aP college physics oach - Pearson Schoolassets.pearsonschool.com/asset_mgr/current/201412/pdf... ·...

Randall d. KnightCalifornia Polytechnic State University, San Luis Obispo

BRian JonesColorado State University

stuaRt FieldColorado State University

a strategic approachcollege

physics

a P ® e d i t i o n

t h i R d e d i t i o n

KNIG9721_NASTA_AP_FM_ppi-xxv.indd 1 27/11/13 12:43 PM

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About the Authors

Randy Knight taught introductory physics for 32 years at Ohio State University and California Polytechnic University, where he is Professor Emeritus of Physics. Randy received a Ph.D. in physics from the University of California, Berkeley and was a post-doctoral fellow at the Harvard-Smithsonian Center for Astrophysics before join-ing the faculty at Ohio State University. It was at Ohio that he began to learn about the research in physics education that, many years later, led to Five Easy Lessons: Strategies for Successful Physics Teaching, Physics for Scientists and Engineers: A Strategic Approach, and now to this book. Randy’s research interests are in the fields of laser spectroscopy and environmental science. When he’s not in front of a com-puter, you can find Randy hiking, sea kayaking, playing the piano, or spending time with his wife Sally and their six cats.

Brian Jones has won several teaching awards at Colorado State University during his 25 years teaching in the Department of Physics. His teaching focus in recent years has been the College Physics class, including writing problems for the MCAT exam and helping students review for this test. In 2011, Brian was awarded the Robert A. Millikan Medal of the American Association of Physics Teachers for his work as director of the Little Shop of Physics, a hands-on science outreach program. He is actively exploring the effectiveness of methods of informal science education and how to extend these lessons to the college classroom. Brian has been invited to give workshops on techniques of science instruction throughout the United States and in Belize, Chile, Ethiopia, Azerbaijan, Mexico and Slovenia. Brian and his wife Carol have dozens of fruit trees and bushes in their yard, including an apple tree that was propagated from a tree in Isaac Newton’s garden.

Stuart Field has been interested in science and technology his whole life. While in school he built telescopes, electronic circuits, and computers. After attending Stan-ford University, he earned a Ph.D. at the University of Chicago, where he studied the properties of materials at ultralow temperatures. After completing a postdoctoral position at the Massachusetts Institute of Technology, he held a faculty position at the University of Michigan. Currently at Colorado State University, Stuart teaches a variety of physics courses, including algebra-based introductory physics, and was an early and enthusiastic adopter of Knight’s Physics for Scientists and Engineers. Stuart maintains an active research program in the area of superconductivity. Stuart enjoys Colorado’s great outdoors, where he is an avid mountain biker; he also plays in local ice hockey leagues.


iv

Preface to the TeacherIn 2006, we published College Physics: A Strategic Approach, a new algebra-based physics textbook for students majoring in the biological and life sciences, archi-tecture, natural resources, and other disciplines. As the first such book built from the ground up on research into how students can more effectively learn physics, it quickly gained widespread critical acclaim from educators and students alike. For the second edition, and now for this third edition, we have continued to build on the research-proven instructional techniques introduced in the first edition and the exten-sive feedback from thousands of users to take student learning even further.

ObjectivesOur primary goals in writing College Physics: A Strategic Approach have been:

■ To provide students with a textbook that’s a more manageable size, less encyclo-pedic in its coverage, and better designed for learning.

■ To integrate proven techniques from physics education research into the class-room in a way that accommodates a range of teaching and learning styles.

■ To help students develop both quantitative reasoning skills and solid conceptual understanding, with special focus on concepts well documented to cause learning difficulties.

■ To help students develop problem-solving skills and confidence in a systematic manner using explicit and consistent tactics and strategies.

■ To motivate students by integrating real-world examples—especially from biol-ogy, sports, medicine, the animal world—and that build upon their everyday experiences.

■ To utilize proven techniques of visual instruction and design from educational research and cognitive psychology that improve student learning and retention and address a range of learner styles.

A more complete explanation of these goals and the rationale behind them can be found in Randy Knight’s paperback book, Five Easy Lessons: Strategies for Success-ful Physics Teaching.

What’s New to This EditionIn revising the book for this third edition, we have renewed our basic focus on students and how they learn. We’ve considered extensive feedback from scores of teachers and thousands of students, including our student advisory panel, in order to enhance and improve the text, figures, and the end-of-chapter problems. Changes include the following:

■ More focused Chapter Previews provide a brief, visual, and non-technical preview, proven to help students organize their thinking and improve their understanding of the upcoming material.

■ New Synthesis boxes bring together key concepts, principles, and equations in order to highlight connections and differences.

■ New Concept Check figures encourage students to actively engage with key or complex figures by asking them to reason with a related Stop To Think question.

■ Additional Stop To Think questions provide students with more crucial practice and concept checks as they go through the chapters.


Preface to the Teacher v

■ New in-line Looking Back pointers encourage students to review important material from earlier chapters. These are given right at the moment they are need-ed, rather than at the start of the chapter (where they are often overlooked).

■ New Problem-Solving Strategy Overviews give students the “big picture” of the strategy before delving into details, just as the chapter previews give the “big picture” of the chapter.

■ Streamlined text and figures tighten and focus the presentation to be more closely matched to student needs. We’ve scrutinized every figure, caption, discus-sion, and photo in order to enhance their clarity and focus their role.

■ Expanded use of annotated equations helps students decipher what they “say,” and what the variables and units are.

■ Increased emphasis on critical thinking and reasoning, both in worked examples and end-of-chapter problems, promotes these key skills. These skills are especially important for those taking the MCAT exam.

■ Expanded use of realistic and real-world data ensures students can make sense of answers that are grounded in the real world. Our examples and problems use real numbers and real data, and test different types of reasoning using equations, ratios, and graphs.

■ Enhanced end-of-chapter problems, based on the wealth of data from MasteringPhysics, student advisory panel input, and a rigorous blind-solving and accuracy cross-checking process, optimize clarity, utility, and variety. We’ve added problems based on real-world and biomedical situations and problems that expand the range of reasoning skills students need to use in the solution.

We have made many small changes to the flow of the text throughout, streamlining derivations and discussions, providing more explanation for complex concepts and situations, and reordering and reorganizing material so that each section and each chapter has a clearer focus. There are small changes on nearly every page. The more significant content changes include:

■ The circular motion material in Chapters 3, 6 and 7 has been reworked for a more natural progression of topics. Acceleration in circular motion is now introduced in Chapter 3, frequency and period are now introduced in Chapter 6, while angular position and angular velocity are now in Chapter 7. The treatment of circular motion in Chapter 3 emphasizes the use of vectors to understand the nature of centripetal acceleration. In Chapter 6, the focus is on dynamics, and in Chapter 7, we extend these ideas to rotational motion.

■ The discussion of the law of conservation of energy in Section 10.6 has been updated to provide a more logical and coherent flow from the most general form of the law to more specialized versions for isolated systems and then to systems with only mechanical energy.

■ The material in Chapter 11 making the microscopic connection between thermal energy and temperature for an ideal gas has been moved to Chapter 12, where it fits better with the atomic model of an ideal gas presented there.

■ Minor topics that have been removed to focus the presentation include antinodal lines for sound waves in Chapter 16, maximum intensity of a diffraction grating’s bright fringes in Chapter 17, exposure in Chapter 19, and elevation graphs in Chapter 21.

■ The start of Chapter 21 has been revised to clarify the origin of electric potential energy by making a more concrete connection between electric potential energy and more familiar potential energies, such as gravitational and elastic potential energy.

■ The treatment of electromagnetic waves in Chapter 25 was streamlined to focus on the nature of the waves, the meaning of polarization, and the application of these ideas to real-world situations.

■ Chapters 29 and 30 have been significantly streamlined, improving the overall flow and removing some extraneous details so that students can better focus on the physics.

We know that students increasingly rely on sources of information beyond the text, and teachers are looking for quality resources that prepare students for engagement


vi Preface to the Teacher

in class. The text will always be the central focus, but we are adding additional media elements closely tied to the text that will enhance student understanding. In the Technology Update to the Second Edition, we added Class Videos, Video Tutor Solutions, and Video Tutor Demonstrations. In the Third Edition, we are adding an exciting new supplement, Prelecture Videos, short videos with author Brian Jones that introduce the topics of each chapter with accompanying assessment questions.

Textbook OrganizationCollege Physics: A Strategic Approach is a 30-chapter text. The textbook is divided into seven parts: Part I: Force and Motion, Part II: Conservation Laws, Part III: Properties of Matter, Part IV: Oscillations and Waves, Part V: Optics, Part VI: Electricity and Magne-tism, and Part VII: Modern Physics.

Part I covers Newton’s laws and their applications. The coverage of two fundamental conserved quantities, momentum and energy, is in Part II, for two reasons. First, the way that problems are solved using conservation laws—comparing an after situation to a before situation—differs fundamentally from the problem-solving strategies used in Newtonian dynamics. Second, the concept of energy has a significance far beyond mechanical (kinetic and potential) energies. In particular, the key idea in thermodynam-ics is energy, and moving from the study of energy in Part II into thermal physics in Part III allows the uninterrupted development of this important idea.

Optics (Part V) is covered directly after oscillations and waves (Part IV), but before electricity and magnetism (Part VI). Further, we treat wave optics before ray optics. Our motivations for this organization are twofold. First, wave optics is largely just an extension of the general ideas of waves; in a more traditional organization, students will have forgotten much of what they learned about waves by the time they get to wave optics. Second, optics as it is presented in introductory physics makes no use of the properties of electromagnetic fields. The documented difficulties that students have with optics are difficulties with waves, not difficulties with electricity and magnetism. There’s little reason other than historical tradition to delay optics. However, the optics chapters are easily deferred until after Part VI for teachers who prefer that ordering of topics.

10.6 Potential Energy

17.�Below we see a 1 kg object that is initially 1 m above the ground and rises to a height of 2 m.�Anjay and Brittany each measure its position but use a dif�ferent coordinate system to do so.�Fill in the table to show the initial and final gravitational potential ener�gies and � as�measured by �Anjay and Brittany�.�

18.�Three balls of equal mass are fired simultaneously with �equal�speeds�from the same height above the ground. Ball 1 is fired straight up,�ball 2 is fired straight down, and ball 3 is fired horizontally�. Rank in�order�, from lar�gest to smallest, their speeds �v�1�, �v�2�, and �v�3�as they hit�the ground.�Or�der:�

Explanation:�

19.�Below are shown three frictionless tracks. �A�block is released from rest at the position shown�on the left. �T�o which point does the block make it on the right before reversing direction and�sliding back? Point B is the same height as the starting position.�

A�B�

C�

A�B�

C�

A�B�

C�

Makes it to� Makes it to� Makes it to�

Anjay�

Ends here�

2 m� Starts here�

Brittany�

0�

0�

DU�

10-8 C H A P T E R �1�0�.�Ener�gy and �W�ork�

U�i� U�f� �U�Anjay�Brittany�

Ball 1�

Ball 3�

Ball 2�

The Student WorkbookA key component of College Physics: A Strategic Approach is the accompanying Student Workbook. The workbook bridges the gap between textbook and homework problems by providing students the opportunity to learn and practice skills prior to using those skills in quantitative end-of-chapter problems, much as a musician practices technique separately from performance pieces. The workbook exercises, which are keyed to each section of the textbook, focus on developing specific skills, ranging from identifying forces and drawing free-body diagrams to interpreting field diagrams.

The workbook exercises, which are generally qualitative and/or graphical, draw heavily upon the physics education research literature. The exercises deal with issues known to cause student difficulties and employ techniques that have proven to be effective at overcoming those difficulties. New to the third edition workbook are jeopardy problems that ask students to work backwards from equa-tions to physical situations, enhancing their understanding and critical thinking skills. The workbook exercises can be used in-class as part of an active-learning teaching strategy, in recitation sections, or as assigned homework. More informa-tion about effective use of the Student Workbook can be found in the Instructor’s Guide.


Preface to the Teacher vii

Teacher SupplementsFor most of the the teacher supplements and resources listed above, they are available electronically to qualified adopters on the Instructor Resource Center (IRC). Upon adoption or to pre-view, please go to www.pearsonschool.com/access_request and select Instructor Resource Center. You will be required to complete a brief one-time registration subject to verification of educator status. Upon verification, access information and instructions will be sent to you via email. Once logged into the IRC, enter ISBN 978-0-13-353967-7 in the “Search our Catalog” box to locate resources. Electronic teacher sup-plements are also available within the Instructor’s tab of MasteringPhysics.

