations in a quick reference table at the end of the chapter. The table shows students the formulas that will be applied in the Exercises so they do not need to recall all of the derivations shown in the chapter and can focus on understanding the use of the end equations.
Chapter Summary--Highlights key points of the chapter and includes problem-solving and calculator use tips and dimensional analysis notes.
Math Appendix--This appendix supports the math in the text. Several chapter cross-references to the math appendix are provided to help students use the math in the text. The appendix covers trigonometric identities and rules for working with logarithms.
Also Available for Students
Lab Manual--Includes 27 experiments that begin with a Pre-Lab Activity to test students' readiness for the lab. Also includes a master Equipment List.
Companion Website at http://www.prenhall.com/romine 51;An additional learning resource, this provides scenarios and related multiple-choice questions for each of the five main parts of the text.
Supplements for Instructors
Instructors Resource and Solutions Manual--Includes answers to all Conceptual Problems and complete step-by-step solutions for all Exercises in the text. The answers and solutions have been thoroughly checked for accuracy. Also includes selected classroom demonstration ideas.
Lab Solutions Manual--Provides instructors with worked out solutions to lab assignments.
PowerPoint CD-ROM--Includes slides for all figures in the textbook and lab manual for instructors to use in classroom and lab presentations.
Test Item File--Provides both conceptual and mathematics-oriented multiple-choice questions and essay questions for each chapter. Questions are tied to specific Chapter Objectives in the textbook.
Prentice Hall Test Manager--This electronic version of the Test Item File can be used to create variations of exams; instructors can rearrange and edit provided questions, and can add their own questions to create unique exams.
Interactive Journey Through Physics CD-ROM--This salable product features physics animations and simulations.
This text has taken me roughly five years to complete. Over that period of time something has had to keep me motivated and productive through the initial writing, revisions, ancillary projects, and publishing. I want to thank the people at Prentice Hall for having faith in me and sticking with me through the long incubation of this book, especially Steve Helba for giving me the go-ahead for the project, and Katie Bradford, development editor, who cajoled, threatened, pleaded, promised, cursed, pushed, prodded, placated, and in general babysat me through at least three years of this process. I want to thank the reviewers whose constructive criticisms have given direction to the text and kept it from heretical utterings. These reviewers are:
Bobby K. Adams, College of the Albemarle; Michael Crittenden, Genessee Community College; William T. Divver, Jr., Spartanburg Technical College; Tony Nelson, Oklahoma State University, Okmulgee; Phyllis Salmons, Embry-Riddle Aeronautical University; Lynn P Thomson, Ricks College; Clark H. Vangilder, DeVry, Phoenix; Timothy R. Vierheller, The University of Akron, Wayne College; and Michael W. Wolf, Ph.D., Embry-Riddle Aeronautical University.
Special thanks are due to Maggie Diehl, copy editor, and Louise Sette and Tricia Huhn, production editors, who helped bring the text, lab manual, and supplements to fruition. Also, I want to thank my colleague Steve Schuh, the master-distractor, who bought me some time by writing about a quarter of the exercises for the text, the objectives and summaries for each chapter, and for writing a large part of the Test Item File.
I especially want to thank my wife, Nevenka, who put up with my egotistical ravings and saw to it that I had the love and support that helps keep dreams alive. She has had faith in me and the book when faith was a hard commodity to come by. Without her, this project would have foundered long ago.
Gregory S. Romine
1. Uniformly Accelerated Motion in One Dimension.
3. Force and Motion.
4. Work and Energy.
6. Circular Motion.
7. Centripetal Force, Centrifugal Force, and Gravitation.
8. Wave Motion.
9. Simple Harmonic Motion.
10. Equilibrium and Simple Machines.
11. Some Properties of Solids.
14. Heat Capacity and Heat Conduction.
16. Electric Charge.
17. Electric Energy and Voltage.
18. Electric Current and Resistance.
20. Induced Voltages and Currents.
21. Sinusoidal Currents and Voltages.
23. Spherical Mirrors and Lenses.
24. The Wave Nature of Light.
V. MODERN PHYSICS.
25. Waves, Particles, and Special Relativity.
26. Physics inside the Atom.
27. Chemical Bonding among and between Atoms.
B. Calculator Usage.
C. Dimensional Analysis.
D. Conversion Factors.
E. Periodic Table of the Elements.
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