Note ▶ For convenience, most teacher supplements can be downloaded from the “Instructor Resources” area of MasteringPhysics®. ◀

■ The Instructor’s Resource DVD provides invaluable and easy-to-use resources for your class, organized by text-book chapter. The Instructor’s Solutions Manual and the Instructor’s Guide are provided in PDF format and as editable Word files. Comprehensive Lecture Slides (with embedded classroom response system “Clicker” Ques-tions) are provided in PowerPoint, as well as high-quality versions of all the Prelecture Videos. In addition, all fig-ures, photos, tables, previews, and summaries from the textbook are given in JPEG format. All Problem-Solving Strategies, Math Rela-tionships Boxes, Tactics Boxes, and Key Equations are provided in editable Word and JPEG format.

■ The Instructor’s Solutions Manual, written by Professor Larry Smith, Snow College, provides complete solutions to all the end-of-chapter questions and problems. All solutions follow the Prepare/Solve/Assess problem-solving strategy used in the textbook for quantitative problems, and Reason/Assess strategy for qualitative ones. The solu-tions are available by chapter in Word and PDF format, are included on the Instructor’s Resource DVD, and can also be downloaded from the Instructor Resource Center (www.pearsonhighered.com/educator).

■ The Instructor’s Guide for College Physics: A Strategic Approach, a comprehensive and highly acclaimed resource, provides chapter-by-chapter creative ideas and teaching tips for using College Physics: A Strate-gic Approach in your class. In addition, it contains an extensive review of what has been learned from phys-ics education research, and provides guidelines for using active-learning techniques in your classroom. Instructor Guide chapters are provided in Word and PDF format, are included on the Instructor’s Resource DVD, and can also be downloaded from the Instructor Resource Center (www.pearsonhighered.com/educator).

■ The Test Bank contains 4,000 high-quality problems, with a range of multiple-choice and regular homework-type questions. Test files are provided in both TestGen® (an easy-to-use, fully networkable program for creating and editing quizzes and exams) and Word format, and can also be downloaded from www.pearsonhighered.com/educator. The Test Bank problems are also assignable via MasteringPhysics.

with Pearson eText (www. mastering

physics.com) is a powerful, yet simple, online homework, tutorial, and assessment system designed to improve student learning and results. Students benefit from wrong-answer specific feedback, hints, and a huge variety of educationally effective content while unrivalled gradebook diagnostics allow an instructor to pinpoint the weaknesses and misconceptions of their class.

Upon textbook purchase, students and teachers are granted access to MasteringPhysics with Pearson eText. Teachers canobtain preview or adoption access for MasteringPhysics in one of the following ways:

Preview Access■ Teachers can request preview access online by visiting

PearsonSchool.com/Access_Request (choose Initial Access then Option 2). Preview Access information will be sent to the teacher via email.

Adoption Access■ A Pearson Adoption Access Card, with codes and com-

plete instructions, will be delivered with your textbook purchase (ISBN: 0-13-353986-5).

■ Ask your sales representative for an Adoption Access Code Card (ISBN: 0-13-353986-5).

OR

■ Visit PearsonSchool.com/Access_Request (choose Ini-tial Access then option 3). Adoption access information will be sent to the teacher via email.

Students, ask your teacher for access.


viii Preface to the Teacher

Student Supplements

■ The Student Workbook is a key component of College Physics: A Strategic Approach. The workbook bridges the gap between textbook and homework problems by provid-ing students the opportunity to learn and practice skills prior to using those skills in quantitative end-of-chapter problems, much as a musician practices technique sepa-rately from performance pieces.

■ Pearson eText is available through MasteringPhysics. Allowing students access to the text wherever they have access to the Internet, Pearson eText comprises the full text, including figures that can be enlarged for better viewing. Within eText, students are also able to pop up definitions and terms to help with vocabulary and the reading of the material. Students can also take notes in eText using the annotation feature at the top of each page.

■

Class Video

Over 140 Video Tutors about relevant demonstrations or problem-solving strategies play directly on a smartphone or tablet via scan-nable QR codes in the printed book. These inter-active videos are also viewable via links within

the Pearson eText and the Study Area of MasteringPhysics.■ ActivPhysics OnlineTM applets and applet-based tuto-

rials, developed by education pioneers Professors Alan Van Heuvelen and Paul D’Alessandris, are available in the Study Area of MasteringPhysics. Also provided are over 70 PhET Simulations from the University of Colorado.

■ The Student Solutions Manuals, written by Professor Larry Smith, Snow College, provide detailed solutions to more than half of the odd-numbered end-of-chapter problems. Following the problem-solving strategy presented in the text, thorough solutions are provided to carefully illustrate both the qualitative (Reason/Assess) and quantitative (Pre-pare/Solve/Assess) steps in the problem-solving process.

Martha to be certain that one of us attends to all details, and on Alice’s tireless efforts and keen editorial eye as she helps us synthesize our visions into a coherent whole.

Rose Kernan and the team at Nesbitt Graphics/Cenveo, copy editor Carol Reitz, and photo researcher Eric Schrader get much credit for making this complex project all come together. In addition to the reviewers and classroom testers listed below, who gave invaluable feedback, we are particu-larly grateful to Charlie Hibbard for his close scrutiny of every word, symbol, number, and figure.

Randy Knight: I would like to thank my Cal Poly colleagues, especially Matt Moelter, for many valuable con-versations and suggestions. I am endlessly grateful to my wife Sally for her love, encouragement, and patience, and to our many cats for nothing in particular other than being cats.

Brian Jones: I would like to thank my fellow AAPT and PIRA members for their insight and ideas, the creative stu-dents and colleagues who are my partners in the Little Shop of Physics, the students in my College Physics classes who help me become a better teacher, and, most of all, my wife Carol, my best friend and gentlest editor, whose love makes the journey worthwhile.

Stuart Field: I would like to thank my wife Julie and my chil-dren, Sam and Ellen, for their love, support, and encouragement.

AcknowledgmentsWe have relied upon conversations with and, especially, the written publications of many members of the physics education community. Those who may recognize their influence include Arnold Arons, Uri Ganiel, Fred Goldberg, Ibrahim Halloun, David Hestenes, Leonard Jossem, Jill Larkin, Priscilla Laws, John Mallinckrodt, Lillian McDermott and members of the Physics Education Research Group at the University of Washington, Edward “Joe” Redish, Fred Reif, John Rigden, Rachel Scherr, Bruce Sherwood, David Sokoloff, Ronald Thornton, Sheila Tobias, and Alan Van Heuleven.

We are very grateful to Larry Smith for the difficult task of writing the Instructor Solutions Manual; to Scott Nutter for writing out the Student Workbook answers; to Wayne Ander-son, Jim Andrews, Nancy Beverly, David Cole, Karim Diff, Jim Dove, Marty Gelfand, Kathy Harper, Charlie Hibbard, Robert Lutz, Matt Moelter, Kandiah Manivannan, Ken Rob-inson, and Cindy Schwarz-Rachmilowitz for their contribu-tions to the end-of-chapter questions and problems; to Wayne again for helping with the Test Bank questions; and to Steven Vogel for his careful review of the biological content of many chapters and for helpful suggestions.

We especially want to thank our editor Becky Ruden, development editor Alice Houston, project manager Martha Steele, and all the other staff at Pearson for their enthusiasm and hard work on this project. Having a diverse author team is one of the strengths of this book, but it has meant that we rely a great deal on Becky to help us keep to a single focus, on


ix

It’s almost certain that you are taking physics because you are required to. Someone, somewhere, has decided that it’s important for you to take this class. And they are right. There is a lot you can learn from physics, even if you don’t plan to be a physicist. We regularly hear from doctors, physical thera-pists, biologists and others that physics was one of the most interesting and valuable classes they took.

So, what can you expect to learn in this class? Let’s start by talking about what physics is. Physics is a way of think-ing about the physical aspects of nature. Physics is not about “facts.” It’s far more focused on discovering relationships between facts and the patterns that exist in nature than on learning facts for their own sake. Our emphasis will be on thinking and reasoning. We are going to look for patterns and relationships in nature, develop the logic that relates dif-ferent ideas, and search for the reasons why things happen as they do.

The concepts and techniques you will learn will have a wide application. In this text we have a special emphasis on applying physics to understanding the living world. You’ll use your understand-ing of charges and electric potential to analyze the elec-tric signal produced when your heart beats. You’ll learn how sharks can

detect this signal to locate prey and, further, how and why this electric sensitivity seems to allow hammerhead sharks to detect magnetic fields, aiding navigation in the open ocean.

Like any subject, physics is best learned by doing. “Do-ing physics” in this class means solving problems, apply-

ing what you have learned to answer questions at the end of the chapter. When you are given a homework assignment, you may find yourself tempted to simply solve the problems by thumbing through the text looking for a formula that seems like it will work. This isn’t how to do physics; if it was, who-ever required you to take this class wouldn’t bother. The folks who designed your class want you to learn to reason, not to “plug and chug.” Whatever you end up studying or doing for a career, this ability will serve you well.

How do you learn to reason in this way? There’s no single strategy for studying physics that will work for all students, but we can make some suggestions that will certainly help:

■ Read each chapter before it is discussed in class. Class attendance is much more effective if you have prepared.

■ Participate actively in class. Take notes, ask and answer questions, take part in discussion groups. There is ample scientific evidence that active participation is far more effective for learning science than is passive listening.

■ After class, go back for a careful rereading of the chap-ter. In your second reading, pay close attention to the de-tails and the worked examples. Look for the logic behind each example, not just at what formula is being used.

■ Apply what you have learned to the homework prob-lems at the end of each chapter. By following the tech-niques of the worked examples, applying the tactics and problem-solving strategies, you’ll learn how to apply the knowledge you are gaining.

■ Form a study group with two or three classmates. There’s good evidence that students who study regularly with a group do better than the rugged individualists who try to go it alone.

And we have one final suggestion. As you read the book, take part in class, and work through problems, step back every now and then to appreciate the big picture. You are going to study topics that range from motions in the solar system to the electrical signals in the nervous system that let you tell your hand to turn the pages of this book. It’s a remarkable breadth of topics and techniques that is based on a very compact set of organizing principles.

Now, let’s get down to work.

Preface to the Student

The most incomprehensible thing about the universe is that it is comprehensible.—Albert Einstein


Correlation to the AP® Physics 1 and AP® Physics 2 Curriculum FrameworkThis chart correlates the College Board’s Advanced Placement Physics Curriculum Framework (effective Fall 2014) to the corresponding chapters and sections in Knight/Jones/Field AP Edition of College Physics: A Strategic Approach, 3rd Edition, AP Edition.

Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.

Enduring understanding 1.A: Chapter/Section

The internal structure of a system determines many properties of the system.1.A.1. A system is an object or a collection of objects. Objects are treated as having no internal structure. 2.6, 7.2, 7.4, 9.4, 20.3, 30.7 Phys. 1

1.A.2. Fundamental particles have no internal structure. 28.3, 30.7 SP 1.1, 7.2 Phys. 2

1.A.3. Nuclei have internal structures that determine their properties. 29.2, 30.1, 30.2, 30.4, 30.5 Phys. 2

1.A.4. Atoms have internal structures that determine their properties. 29.2–29.7 SP 1.1, 7.1 Phys. 2

1.A.5. Systems have properties determined by the properties and interactions of their constituent atomic and 11.3, 12.1, 12.2, 12.4, 12.5, molecular substructures. In AP Physics, when the properties of the constituent parts are not important in 12.7, 12.8, 13.1 modeling the behavior of the macroscopic system, the system itself may be referred to as an object. SP 1.1, 1.4, 7.1 Phys. 1, 2

Enduring Understanding 1.B:

Electric charge is a property of an object or system that affects its interactions with other objects or systems containing charge.1.B.1. Electric charge is conserved. The net charge of a system is equal to the sum of the charges of all the objects 20.1, 20.2, 22.1, 22.2 in the system. SP 6.4, 7.2 Phys. 1, 2

1.B.2. There are only two kinds of electric charge. Neutral objects or systems contain equal quantities of positive 20.1–20.3, 30.1, 30.7 and negative charge, with the exception of some fundamental particles that have no electric charge. SP 6.1, 6.2, 6.4, 7.2 Phys. 1, 2

1.B.3. The smallest observed unit of charge that can be isolated is the electron charge, also known as 20.1, 20.2, 29.2, 30.7 the elementary charge. SP 1.5, 6.1, 7.2 Phys. 1, 2

Enduring Understanding 1.C:

Objects and systems have properties of inertial mass and gravitational mass that are experimentally verified to be the same and that satisfy conservation principles.1.C.1. Inertial mass is the property of an object or a system that determines how its motion changes when it 4.5, 9.4–9.6 interacts with other objects or systems. SP 4.2 Phys. 1

1.C.2. Gravitational mass is the property of an object or a system that determines the strength of the 2.7, 6.5 gravitational interaction with other objects, systems, or gravitational fields. Phys. 1

1.C.3. Objects and systems have properties of inertial mass and gravitational mass that are 6.5 experimentally verified to be the same and that satisfy conservation principles. SP 4.2 Phys. 1

1.C.4. In certain processes, mass can be converted to energy and energy can be converted to mass according to 27.10 E = mc2, the equation derived from the theory of special relativity. SP 6.3 Phys. 2

Enduring Understanding 1.D:

Classical mechanics cannot describe all properties of objects.1.D.1. Objects classically thought of as particles can exhibit properties of waves. 28.4 SP 6.3 Phys. 2

1.D.2. Certain phenomena classically thought of as waves can exhibit properties of particles. 28.2, 28.3, 28.6, 28.7 Phys. 2

1.D.3. Properties of space and time cannot always be treated as absolute. 27.1, 27.5, 27.6, 27.10 SP 6.3, 7.1 Phys. 2


Enduring Understanding 1.E:

Materials have many macroscopic properties that result from the arrangement and interactions of the atoms and molecules that make up the material.1.E.1. Matter has a property called density. 13.1, 13.4 SP 4.1, 4.2, 6.4 Phys. 2

1.E.2. Matter has a property called resistivity. 22.4 SP 4.1 Phys. 1, 2

1.E.3. Matter has a property called thermal conductivity. 12.8 SP 4.1, 4.2, 5.1 Phys. 2

1.E.4. Matter has a property called electric permittivity. 20.4, 21.7 Phys. 2

1.E.5. Matter has a property called magnetic permeability. 24.4 Phys. 2

1.E.6. Matter has a property called magnetic dipole moment. 24.8 Phys. 2

Big Idea 2: Fields existing in space can be used to explain interactions.

Enduring Understanding 2.A: Chapter/Section

A field associates a value of some physical quantity with every point in space. Field models are useful for describing interactions that occur at a distance (long-range forces) as well as a variety of other physical phenomena.2.A.1. A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is 20.4, 20.5 described by a vector. Phys. 1, 2

2.A.2. A scalar field gives, as a function of position (and perhaps time), the value of a physical quantity that is 21.4, 21.5 described by a scalar. In Physics 2, this should include electric potential. Phys. 2


A gravitational field is caused by an object with mass.2.B.1. A gravitational field gu at the location of an object with mass m causes a gravitational force of magnitude 5.3, 6.5 mg to be exerted on the object in the direction of the field. SP 2.2, 7.2 Phys. 1

2.B.2. The gravitational field caused by a spherically symmetric object with mass is radial and, outside the object, 6.5 varies as the inverse square of the radial distance from the center of that object. SP 2.2 Phys. 1


An electric field is caused by an object with electric charge.2.C.1. The magnitude of the electric force F exerted on an object with electric charge q by an electric field E

u

is 20.4, 20.5 Fu

= qEu

. The direction of the force is determined by the direction of the field and the sign of the charge, with positively charged objects accelerating in the direction of the field and negatively charged objects accelerating in the direction opposite the field. This should include a vector field map for positive point charges, negative point charges, spherically symmetric charge distribution, and uniformly charged parallel plates. SP 2.2, 6.4, 7.2 Phys. 2

2.C.2. The magnitude of the electric field vector is proportional to the net electric charge of the object(s) creating 20.4, 20.5 that field. This includes positive point charges, negative point charges, spherically symmetric charge distributions, and uniformly charged parallel plates. SP 2.2, 6.4 Phys. 2

2.C.3. The electric field outside a spherically symmetric charged object is radial and its magnitude varies as the 20.4 inverse square of the radial distance from the center of that object. Electric field lines are not in the curriculum. Students will be expected to rely only on the rough intuitive sense underlying field lines, wherein the field is viewed as analogous to something emanating uniformly from a source. SP 6.2 Phys. 2

2.C.4. The electric field around dipoles and other systems of electrically charged objects (that can be modeled as 20.5 point objects) is found by vector addition of the field of each individual object. Electric dipoles are treated quali- tatively in this course as a teaching analogy to facilitate student understanding of magnetic dipoles. SP 1.4, 2.2, 6.4, 7.2 Phys. 2

2.C.5. Between two oppositely charged parallel plates with uniformly distributed electric charge, at points far from 20.5 the edges of the plates, the electric field is perpendicular to the plates and is constant in both magnitude and direction. SP 1.1, 2.2, 7.1 Phys. 2



A magnetic field is caused by a magnet or a moving electrically charged object. Magnetic fields observed in nature always seem to be produced either by moving charged objects or by magnetic dipoles or combinations of dipoles and never by single poles.2.D.1. The magnetic field exerts a force on a moving electrically charged object. That magnetic force is perpendicular to 24.5 the direction of velocity of the object and to the magnetic field and is proportional to the magnitude of the charge, the magnitude of the velocity and the magnitude of the magnetic field. It also depends on the angle between the velocity, and the magnetic field vectors. Treatment is quantitative for angles of 0°, 90°, or 180° and qualitative for other angles. SP 2.2 Phys. 22.D.2. The magnetic field vectors around a straight wire that carries electric current are tangent to concentric 24.3, 24.4 circles centered on that wire. The field has no component toward the current-carrying wire. SP 1.1 Phys. 22.D.3. A magnetic dipole placed in a magnetic field, such as the ones created by a magnet or the Earth, will tend 24.7 to align with the magnetic field vector. SP 1.2 Phys. 22.D.4. Ferromagnetic materials contain magnetic domains that are themselves magnets. 24.8 SP 1.4 Phys. 2


Physicists often construct a map of isolines connecting points of equal value for some quantity related to a field and use these maps to help visualize the field.2.E.1. Isolines on a topographic (elevation) map describe lines of approximately equal gravitational potential 21.4 energy per unit mass (gravitational equipotential). As the distance between two different isolines decreases, the steepness of the surface increases. [Contour lines on topographic maps are useful teaching tools for introducing the concept of equipotential lines. Students are encouraged to use the analogy in their answers when explaining gravitational and electrical potential and potential differences.] SP 1.4, 6.4, 7.2 Phys. 22.E.2. Isolines in a region where an electric field exists represent lines of equal electric potential, 21.4 referred to as equipotential lines. SP 1.4, 6.4, 7.2 Phys. 22.E.3. The average value of the electric field in a region equals the change in electric potential across that region 21.5 divided by the change in position (displacement) in the relevant direction. Phys. 2

Big Idea 3: The interactions of an object with other objects can be described by forces.


All forces share certain common characteristics when considered by observers in inertial reference frames.3.A.1. An observer in a particular reference frame can describe the motion of an object using such quantities as 1.2, 1.3, 1.5, 2.1, 2.2, 2.4, 2.5, position, displacement, distance, velocity, speed, and acceleration. 3.2, 3.3, 3.5, 27.2, 27.3 SP 1.5, 2.1, 2.2, 4.2, 5.1 Phys. 13.A.2. Forces are described by vectors. 4.1, 4.4 SP 1.1 Phys. 1, 23.A.3. A force exerted on an object is always due to the interaction of that object with another object. 4.1, 4.2, 4.5, 5.1, 5.7, 6.2, 6.5, 9.2 SP 1.4, 6.1, 6.4, 7.2 Phys. 1, 23.A.4. If one object exerts a force on a second object, the second object always exerts a force of equal magnitude 4.7, 5.7, 6.5, 9.4 on the first object in the opposite direction. SP 1.4, 6.2, 6.4, 7.2 Phys. 1, 2


Classically, the acceleration of an object interacting with other objects can be predicted by using au = aFu

m.

3.B.1. If an object of interest interacts with several other objects, the net force is the vector sum of the individual 4.6, 5.1–5.3, 5.8, 5.9, 6.1, 20.3 forces. SP 1.5, 2.2, 4.2, 5.1, 6.4, 7.2 Phys. 1, 23.B.2. Free-body diagrams are useful tools for visualizing forces being exerted on a single object and writing the 4.1–4.3, 4.6, 4.7, 5.1, 5.3, equations that represent a physical situation. 5.8, 5.9, 6.1 SP 1.1, 1.4, 2.2 Phys. 1, 23.B.3. Restoring forces can result in oscillatory motion. When a linear restoring force is exerted on an object 14.2–14.5 displaced from an equilibrium position, the object will undergo a special type of motion called simple harmonic motion. Examples should include gravitational force exerted by the Earth on a simple pendulum, mass-spring oscillator. SP 2.2, 4.2, 5.1, 6.2, 6.4, 7.2 Phys. 1



At the macroscopic level, forces can be categorized as either long-range (action-at-a-distance) forces or contact forces.3.C.1. Gravitational force describes the interaction of one object that has mass with another object that has mass. 5.3, 6.5 SP 2.2 Phys. 13.C.2. Electric force results from the interaction of one object that has an electric charge with another object that 20.1, 20.2, 20.3 has an electric charge. SP 2.2, 6.4, 7.2 Phys. 1, 23.C.3. A magnetic force results from the interaction of a moving charged object or a magnet with other moving 24.1, 24.5, 24.7 charged objects or another magnet. SP 1.4, 4.2, 5.1 Phys. 23.C.4. Contact forces result from the interaction of one object touching another object and they arise from inter- 4.2, 4.7, 9.1, 9.2, 9.4, 14.2 atomic electric forces. These forces include tension, friction, normal, spring (Physics 1), and buoyant (Physics 2). SP 6.1, 6.2 Phys. 1, 2


A force exerted on an object can change the momentum of the object.3.D.1. The change in momentum of an object is a vector in the direction of the net force exerted on the object. 9.2, 9.4 SP 4.1 Phys. 13.D.2. The change in momentum of an object occurs over a time interval. 9.2, 9.4 SP 2.1, 4.2, 5.1, 6.4 Phys. 1


A force exerted on an object can change the kinetic energy of the object.3.E.1. The change in the kinetic energy of an object depends on the force exerted on the object and on the 10.2, 10.3, 10.4 displacement of the object during the interval that the force is exerted. SP 1.4, 2.2, 6.4, 7.2 Phys. 1

Enduring Understanding 3.F:

A force exerted on an object can cause a torque on that object.3.F.1. Only the force component perpendicular to the line connecting the axis of rotation and the 7.3, 8.1 point of application of the force results in a torque about that axis. SP 1.4, 2.2, 2.3, 4.1, 4.2, 5.1 Phys. 13.F.2. The presence of a net torque along any axis will cause a rigid system to change its rotational 7.1–7.3, 7.5–7.7 motion or an object to change its rotational motion about that axis. SP 4.1, 4.2, 5.1, 6.4 Phys. 13.F.3. A torque exerted on an object can change the angular momentum of an object. 9.7 SP 2.1, 4.1, 4.2, 5.1, 5.3, 6.4, 7.2 Phys. 1

Enduring Understanding 3.G:

Certain types of forces are considered fundamental.3.G.1. Gravitational forces are exerted at all scales and dominate at the largest distance and mass scales. 6.6 SP 7.1 Phys. 1, 23.G.2. Electromagnetic forces are exerted at all scales and can dominate at the human scale. 20.1, 20.2 SP 7.1 Phys. 23.G.3. The strong force is exerted at nuclear scales and dominates the interactions of nucleons. 30.3 SP 7.2 Phys. 2

Big Idea 4: Interactions between systems can result in changes in those systems.


The acceleration of the center of mass of a system is related to the net force exerted on the system, where au = aFu

m.

4.A.1. The linear motion of a system can be described by the displacement, velocity, and acceleration of its 7.3 center of mass. SP 1.2, 1.4, 2.3, 6.4 Phys. 14.A.2. The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of 2.1–2.5, 4.1, 4.5, 9.4 change of position with time. SP 1.4, 2.2, 5.3, 6.4 Phys. 14.A.3. Forces that systems exert on each other are due to interactions between objects in the systems. If the inter- 9.4 acting objects are parts of the same system, there will be no change in the center-of-mass velocity of that system. SP 1.4, 2.2 Phys. 1



Interactions with other objects or systems can change the total linear momentum of a system.4.B.1. The change in linear momentum for a constant-mass system is the product of the mass of the system and 9.2 the change in velocity of the center of mass. SP 1.4, 2.2, 5.1 Phys. 14.B.2. The change in linear momentum of the system is given by the product of the average force on that system 9.2–9.4 and the time interval during which the force is exerted. SP 2.2, 5.1 Phys. 1


Interactions with other objects or systems can change the total energy of a system.4.C.1. The energy of a system includes its kinetic energy, potential energy, and microscopic internal energy. 10.1–10.7, 21.1–21.4 Examples should include gravitational potential energy, elastic potential energy, and kinetic energy. SP 1.4, 2.1, 2.2, 6.4 Phys. 14.C.2. Mechanical energy (the sum of kinetic and potential energy) is transferred into or out of a system when 10.1–10.3, 12.3 an external force is exerted on a system such that a component of the force is parallel to its displacement. The process through which the energy is transferred is called work. SP 1.4, 2.2, 6.4, 7.2 Phys. 14.C.3. Energy is transferred spontaneously from a higher temperature system to a lower temperature system. The 12.5, 12.6, 12.8 process through which energy is transferred between systems at different temperatures is called heat. SP 6.4 Phys. 24.C.4. Mass can be converted into energy and energy can be 27.10, 30.2, 30.4 SP 2.2, 2.3, 7.2 Phys. 2


A net torque exerted on a system by other objects or systems will change the angular momentum of the system.4.D.1. Torque, angular velocity, angular acceleration, and angular momentum are vectors and can be 7.2, 7.3, 8.1 characterized as positive or negative depending upon whether they give rise to or correspond to counterclockwise or clockwise rotation with respect to an axis. SP 1.2, 1.4, 3.2, 4.1, 4.2, 5.1, 5.3 Phys. 14.D.2. The angular momentum of a system may change due to interactions with other objects or systems. 9.7 SP 1.2, 1.4, 4.2 Phys. 14.D.3. The change in angular momentum is given by the product of the average torque and the time interval 9.7 during which the torque is exerted. SP 2.2, 4.1, 4.2 Phys. 1


The electric and magnetic properties of a system can change in response to the presence of, or changes in, other objects or systems.4.E.1. The magnetic properties of some materials can be affected by magnetic fields at the system. Students 24.8 should focus on the underlying concepts and not the use of the vocabulary. SP 1.1, 1.4, 2.2 Phys. 24.E.2. Changing magnetic flux induces an electric field that can establish an induced emf in a system. 25.1–25.4 SP 6.4 Phys. 24.E.3. The charge distribution in a system can be altered by the effects of electric forces produced by a charged object. 20.1, 20.2, 22.1, 22.2 SP 1.1, 1.4, 3.2, 4.1, 4.2, 5.1, Phys. 2 5.3, 6.4, 7.24.E.4. The resistance of a resistor, and the capacitance of a capacitor, can be understood from the basic 20.5, 21.7, 22.4, 22.5, 22.6 properties of electric fields and forces, as well as the properties of materials and their geometry. SP 2.2, 4.1, 4.2, 5.1, 6.4 Phys. 24.E.5. The values of currents and electric potential differences in an electric circuit are determined by the 23.1–23.7 properties and arrangement of the individual circuit elements such as sources of emf, resistors, and capacitors. SP 2.2, 4.2, 5.1, 6.1, 6.4 Phys. 2

Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.


Certain quantities are conserved, in the sense that the changes of those quantities in a given system are always equal to the transfer of that quantity to or from the system by all possible interactions with other systems.5.A.1. A system is an object or a collection of objects. The objects are treated as having no internal structure. 9.4 Phys. 15.A.2. For all systems under all circumstances, energy, charge, linear momentum, and angular momentum are 9.4–9.7, 10.1, 20.1, 20.2, 22.1, 22.2 conserved. For an isolated or a closed system, conserved quantities are constant. An open system is one that exchanges any conserved quantity with its surroundings. SP 6.4, 7.2 Phys. 1


5.A.3. An interaction can be either a force exerted by objects outside the system or the transfer of some quantity 9.1–9.3, 9.7, 10.1–10.3, 10.5, 10.6, with objects outside the system. 11.2, 11.3, 11.4, 14.6, 14.7, 20.1 Phys. 15.A.4. The boundary between a system and its environment is a decision made by the person considering the 9.4 situation in order to simplify or otherwise assist in analysis. Phys. 1


The energy of a system is conserved.5.B.1. Classically, an object can only have kinetic energy since potential energy requires an interaction 10.1, 10.3 between two or more objects. SP 1.4, 1.5, 2.2 Phys. 15.B.2. A system with internal structure can have internal energy, and changes in a system’s internal structure can result in changes in internal energy. [Physics 1: includes mass-spring oscillators and simple pendulums. Physics 2: includes charged object in electric fields and examining changes in internal energy with changes in configuration.] SP 1.4, 2.1 Phys. 1, 25.B.3. A system with internal structure can have potential energy. Potential energy exists within a system if the 10.1, 10.2, 10.4, 21.1–21.3, 22.4–22.6 objects within that system interact with conservative forces. SP 1.4, 2.2, 6.4, 7.2 Phys. 15.B.4. The internal energy of a system includes the kinetic energy of the objects that make up the system and the 10.1, 10.3, 10.4, 14.4 potential energy of the configuration of the objects that make up the system. SP 1.4, 2.1, 2.2, 6.4, 7.2 Phys. 1, 25.B.5. Energy can be transferred by an external force exerted on an object or system that moves the object or 10.1–10.4, 10.8, 12.3, 22.6 system through a distance; this energy transfer is called work. Energy transfer in mechanical or electrical systems may occur at different rates. Power is defined as the rate of energy transfer into, out of, or within a system. [A piston filled with gas getting compressed or expanded is treated in Physics 2 as a part of thermodynamics.] SP 1.4, 2.2, 4.2, 5.1, 6.4, 7.2 Phys. 1, 25.B.6. Energy can be transferred by thermal processes involving differences in temperature; the amount of energy 11.1, 11.3, 12.5–12.8 transferred in this process of transfer is called heat. SP 1.2 Phys. 25.B.7. The first law of thermodynamics is a specific case of the law of conservation of energy involving the 11.1, 11.3–11.6, 12.3 internal energy of a system and the possible transfer of energy through work and/or heat. Examples should include P-V diagrams—isovolumetric process, isothermal process, isobaric process, adiabatic process. No calculations of heat or internal energy from temperature change; and in this course, examples of these relationships are qualitative and/or semi-quantitative. SP 1.1, 1.4, 2.2, 6.4, 7.2 Phys. 25.B.8. Energy transfer occurs when photons are absorbed or emitted, for example, by atoms or nuclei. 28.5, 28.6 SP 1.2, 7.2 Phys. 25.B.9. Kirchhoff’s loop rule describes conservation of energy in electrical circuits. The application of Kirchhoff’s 21.1, 21.2, 22.3, 22.4, 22.5, 22.6, laws to circuits is introduced in Physics 1 and further developed in Physics 2 in the context of more complex 23.2–23.7 circuits, including those with capacitors. SP 1.1, 1.4, 1.5, 2.1, 2.2, 4.1, 4.2, Phys. 1, 2 5.1, 5.3, 6.4, 7.25.B.10. Bernoulli’s equation describes the conservation of energy in fluid flow. 13.6 SP 2.2, 6.2 Phys. 25.B.11. Beyond the classical approximation, mass is actually part of the internal energy of an object or system 27.10 with E = mc2. SP 2.2, 7.2 Phys. 2


The electric charge of a system is conserved.5.C.1. Electric charge is conserved in nuclear and elementary particle reactions, even when elementary particles 30.4, 30.7 are produced or destroyed. Examples should include equations representing nuclear decay. SP 6.4, 7.2 Phys. 25.C.2. The exchange of electric charges among a set of objects in a system conserves electric charge. 20.1, 20.2 SP 4.1, 4.2, 5.1, 6.4 Phys. 25.C.3. Kirchhoff’s junction rule describes the conservation of electric charge in electrical circuits. Since charge is 22.1, 22.2, 23.2, 23.6–23.8 conserved, current must be conserved at each junction in the circuit. Examples should include circuits that combine resistors in series and parallel. [Physics 1: covers circuits with resistors in series, with at most one parallel branch, one battery only. Physics 2: includes capacitors in steady-state situations. For circuits with capacitors, situations should be limited to open circuit, just after circuit is closed, and a long time after the circuit is closed.] SP 1.4, 2.2, 4.1, 4.2, 5.1, 6.4, 7.2 Phys. 1, 2

Enduring Understanding 5.A:



The linear momentum of a system is conserved.5.D.1. In a collision between objects, linear momentum is conserved. In an elastic collision, kinetic energy is the 9.4, 10.7 same before and after. SP 2.1, 2.2, 3.2, 4.2, 5.1, 5.3, 6.4, 7.2 Phys. 1, 25.D.2. In a collision between objects, linear momentum is conserved. In an inelastic collision, kinetic energy is 9.4–9.6, 10.7 not the same before and after the collision. SP 2.1, 2.2, 4.1, 4.2, 4.4, 5.1, Phys. 1, 2 5.3, 6.4, 7.25.D.3. The velocity of the center of mass of the system cannot be changed by an interaction within the system. 7.3 [Physics 1: includes no calculations of centers of mass; the equation is not provided until Physics 2. However, without doing calculations, Physics 1 students are expected to be able to locate the center of mass of highly symmetric mass distributions, such as a uniform rod or cube of uniform density, or two spheres of equal mass.] SP 6.4 Phys. 1, 2


The angular momentum of a system is conserved.5.E.1. If the net external torque exerted on the system is zero, the angular momentum of the system does not change. 9.7 SP 2.1, 2.2, 6.4, 7.2 Phys. 15.E.2. The angular momentum of a system is determined by the locations and velocities of the objects that make 9.7 up the system. The rotational inertia of an object or system depends upon the distribution of mass within the object or system. Changes in the radius of a system or in the distribution of mass within the system result in changes in the system’s rotational inertia, and hence in its angular velocity and linear speed for a given angular momentum. Examples should include elliptical orbits in an Earth-satellite system. Mathematical expressions for the moments of inertia will be provided where needed. Students will not be expected to know the parallel axis theorem. SP 2.2 Phys. 1


Classically, the mass of a system is conserved.5.F.1. The continuity equation describes conservation of mass flow rate in fluids. Examples should include 13.5 volume rate of flow, mass flow rate. SP 2.1, 2.2, 7.2 Phys. 2


Nucleon number is conserved.5.G.1. The possible nuclear reactions are constrained by the law of conservation of nucleon number. 30.2, 30.4 SP 6.4 Phys. 2

Big Idea 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.


A wave is a traveling disturbance that transfers energy and momentum.6.A.1. Waves can propagate via different oscillation modes such as transverse and longitudinal. 15.1, 25.5 SP 1.2, 5.1, 6.2 Phys. 1, 26.A.2. For propagation, mechanical waves require a medium, while electromagnetic waves do not require a 15.1, 15.2, 15.4, 25.5 physical medium. Examples should include light traveling through a vacuum and sound not traveling through a vacuum. SP 6.4, 7.2 Phys. 1, 26.A.3. The amplitude is the maximum displacement of a wave from its equilibrium value. 15.3 SP 1.4 Phys. 16.A.4. Classically, the energy carried by a wave depends upon and increases with amplitude. Examples should 15.5, 15.6, 25.5 include sound waves. SP 6.4 Phys. 1


A periodic wave is one that repeats as a function of both time and position and can be described by its amplitude, frequency, wavelength, speed, and energy.6.B.1. For a periodic wave, the period is the repeat time of the wave. The frequency is the number of repetitions 15.3, 25.5 of the wave per unit time. SP 1.4, 2.2 Phys. 16.B.2. For a periodic wave, the wavelength is the repeat distance of the wave. 15.3, 25.5 SP 1.4 Phys. 1


6.B.3. A simple wave can be described by an equation involving one sine or cosine function involving the 15.3, 25.5 wavelength, amplitude, and frequency of the wave. SP 1.5 Phys. 26.B.4. For a periodic wave, wavelength is the ratio of speed over frequency. 15.3, 25.5 SP 4.2, 5.1, 7.2 Phys. 16.B.5. The observed frequency of a wave depends on the relative motion of source and observer. This is a qualitative 15.7 treatment only. SP 1.4 Phys. 1


Only waves exhibit interference and diffraction.6.C.1. When two waves cross, they travel through each other; they do not bounce off each other. Where the 16.1 waves overlap, the resulting displacement can be determined by adding the displacements of the two waves. This is called superposition. SP 1.4, 6.4, 7.2 Phys. 26.C.2. When waves pass through an opening whose dimensions are comparable to the wavelength, a diffraction 17.1, 17.5, 17.6, 28.1, 28.4 pattern can be observed. SP 1.4, 6.4, 7.2 Phys. 26.C.3. When waves pass through a set of openings whose spacing is comparable to the wavelength, an 17.2–17.4 interference pattern can be observed. Examples should include monochromatic double-slit interference. SP 1.4, 6.4 Phys. 26.C.4. When waves pass by an edge, they can diffract into the “shadow region” behind the edge. Examples 17.1 should include hearing around corners, but not seeing around them, and water waves bending around obstacles. SP 6.4, 7.2 Phys. 2


Interference and superposition lead to standing waves and beats.6.D.1. Two or more wave pulses can interact in such a way as to produce amplitude variations in the resultant 16.1 wave. When two pulses cross, they travel through each other; they do not bounce off each other. Where the pulses overlap, the resulting displacement can be determined by adding the displacements of the two pulses. This is called superposition. SP 1.1, 1.4, 4.2, 5.1 Phys. 16.D.2. Two or more traveling waves can interact in such a way as to produce amplitude variations in the resultant 16.7 wave. SP 5.1 Phys. 16.D.3. Standing waves are the result of the addition of incident and reflected waves that are confined to a region 16.2–16.4 and have nodes and antinodes. Examples should include waves on a fixed length of string, and sound waves in both closed and open tubes. SP 1.2, 2.1, 3.2, 4.1, 4.2, 5.1, Phys. 1 5.2, 5.3, 6.46.D.4. The possible wavelengths of a standing wave are determined by the size of the region to which it is confined. 16.2–16.4 SP 1.5, 2.2, 6.1 Phys. 16.D.5. Beats arise from the addition of waves of slightly different frequency. 16.7 SP 1.2 Phys. 1


The direction of propagation of a wave such as light may be changed when the wave encounters an interface between two media.6.E.1. When light travels from one medium to another, some of the light is transmitted, some is 18.1 reflected, and some is absorbed. (Qualitative understanding only.) SP 6.4, 7.2 Phys. 26.E.2. When light hits a smooth reflecting surface at an angle, it reflects at the same angle on the other side of 18.2 the line perpendicular to the surface (specular reflection); and this law of reflection accounts for the size and location of images seen in plane mirrors. SP 6.4, 7.2 Phys. 26.E.3. When light travels across a boundary from one transparent material to another, the speed of propagation 18.3 changes. At a non-normal incident angle, the path of the light ray bends closer to the perpendicular in the optically slower substance. This is called refraction. SP 1.1, 1.4, 4.1, 5.1, 5.2, 5.3, 6.4, 7.2 Phys. 26.E.4. The reflection of light from surfaces can be used to form images. 18.2 SP 1.4, 2.2, 3.2, 4.1, 5.1, 5.2, 5.3 Phys. 26.E.5. The refraction of light as it travels from one transparent medium to another can be used to form images. 18.4, 18.5, 19.1–19.5 SP 1.4, 2.2, 3.2, 4.1, 5.1, 5.2, 5.3 Phys. 2




Electromagnetic radiation can be modeled as waves or as fundamental particles.6.F.1. Types of electromagnetic radiation are characterized by their wavelengths, and certain ranges of wave- 15.1, 15.4, 25.5 length have been given specific names. These include (in order of increasing wavelength spanning a range from picometers to kilometers) gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, and radio waves. SP 6.4, 7.2 Phys. 26.F.2. Electromagnetic waves can transmit energy through a medium and through a vacuum. 15.1, 15.4, 25.5 SP 1.1 Phys. 26.F.3. Photons are individual energy packets of electromagnetic waves, with Ephoton = hf , where h is Planck’s 28.2, 28.3, 28.6 constant and f is the frequency of the associated light wave. SP 6.4 Phys. 26.F.4. The nature of light requires that different models of light are most appropriate at different scales. 28.3 SP 6.4, 7.1 Phys. 2


All matter can be modeled as waves or as particles.6.G.1. Under certain regimes of energy or distance, matter can be modeled as a classical particle. 28.4 SP 6.4, 7.1 Phys. 26.G.2. Under certain regimes of energy or distance, matter can be modeled as a wave. The behavior in these 28.4 regimes is described by quantum mechanics. SP 6.1, 6.4 Phys. 2

Big Idea 7: The mathematics of probability can be used to describe the behavior of complex systems and to interpret the behavior of quantum mechanical systems.


The properties of an ideal gas can be explained in terms of a small number of macroscopic variables including temperature and pressure.7.A.1. The pressure of a system determines the force that the system exerts on the walls of its container and is a 12.2 measure of the average change in the momentum or impulse of the molecules colliding with the walls of the container. The pressure also exists inside the system itself, not just at the walls of the container. SP 1.4, 2.2, 6.4, 7.2 Phys. 27.A.2. The temperature of a system characterizes the average kinetic energy of its molecules. 11.3, 12.2 SP 7.1 Phys. 27.A.3. In an ideal gas, the macroscopic (average) pressure (P ), temperature (T), and volume (V ), are related by 12.2, 12.3 the equation PV = nkT . SP 3.2, 4.2, 5.1, 6.4, 7.2 Phys. 2


The tendency of isolated systems to move toward states with higher disorder is described by probability.7.B.1. The approach to thermal equilibrium is a probability process. 11.3, 11.4, 12.5, 12.8 SP 6.2 Phys. 27.B.2. The second law of thermodynamics describes the change in entropy for reversible and irreversible 11.7 processes. Only a qualitative treatment is considered in this course. SP 7.1 Phys. 2


At the quantum scale, matter is described by a wave function, which leads to a probabilistic description of the microscopic world.7.C.1. The probabilistic description of matter is modeled by a wave function, which can be assigned to an 28.4 object and used to describe its motion and interactions. The absolute value of the wave function is related to the probability of finding a particle in some spatial region. (Qualitative treatment only, using graphical analysis.) SP 1.4 Phys. 27.C.2. The allowed states for an electron in an atom can be calculated from the wave model of an electron. 28.4–28.6 SP 1.4 Phys. 27.C.3. The spontaneous radioactive decay of an individual nucleus is described by probability. 30.1, 30.4, 30.5 SP 6.4 Phys. 27.C.4. Photon emission and absorption processes are described by probability. 28.6, 29.3, 29.4, 29.7, 29.9

SP 1.1, 1.2 Phys. 2


xix

Preface to the Teacher ivPreface to the Student ixTopic Correlation for AP x

PArT I Force and Motion oVeRVIeW Why Things Change 1

chapter 3 Vectors and Motion in Two Dimensions 64

3.1 Using Vectors 65 3.2 Using Vectors on Motion Diagrams 67 3.3 Coordinate Systems and Vector

Components 71 3.4 Motion on a Ramp 75 3.5 Relative Motion 78 3.6 Motion in Two Dimensions:

Projectile Motion 80 3.7 Projectile Motion: Solving Problems 82 3.8 Motion in Two Dimensions:

Circular Motion 85 SummARy 89 QueStIoNS ANd PRoblemS 90

chapter 4 Forces and Newton’s Laws of Motion 97

4.1 Motion and Force 98 4.2 A Short Catalog of Forces 101 4.3 Identifying Forces 105 4.4 What Do Forces Do? 107 4.5 Newton’s Second Law 109 4.6 Free-Body Diagrams 112 4.7 Newton’s Third Law 114 SummARy 118 QueStIoNS ANd PRoblemS 119

chapter 5 Applying Newton’s Laws 125 5.1 Equilibrium 126 5.2 Dynamics and Newton’s Second

Law 129 5.3 Mass and Weight 132 5.4 Normal Forces 135 5.5 Friction 137 5.6 Drag 142 5.7 Interacting Objects 145 5.8 Ropes and Pulleys 147 SummARy 152 QueStIoNS ANd PRoblemS 153

Detailed Contents

chapter 1 Representing Motion 2 1.1 Motion: A First Look 3 1.2 Position and Time: Putting Numbers

on Nature 5 1.3 Velocity 8 1.4 A Sense of Scale: Significant Figures,

Scientific Notation, and Units 11 1.5 Vectors and Motion: A First Look 16 1.6 Where Do We Go From Here? 20 SummARy 22 QueStIoNS ANd PRoblemS 23

chapter 2 Motion in One Dimension 28 2.1 Describing Motion 29 2.2 Uniform Motion 33 2.3 Instantaneous Velocity 36 2.4 Acceleration 38 2.5 Motion with Constant Acceleration 42 2.6 Solving One-Dimensional Motion

Problems 45 2.7 Free Fall 49 SummARy 55 QueStIoNS ANd PRoblemS 56


chapter 6 Circular Motion, Orbits, and Gravity 160

6.1 Uniform Circular Motion 161 6.2 Dynamics of Uniform Circular

Motion 163 6.3 Apparent Forces in Circular Motion 169 6.4 Circular Orbits and Weightlessness 172 6.5 Newton’s Law of Gravity 175 6.6 Gravity and Orbits 178 SummARy 182 QueStIoNS ANd PRoblemS 183

chapter 7 Rotational Motion 189 7.1 Describing Circular and Rotational

Motion 190 7.2 The Rotation of a Rigid Body 195 7.3 Torque 198 7.4 Gravitational Torque and the

Center of Gravity 203 7.5 Rotational Dynamics and Moment

of Inertia 206 7.6 Using Newton’s Second Law for

Rotation 210 7.7 Rolling Motion 213 SummARy 217 QueStIoNS ANd PRoblemS 218

chapter 8 Equilibrium and Elasticity 225 8.1 Torque and Static Equilibrium 226 8.2 Stability and Balance 230 8.3 Springs and Hooke’s Law 232 8.4 Stretching and Compressing

Materials 235 SummARy 240 QueStIoNS ANd PRoblemS 241

PARt I SummARy Force and Motion 248oNe SteP beyoNd Dark Matter and the Structure

of the Universe 249PARt I PRoblemS 250

PArT II Conservation Laws

oVeRVIeW Why Some Things Stay the Same 253

chapter 9 Momentum 254 9.1 Impulse 255 9.2 Momentum and the Impulse-

Momentum Theorem 256 9.3 Solving Impulse and Momentum

Problems 260 9.4 Conservation of Momentum 262 9.5 Inelastic Collisions 268 9.6 Momentum and Collisions in Two

Dimensions 269 9.7 Angular Momentum 270 SummARy 275 QueStIoNS ANd PRoblemS 276

chapter 10 Energy and Work 283 10.1 The Basic Energy Model 284 10.2 Work 288 10.3 Kinetic Energy 292 10.4 Potential Energy 295 10.5 Thermal Energy 298 10.6 Using the Law of Conservation

of Energy 300 10.7 Energy in Collisions 304 10.8 Power 307 SummARy 310 QueStIoNS ANd PRoblemS 311

xx Detailed Contents


chapter 11 Using Energy 318 11.1 Transforming Energy 319 11.2 Energy in the Body 322 11.3 Temperature, Thermal Energy

and Heat 327 11.4 The First Law of Thermodynamics 330 11.5 Heat Engines 332 11.6 Heat Pumps, Refrigerators,

and Air Conditioners 335 11.7 Entropy and the Second Law

of Thermodynamics 339 11.8 Systems, Energy, and Entropy 340 SummARy 343 QueStIoNS ANd PRoblemS 344

PARt II SummARy Conservation Laws 350oNe SteP beyoNd Order Out of Chaos 351PARt II PRoblemS 352

chapter 13 Fluids 398 13.1 Fluids and Density 399 13.2 Pressure 400 13.3 Measuring and Using Pressure 404 13.4 Buoyancy 407 13.5 Fluids in Motion 412 13.6 Fluid Dynamics 415 13.7 Viscosity and Poiseuille’s Equation 420 SummARy 424 QueStIoNS ANd PRoblemS 425

PARt III SummARy Properties of Matter 432oNe SteP beyoNd Size and Life 433PARt II PRoblemS 434

PArT IV Oscillations and Waves oVeRVIeW Motion That Repeats Again and Again 437

PArT III Properties of Matter oVeRVIeW Beyond the Particle Model 355

chapter 12 Thermal Properties of Matter 356 12.1 The Atomic Model of Matter 357 12.2 The Atomic Model of an Ideal Gas 359 12.3 Ideal-Gases Processes 366 12.4 Thermal Expansion 373 12.5 Specific Heat and Heat

of Transformation 375 12.6 Calorimetry 379 12.7 Specific Heats of Gases 381 12.8 Heat Transfer 383 SummARy 389 QueStIoNS ANd PRoblemS 390

chapter 14 Oscillations 438 14.1 Equilibrium and Oscillation 439 14.2 Linear Restoring Forces and

Simple Harmonic Motion 441 14.3 Describing Simple Harmonic Motion 443 14.4 Energy in Simple Harmonic Motion 448 14.5 Pendulum Motion 453 14.6 Damped Oscillations 455 14.7 Driven Oscillations and Resonance 457 SummARy 462 QueStIoNS ANd PRoblemS 463

chapter 15 Traveling Waves and Sound 470 15.1 The Wave Model 471 15.2 Traveling Waves 472 15.3 Graphical and Mathematical

Descriptions of Waves 476 15.4 Sound and Light Waves 480 15.5 Energy and Intensity 483 15.6 Loudness of Sound 485 15.7 The Doppler Effect and Shock Waves 488 SummARy 493 QueStIoNS ANd PRoblemS 494

Detailed Contents xxi


chapter 16 Superposition and Standing Waves 500

16.1 The Principle of Superposition 501 16.2 Standing Waves 502 16.3 Standing Waves on a String 504 16.4 Standing Sound Waves 509 16.5 Speech and Hearing 514 16.6 The Interference of Waves from

Two Sources 516 16.7 Beats 520 SummARy 523 QueStIoNS ANd PRoblemS 524

PARt IV SummARy Oscillations and Waves 530oNe SteP beyoNd Waves in the Earth and the Ocean 531PARt IV PRoblemS 532

PArT V Optics oVeRVIeW Light is a Wave 535

18.6 Image Formation with Spherical Mirrors 584

18.7 The Thin-Lens Equation 588 SummARy 593 QueStIoNS ANd PRoblemS 594

chapter 19 Optical Instruments 600 19.1 The Camera 601 19.2 The Human Eye 603 19.3 The Magnifier 606 19.4 The Microscope 608 19.5 The Telescope 610 19.6 Color and Dispersion 611 19.7 Resolution of Optical Instruments 614 SummARy 620 QueStIoNS ANd PRoblemS 621

PARt V SummARy Optics 626oNe SteP beyoNd Scanning Confocal Microscopy 627PARt V PRoblemS 628

PArT VI Electricity and Magnetism oVeRVIeW Charges, Currents, and Fields 631

chapter 20 Electric Fields and Forces 632 20.1 Charges and Forces 633 20.2 Charges, Atoms, and Molecules 639 20.3 Coulomb’s Law 641 20.4 The Concept of the Electric Field 645 20.5 Applications of the Electric Field 648 20.6 Conductors and Electric Fields 652 20.7 Forces and Torques in Electric Fields 654 SummARy 657 QueStIoNS ANd PRoblemS 658

chapter 21 Electrical Potential 665 21.1 Electric Potential Energy

and the Electric Potential 666 21.2 Sources of Electric Potential 668 21.3 Electric Potential and Conservation

of Energy 670 21.4 Calculating The Electric Potential 674 21.5 Connecting Potential and Field 681 21.6 The Electrocardiogram 684 21.7 Capacitance and Capacitors 685 21.8 Energy and Capacitors 689 SummARy 693 QueStIoNS ANd PRoblemS 694

chapter 17 Wave Optics 536 17.1 What is Light? 537 17.2 The Interference of Light 540 17.3 The Diffraction Grating 544 17.4 Thin-Film Interference 548 17.5 Single-Slit Diffraction 552 17.6 Circular-Aperture Diffraction 555 SummARy 558 QueStIoNS ANd PRoblemS 559

chapter 18 Ray Optics 565 18.1 The Ray Model of Light 566 18.2 Reflection 569 18.3 Refraction 571 18.4 Image Formation by Refraction 576 18.5 Thin Lenses: Ray Tracing 577

xxii Detailed Contents


chapter 22 Current and Resistance 702 22.1 A Model of Current 703 22.2 Defining and Describing Current 705 22.3 Batteries and emf 707 22.4 Connecting Potential and Current 708 22.5 Ohm’s Law and Resistor Circuits 712 22.6 Energy and Power 716 SummARy 720 QueStIoNS ANd PRoblemS 721

chapter 23 Circuits 727 23.1 Circuit Elements and Diagrams 728 23.2 Kirchhoff’s Laws 729 23.3 Series and Parallel Circuits 732 23.4 Measuring Voltage and Current 736 23.5 More Complex Circuits 737 23.6 Capacitors in Parallel and

Series 740 23.7 RC Circuits 742 23.8 Electricity in the Nervous

System 745 SummARy 753 QueStIoNS ANd PRoblemS 754

chapter 24 Magnetic Fields and Forces 764

24.1 Magnetism 765 24.2 The Magnetic Field 766

24.3 Electric Currents Also Create Magnetic Fields 770

24.4 Calculating the Magnetic Field Due to a Current 773

24.5 Magnetic Fields Exert Forces on Moving Charges 777

24.6 Magnetic Fields Exert Forces on Currents 783

24.7 Magnetic Fields Exert Torques on Dipoles 787

24.8 Magnets and Magnetic Materials 790

SummARy 794 QueStIoNS ANd PRoblemS 795

chapter 25 Electromagnetic Induction and Electromagnetic Waves 804

25.1 Induced Currents 805 25.2 Motional emf 806 25.3 Magnetic Flux 809 25.4 Faraday’s Law 814 25.5 Electromagnetic Waves 817 25.6 The Photon Model of

Electromagnetic Waves 823 25.7 The Electromagnetic Spectrum 825 SummARy 831 QueStIoNS ANd PRoblemS 832

chapter 26 AC Electricity 840 26.1 Alternating Current 841 26.2 AC Electricity and

Transformers 843 26.3 Household Electricity 847 26.4 Biological Effects and Electrical

Safety 849 26.5 Capacitor Circuits 851 26.6 Inductors and Inductor

Circuits 853 26.7 Oscillation Circuits 856 SummARy 861 QueStIoNS ANd PRoblemS 862

PARt VI SummARy Electricity and Magnetism 868oNe SteP beyoNd The Greenhouse Effect

and Global Warming 869PARt VI PRoblemS 870

Detailed Contents xxiii


chapter 27 Relativity 874 27.1 Relativity: What’s It All About? 875 27.2 Galilean Relativity 875 27.3 Einstein’s Principle of Relativity 878 27.4 Events and Measurements 881 27.5 The Relativity of Simultaneity 884 27.6 Time Dilation 886 27.7 Length Contraction 891 27.8 Velocities of Objects

in Special Relativity 894 27.9 Relativistic Momentum 895 27.10 Relativistic Energy 897 SummARy 901 QueStIoNS ANd PRoblemS 902

chapter 28 Quantum Physics 908 28.1 X Rays and X-Ray Diffraction 909 28.2 The Photoelectric Effect 911 28.3 Photons 917 28.4 Matter Waves 919 28.5 Energy Is Quantized 922 28.6 Energy Levels and Quantum Jumps 924 28.7 The Uncertainty Principle 927 28.8 Applications and Implications

of Quantum Theory 929 SummARy 932 QueStIoNS ANd PRoblemS 933

chapter 29 Atoms and Molecules 940 29.1 Spectroscopy 941 29.2 Atoms 943 29.3 Bohr’s Model of Atomic

Quantization 946 29.4 The Bohr Hydrogen Atom 948 29.5 The Quantum-Mechanical

Hydrogen Atom 954 29.6 Multielectron Atoms 956 29.7 Excited States and Spectra 959 29.8 Molecules 962 29.9 Stimulated Emission and Lasers 964 SummARy 968 QueStIoNS ANd PRoblemS 969

chapter 30 Nuclear Physics 975 30.1 Nuclear Structure 976 30.2 Nuclear Stability 978 30.3 Forces and Energy in the Nucleus 981 30.4 Radiation and Radioactivity 982 30.5 Nuclear Decay and Half-Lives 987 30.6 Medical Applications of Nuclear

Physics 992 30.7 The Ultimate Building Blocks of

Matter 997 SummARy 1001 QueStIoNS ANd PRoblemS 1002

PARt VII SummARy Modern Physics 1008oNe SteP beyoNd The Physics of Very Cold Atoms 1009PARt VII PRoblemS 1010

Appendix A Mathematics Review A-1Appendix B Atomic and Nuclear Data A-3Useful Data A-6Answers to Odd-Numbered Problems A-9Credits C-1Index I-1

PArT VII Modern Physics oVeRVIeW New Ways of Looking at the World 873

xxiv Detailed Contents


ocus on thebig picture

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a strategic approachcollege

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knight • jones • fieldt H i R dE d i t i o n

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knightjonesfieldcolleg

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PearsonSchool.com/Advanced

focus on the big pictureBuilt from the ground up for optimal learning; refined to help students focus on the big picture.

Building on the research-proven instructional techniques introduced in Knight’s Physics for Scientists and Engineers, College Physics: A Strategic Approach sets a new standard for algebra-based introductory physics—gaining widespread critical acclaim from professors and students alike. The text, supplements, and MasteringPhysics® work together to help students see and understand the big picture, gain crucial problem-solving skills and confidence, and better prepare for lecture and their futures.

For the Third Edition, Randy Knight, Brian Jones, and Stuart Field have incorporated student feedback and research to strengthen their focus on student learning, and to apply the best results from educational research and extensive user feedback and metadata.

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about the coverRefraction of light by the water droplet magnifies the image to let us focus on fine details in the oak leaf. This beautiful image represents the authors’ renewed focus on students and how they learn.

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KNIG9721_NASTA_AP_Walkthrough.indd 1 27/11/13 2:59 PM

ocus students...F

Presented by co-author Brian Jones, these engaging videos are assignable through MasteringPhysics and expand on the ideas in the textbook’s chapter previews, giving context, examples, and a chance for students to practice the concepts they are studying via short multiple-choice questions.

With Learning Catalytics, a “bring your own device” student engagement, assessment, and classroom intelligence system, you can:■ Assess students in real time, using

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PrElECturE VidEoS

lEArning CAtAlytiCStm

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during:


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MasteringPhysics s the leading online homework, tutorial, and assessment product, designed to improve results by helping students quickly master concepts. Students benefit from self-paced tutorials, featuring specific wrong-answer feedback, hints, and a wide variety of educationally effective content to keep them engaged and on track.

Robust diagnostics and unrivaled gradebook reporting allow instructors to pinpoint the weaknesses and misconceptions of a student or class to provide timely intervention.

The acclaimed Student Workbook provides straightforward confidence and skill-building exercises—bridging the gap between worked examples in the textbook and end-of-chapter problems. Workbook activities are referenced throughout the text by .

For the Third Edition are Jeopardy questions that ask students to work

backwards from equations to physical situations, enhancing their understanding and critical-thinking skills.

PrElECturE VidEoS

mAStEringPhySiCS

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ocus students...F

Streamlined and focused on the three most important ideas in each chapter, these unique chapter previews are tied to specific learning objectives. In addition, they explicitly mention the one or two most important concepts from past chapters, and finish with a new “Stop to Think” question, giving students a chance to build on their knowledge from previous chapters and integrate it with new content they are about to read.

Chapter previews are mirrored by visual chapter summaries, helping students to review and organize what they’ve learned before moving ahead. They consolidate understanding by providing each concept in words, math, and figures, and organizing these into a coherent hierarchy—from General Principles to Applications.

EnhAnCEd ChAPtEr PrEViEwS

ChAPtEr SummAriES

Looking AheAd ▶▶

goal: To learn about magnetic fields and how magnetic fields exert forces on currents and moving charges.

Magnetic FieldsA compass is a magnetic dipole. It will rotate to line up with a magnetic field.

Sources of the FieldMagnets produce a magnetic field; so do current-carrying wires, loops, and coils.

You’ll learn how to use compasses and other tools to map magnetic fields.

You’ll learn to describe the magnetic fields created by currents. These iron filings show the magnetic-field shape for this current-carrying wire.

You’ll see how the motion of charged particles in the earth’s magnetic field gives rise to the aurora.

effects of the FieldMagnetic fields exert forces on moving charged particles and electric currents.

Magnetic Fields and Forces24

This detailed image of the skeletal system of a dolphin wasn’t made with x rays; it was made with magnetism. how is this done?

You learned how to draw and interpret the electric field of a dipole. In this chapter, you’ll see how a magnetic dipole creates a magnetic field with a similar structure.

STop To Think

An electric dipole in a uniform electric field experiences no net force, but it does experience a net torque. The rotation of this dipole will be

A. Clockwise.B. Counterclockwise.

-q + q

Eu

electric FieldsIn Chapter 20, we described electric interactions between charged objects in terms of the field model.

Looking BAck ◀◀

KNIG9721_03_chap_24.indd 764 03/10/13 1:53 PM

794 cha p t e r 24 Magnetic Fields and Forces

geneRAL pRincipLeS

consequences of MagnetismMagnetic fields exert long-range forces on magnetic materials and on moving charges or currents.

• Unlikepolesofmagnets attract each other; like poles repel each other.

• Amagneticfieldexertsa force on a moving charged particle.

• Parallelwireswithcurrents in the same direction attract each other; when the currents are in opposite directions, the wires repel each other.

Magnetic fields exert torques on magnetic dipoles, aligning their axes with the field.

Sources of MagnetismMagnetic fields can be created by either:

• Electriccurrents or • Permanentmagnets

Three basic kinds Current Permanent Atomic of dipoles are: loop magnet magnet

Macroscopicmovement ofcharges as a current

Microscopicmagnetism ofelectrons

S N

S SN N SS NN

vuBu

Fu

I I

I I

iMpoRTAnT concepTS

Magnetic FieldsThe direction of the magnetic field

• isthedirectioninwhichthenorth pole of a compass needle points.

• duetoacurrentcanbefoundfrom the right-hand rule for fields.

The strength of the magnetic field is

• proportionaltothetorqueonacompass needle when turned slightly from the field direction.

• measuredintesla(T).

Magnetic Forces and TorquesThe magnitude of the magnetic force on a moving charge depends on its charge q, its speed v, and the angle a between the velocity and the field:

F = 0 q 0 vB sin a

The direction of this force on a positive charge is given by the right-hand rule for forces.

The magnitude of the force on a current-carrying wire perpendicular to the magnetic field depends on the current and the length of the wire: F = ILB.

The torque on a current loop in a magnetic field depends on the current, the loop’s area, and how the loop is oriented in the field: t = 1IA2B sin u.

I

vu

Bu

Fu

S u m m a r y Goal: To learn about magnetic fields and how magnetic fields exert forces on currents and moving charges.

AppLicATionS

charged-particle motion

There is no force if vu is parallel to Bu

.

Stability of magnetic dipoles

A magnetic dipole is stable (in a lower energy state) when aligned with the external magnetic field. It is unstable (in a higher energy state) when aligned opposite to the field.

The probe field of an MRI scanner measures the flipping of magnetic dipoles between these two orientations.

Fields due to common currents

B =

Long, straight wire Current loop

Solenoid

m0I2pr

B = m0I___2R

B = m0NI

L

vu

Fu

The most basic unit of magnetism is the magnetic dipole, which consists of a north and a south pole.

If vu is perpendicular to Bu

, the particle undergoes uniform circular motion with radius r = mv/ 0 q 0B.

KNIG9721_03_chap_24.indd 794 03/10/13 1:54 PM


on the big picture

Bringing together key concepts, principles, and equations, this novel feature is designed to highlight connections and differences. More than a summary, they emphasize deeper relations and point out common or contrasting details.

SynthESiS BoxES

82 cha p t e r 3 Vectors and Motion in Two Dimensions

3.7 Projectile Motion: Solving Problems

Now that we have a good idea of how projectile motion works, we can use that knowledge to solve some true two-dimensional motion problems.

In the sport of dock jumping, dogs run at full speed off the end of a dock that sits a few feet above a pool of water. The winning dog is the one that lands farthest from the end of the dock. If a dog runs at 8.5 m/s (a pretty typical speed for this event) straight off the end of a dock that is 0.61 m (2 ft, a standard height) above the water, how far will the dog go before splashing down?

PrePare We start with a visual overview of the situation in FiGURe 3.33. We have chosen to put the origin of the coordinate system at the base of the dock. The dog runs horizontally off the end of the dock, so the initial components of the velocity are (vx)i = 8.5 m/s and (vy)i = 0 m/s. We can treat this as a projectile motion problem, so we can use the details and equations presented in Synthesis 3.1 above.

We know that the horizontal and vertical motions are inde-pendent. The fact that the dog is falling toward the water doesn’t affect its horizontal motion. When the dog leaves the end of

Dock jumping

the dock, it will continue to move horizontally at 8.5 m/s. The vertical motion is free fall. The jump ends when the dog hits the water—that is, when it has dropped by 0.61 m. We are

example 3.11

Stop to think 3.7 A 100 g ball rolls off a table and lands 2 m from the base of the table. A 200 g ball rolls off the same table with the same speed. How far does it land from the base of the table?

A. 61 m B. 1 m C. Between 1 m and 2 m D. 2 m E. Between 2 m and 4 m F. 4 m

Video tutor Demo

Video tutor Demo

Video tutor Demo

Video tutor Demo

After launch,the verticalmotion is free fall.

The verticalcomponent of theinitial velocity is theinitial velocity forthe vertical motion.

Rising Falling

The kinematic equations for projectile motion are those for constant-acceleration motion vertically and constant-velocity horizontally:

After launch, the horizontal motion is uniform motion.

The horizontal component of the initial velocityis the initial velocity for the horizontal motion.

The accelerationis zero.

Rising or falling, theacceleration is thesame, ay = -g.

The vertical motionis free fall.

The free fallacceleration,g = 9.8 m/s2.

The horizontal motionis uniform motion.

The two equations are linked by the time interval ∆t,which is the same for the horizontal and vertical motion.

An object is launchedinto the air at an angleu to the horizontal.

(vy)f = (vy)i -g∆t

yf = yi + (vy)i ∆t - g(∆t)2(vx)f = (vx)i = constant

xf = xi + (vx)i ∆t12

viu

x

y

(vy)i = vi sin u

(vy)i

(vx)i

(vx)i = vi cos u

u

au

a = 0u u

SyntheSiS 3.1

FiGURe 3.33 Visual overview for Example 3.11.

vi

au

u

xi, yi, ti(vx)i, (vy)i

xf, yf, tf(vx)f, (vy)f

00

x

y

0.61 m

Findxf

Knownxi = 0 m(vy)i = 0 m/sti = 0 syi = 0.61 m, yf = 0 m(vx)i = vi = 8.5 m/sax = 0 m/s2

ay = -g

The horizontal and vertical components of projectile motion are independent, but must be analyzed together.

projectile motion

KNIG9721_03_chap_03.indd 82 09/08/13 1:56 PM

7.3 Torque 201

Equations 7.10–7.12 give only the magnitude of the torque. But torque, like a force component, has a sign. A torque that tends to rotate the object in a counter-clockwise direction is positive, while a torque that tends to rotate the object in a clockwise direction is negative. FIGURE 7.21 summarizes the signs. Notice that a force pushing straight toward the pivot or pulling straight out from the pivot exerts no torque.

NOTE ▶ When calculating a torque, you must supply the appropriate sign by observing the direction in which the torque acts. ◀

Class Video Video Tutor Demo

We see that the component of Fu

that is perpendicular to the radial line is F# = F cos 20° = 226 N. The distance from the hinge to the point at which the force is applied is r = 0.75 m.

Solve We can find the torque on the door from Equation 7.10 :

t = rF# = (0.75 m)(226 N) = 170 N # m

The torque depends on how hard Ryan pushes, where he pushes, and at what angle. If he wants to exert more torque, he could push at a point a bit farther out from the hinge, or he could push exactly perpendicular to the door. Or he could simply push harder!

aSSeSS As you’ll see by doing more problems, 170 N # m is a significant torque, but this makes sense if you are trying to free a stuck door.

FIGURE 7.21 Signs and strengths of the torque.

Pivot point

Radial linePoint whereforce is applied

A positive torque tries to rotate the object counterclockwise about the pivot.

Pulling straight out from the pivot exerts zero torque.

A negative torque tries to rotate the object clockwise about the pivot.

Maximum negative torque for a force perpendicular to the radial line

Maximum positive torque for a forceperpendicular to the radial line

Pushing straight toward thepivot exerts zero torque.

STOp TO ThINK 7.3 A wheel turns freely on an axle at the center. Given the details noted in Figure 7.21 , which one of the forces shown in the figure will provide the largest positive torque on the wheel?

D

B

C

F

F

2F

r/2

r

2F

F

A

E

Luis uses a 20-cm-long wrench to tighten a nut, turning it clock-wise. The wrench handle is tilted 30° above the horizontal, and Luis pulls straight down on the end with a force of 100 N. How much torque does Luis exert on the nut?

PrePare FIGURE 7.22 shows the situation. The two illustrations correspond to two methods of calculating torque, corresponding to Equations 7.10 and 7.11 .

Solve According to Equation 7.10 , the torque can be calculated as t = rF# . From Figure 7.22 a, we see that the perpendicular component of the force is

F# = F cos 30° = (100 N)( cos 30°) = 86.6 N

Calculating the torque on a nut ExamplE 7.10

(a) (b)

FIGURE 7.22 A wrench being used to turn a nut.

Continued

KNIG9721_03_chap_07.indd 201 16/08/13 1:56 PM

To encourage students to actively engage with a key or complex figure, they are asked to reason with a related “Stop to Think” question.

Topic-specific Problem-Solving Strategies give students a framework and guidance for broad classes of problems. New overview statements now provide the “big picture,” giving clear statements of what types of problems a strategy is intended for and/or how to use it.

ProBlEm-SolVing StrAtEgiESConCEPt ChECk figurES

9.4 Conservation of Momentum 265

pRoBlEm-SolVInG

S t R a t E G y 9 . 1

We can use the law of conservation of momentum to relate the momenta and velocities of objects after an interaction to their values before the inter-action.

pREpaRE Clearly define the system.

■ If possible, choose a system that is isolated (Fu

net = 0u

) or within which the interactions are sufficiently short and intense that you can ignore external forces for the duration of the interaction (the impulse approximation). Momentum is then conserved.

■ If it’s not possible to choose an isolated system, try to divide the problem into parts such that momentum is conserved during one segment of the motion. Other segments of the motion can be analyzed using Newton’s laws or, as you’ll learn in Chapter 10, conservation of energy.

Following Tactics Box 9.1, draw a before-and-after visual overview. Define symbols that will be used in the problem, list known values, and identify what you’re trying to find.

SolVE The mathematical representation is based on the law of conservation of momentum, Equations 9.15. Because we generally want to solve for the velocities of objects, we usually use Equations 9.15 in the equivalent form

m1(v1x)f + m2(v2x)f + g = m1(v1x)i + m2(v2x)i + gm1(v1y)f + m2(v2y)f + g = m1(v1y)i + m2(v2y)i + g

aSSESS Check that your result has the correct units, is reasonable, and answers the question.

Conservation of momentum problems

Exercise 17

FIGURE 9.17 shows a before-and-after visual overview for the two skaters. The total momentum before they push off is P

u

i = 0u

because both skaters are at rest. Consequently, the total momen-tum will still be 0

u

after they push off.

Solve Since the motion is only in the x-direction, we’ll need to consider only x-components of momentum. We write Sandra’s initial momentum as ( pSx)i = mS (vSx)i , where mS is her mass and (vSx)i her initial velocity. Similarly, we write David’s initial momentum as ( pDx)i = mD (vDx)i . Both these momenta are zero because both skaters are initially at rest.

We can now apply the mathematical statement of momentum conservation, Equation 9.15. Writing the final momentum of Sandra as mS (vSx)f and that of David as mD (vDx)f , we have

mS(vSx)f + mD(vDx)f = mS(vSx)i + mD(vDx)i = 0

The skaters’ �nalmomentum c

cequals their initialmomentum c

cwhichwas zero.

Solving for (vDx)f , we find

(vDx)f = - mS

mD (vSx)f = -

45 kg

80 kg* 2.2 m/s = -1.2 m/s

David moves backward with a speed of 1.2 m/s.Notice that we didn’t need to know any details about the force

between David and Sandra in order to find David’s final speed. Conservation of momentum mandates this result.

aSSeSS It seems reasonable that Sandra, whose mass is less than David’s, would have the greater final speed.

FIGURE 9.17 Before-and-after visual overview for two skaters pushing off from each other.

(vSx)i = 0 m/smS = 45 kg

x

(vSx)f = 2.2 m/s(vDx)f

Find: (vDx)f

Before:

After:

(vDx)i = 0 m/s mD = 80 kg

KNIG9721_03_chap_09.indd 265 16/08/13 1:59 PM


ocus on students...F

Knight/Jones/Field was designed from the ground up with students in mind, and is based on a solid foundation of the latest physics education research . . .

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An Inductive Approach...

24.3 Electric Currents Also Create Magnetic Fields 771

◀ FigURe 24.10 How compasses respond to a current-carrying wire.

Magnetism often requires a three-dimensional perspective of the sort shown in Tactics Box 24.1. But since two-dimensional figures are easier to draw, we will make as much use of them as we can. Consequently, we will often need to indicate field vectors or currents that are perpendicular to the page. FigURe 24.11a shows the notation we will use. FigURe 24.11b demonstrates this notation by showing the compasses around a current that is directed into the page. To use the right-hand rule with this drawing, point your right thumb into the page. Your fingers will curl clockwise, giving the direction in which the north poles of the compass needles point.

To help remember in which direction compasses will point, we use the right-hand rule shown in Tactics Box 24.1. We’ll use this same rule later to find the direction of the magnetic field due to several other shapes of current-carrying wire, so we’ll call this rule the right-hand rule for fields.

Current-carryingwire

Current up The compass needlesare tangent to a circlearound the wire, showingthat the �eld is directed counterclockwise around the wire.

I

Current downWhen the current directionis reversed, the compassneedles turn to point in theopposite direction.

I

FigURe 24.11 The notation for vectors and currents that are perpendicular to the page.

(a)

Vectors into page

Vectors out of page

Current into page

Current out of page

(b)

I

Current into page

(a)

Vectors into page

Vectors out of page

Current into page

Current out of page

(b)

I

Current into page

assess Figure 24.12 illustrates the key features of the field. The direction of the field vectors and field lines matches what we saw in Figure 24.11, and the field strength drops off with distance, as we learned in the atlas figure. We don’t expect you to draw such a figure, but it’s worth looking at the full 3-D picture of the field in FigURe 24.13. This conveys the idea that the field lines exist in every plane along the length of the wire.

drawing the magnetic field of a current-carrying wire

FigURe 24.12 Drawing the magnetic field of a long, straight, current-carrying wire.

FigURe 24.13 Field lines exist everywhere along the wire.

Sketch the magnetic field of a long, current-carrying wire, with the current going into the paper. Draw both magnetic field line and magnetic field vector representations.

Reason From the iron filing picture in the atlas, we have seen that the field lines form circles around the wire, and the magnetic field becomes weaker as the distance from the wire is increased. FigURe 24.12 shows how we construct both field line and field vector representations of such a field.

Magnetic �eld vectors are longerwhere the �eld is stronger.

means currentgoes into the page:point your rightthumb in thisdirection.

Your �ngerscurl clockwise ccso the magnetic�eld lines are clockwisecircles around the wire.

Magnetic �eld vectors aretangent to the �eld lines.

Field lines are closer togetherwhere the �eld is stronger.

I

concepTUAL exAMpLe 24.2

Exercises 6–11

IPoint your right thumb inthe direction of the current.

Wrap your �ngers around thewire to indicate a circle.

Your �ngers curl in thedirection of the magnetic�eld lines around the wire.

Right-hand rule for fieldsTAcTicSB o x 2 4 . 1

KNIG9721_03_chap_24.indd 771 03/10/13 1:53 PM

Emphasis on Explicit Skills...

Addressing Misconceptions...

Figures that Teach...

11.5 Heat Engines 333

It is possible to do something similar with heat. Thermal energy is naturally trans-ferred from a hot reservoir to a cold reservoir; it is possible to take some of this energy as it is transferred and convert it to other forms. This is the job of a device known as a heat engine.

The energy-transfer diagram of FIGURE 11.18a illustrates the basic physics of a heat engine. It takes in energy as heat from the hot reservoir, turns some of it into useful work, and exhausts the balance as waste heat in the cold reservoir. Any heat engine has exactly the same schematic.

heat engines

Most of the electricity that you use was generated by heat engines. Coal or other fossil fuels are burned to produce high-temperature, high-pressure steam. The steam does work by spinning a turbine attached to a genera-tor, which produces electricity. Some of the energy of the steam is extracted in this way, but more than half simply flows “downhill” and is deposited in a cold reservoir, often a lake or a river.

Your car gets the energy it needs to run from the chemical energy in gasoline. The gasoline is burned; the resulting hot gases are the hot reservoir. Some of the thermal energy is converted into the kinetic energy of the moving vehicle, but more than 90% is lost as heat to the surrounding air via the radiator and the exhaust, as shown in this thermogram.

There are many small, simple heat engines that are part of things you use daily. This fan, which can be put on top of a wood stove, uses the thermal energy of the stove to provide power to drive air around the room. Where are the hot and cold reservoirs in this device?

FIGURE 11.18 The operation of a heat engine.

Hot reservoir

Heatengine

Cold reservoir TC

TH

QH

QC

Wout

1. Heat energy QH is transferred from the hot reservoir to the system.

2. Part of the energy is used to do useful work Wout.

3. The remaining energy QC = QH - Wout is exhausted to the cold reservoir as waste heat.

(a)

QCQH

Wout

Useful workdrives generator.

Cold reservoir (a river)at temperature TC

Hot reservoir attemperature TH

(b)

We assume, for a heat engine, that the engine’s thermal energy doesn’t change. This means that there is no net energy transfer into or out of the heat engine. Because energy is conserved, we can say that the useful work extracted is equal to the difference between the

FIGURE 11.18b shows the directions of the energy flows and the locations of the reservoirs for a real heat engine, the power plant discussed earlier in this chapter. The cold reservoir for a power plant can be a river or lake, as shown, or simply the atmosphere, to which heat QC is rejected from cooling towers.

Most of the energy that you use daily comes from the conversion of chemical energy into thermal energy and the subsequent conversion of that energy into other forms. Let’s look at some common examples of heat engines.

KNIG9721_03_chap_11.indd 333 23/08/13 9:52 AM

Balancing Qualitative and Quantitative Reasoning...

Multiple Representations...

2.2 Uniform Motion 33

From Velocity to PositionWe’ve now seen how to move between different representations of uniform motion. There’s one last issue to address: If you have a graph of velocity versus time, how can you determine the position graph?

Suppose you leave a lecture hall and begin walking toward your next class, which is down the hall to the west. You then realize that you left your textbook (which you always bring to class with you!) at your seat. You turn around and run back to the lecture hall to retrieve it. A velocity-versus-time graph for this motion appears as the top graph in FIGURE 2.13. There are two clear phases to the motion: walking away from class (velocity +1.0 m/s) and running back (velocity -3.0 m/s.) How can we deduce your position-versus-time graph?

As before, we can analyze the graph segment by segment. This process is shown in Figure 2.13, in which the upper velocity-versus-time graph is used to deduce the lower position-versus-time graph. For each of the two segments of the motion, the sign of the velocity tells us whether the slope of the graph is positive or negative. The magnitude of the velocity tells how steep the slope is. The final result makes sense: It shows 15 seconds of slowly increasing position (walking away) and then 5 seconds of rapidly decreasing position (running back.) And you end up back where you started.

There’s one important detail that we didn’t talk about in the preceding paragraph: How did we know that the position graph started at x = 0 m? The velocity graph tells us the slope of the position graph, but it doesn’t tell us where the position graph should start. Although you’re free to select any point you choose as the origin of the coordinate system, here it seems reasonable to set x = 0 m at your starting point in the lecture hall; as you walk away, your position increases.

As you move away,your velocity is+1.0 m/s c

cso the slope ofyour position graphis +1.0 m/s.

As you return, your velocity is -3.0 m/s c

cso the slope of your position graphis -3.0 m/s.

1.0

0

-1.0

-2.0

-3.0

5 10 15 20 25

vx (m/s)

t (s)

15

10

5

050 10 15 20 25

x (m)

t (s)

FIGURE 2.13 Deducing a position graph from a velocity-versus-time graph.

t

x

t

x

A. B. C. D.t

x

t

x

2.2 Uniform MotionIf you drive your car on a straight road at a perfectly steady 60 miles per hour (mph), you will cover 60 mi during the first hour, another 60 mi during the second hour, yet another 60 mi during the third hour, and so on. This is an example of what we call uniform motion. Straight-line motion in which equal displacements occur during any succes-sive equal-time intervals is called uniform motion or constant-velocity motion.

NotE ▶ The qualifier “any” is important. If during each hour you drive 120 mph for 30 min and stop for 30 min, you will cover 60 mi during each successive 1 hour interval. But you will not have equal displacements during successive 30 min intervals, so this motion is not uniform. ◀

FIGURE 2.14 shows a motion diagram and a graph for an object in uniform motion. Notice that the position-versus-time graph for uniform motion is a straight line. This follows from the requirement that all values of ∆ x corresponding to the same value of ∆t be equal. In fact, an alternative definition of uniform motion is: An object’s motion is uniform if and only if its position-versus-time graph is a straight line.

Equations of Uniform MotionAn object is in uniform motion along the x-axis with the linear position-versus-time graph shown in FIGURE 2.15 on the next page. Recall from Chapter 1 that we denote the object’s initial position as xi at time ti . The term “initial” refers to the starting point of

Stop to thINk 2.1 Which position-versus-time graph best describes the motion diagram at left?

FIGURE 2.14 Motion diagram and position-versus-time graph for uniform motion.

t

Equaldisplacements

Uniform motion

The displacements betweensuccessive frames are thesame. Dots are equallyspaced. vx is constant.

x

∆x

∆x

The position-versus-time graph is a straight line. The slope of the line is vx.

vu

KNIG9721_03_chap_02.indd 33 16/08/13 12:53 PM


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Visual Analogies...

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I =∆q

∆t (22.1)

Definition of current

22.2 Defining and Describing Current 705

Similarly, the lightbulb doesn’t “use up” current, but, like the turbine, it does use energy. The energy is dissipated by atomic-level friction as the electrons move through the wire, making the wire hotter until, in the case of the lightbulb filament, it glows.

There are many other issues we’ll need to examine, but we can draw a first impor-tant conclusion:

FIGURE 22.7 Water in a pipe turns a turbine.

FIGURE 22.9 Negative and positive charges moving in opposite directions give the same current.

v

The amount of water leaving the turbine equalsthe amount entering; the number of electronsleaving the bulb equals the number entering.

v

Flow ofelectrons

This plate discharges as negative chargeenters it and cancels its positive charge.

This platedischarges asnegative chargeleaves it.

This platedischarges aspositive chargeleaves it.

This plate discharges as positive chargeenters it and cancels its negative charge.

Law of conservation of current The current is the same at all points in a current-carrying wire.

22.2 Defining and Describing CurrentAs we’ve seen, the current in a metal consists of electrons moving from low elec-tric potential to high potential, in a direction opposite the electric field. But, as FIGURE 22.9 shows, a capacitor discharges in exactly the same way whether we consider the current to be negative charges moving opposite the field or positive charges moving in the same direction as the field. In general, for any circuit, the current is in the same direction independent of which of these two perspectives we choose. We thus adopt the convention that current is the flow of positive charge. All our calculations will be correct, and all our circuits will work perfectly well, with this positive-charge-current convention.

Definition of CurrentBecause the coulomb is the SI unit of charge, and because currents are charges in motion, we define current as the rate, in coulombs per second, at which charge moves through a wire. FIGURE 22.10 shows a wire in which the electric field is E

u

. This electric field causes charges to move through the wire. Because we are considering current as the motion of positive charges, the motion is in the direction of the field.

The flow rate of water in a pipe measures the amount of water passing a cross- section area of the pipe per second. We use a similar convention for current. As illus-trated in Figure 22.10, we can measure the amount of charge ∆q that passes through a cross section of the wire in a time interval ∆t. We then define the current in the wire as

concEptUaL ExampLE 22.1

The discharge of a capacitor lights two identical bulbs, as shown in FIGURE 22.8. Compare the brightness of the two bulbs.

Reason Current is conserved, so any current that goes through bulb 1 must go through bulb 2 as well—the currents in the two bulbs are equal. We’ve noted that the brightness of a bulb is propor-tional to the current it carries. Identical bulbs carrying equal currents must have the same brightness.

assess This result makes sense in terms of what we’ve seen about the conserva-tion of current. No charge is “used up” by either bulb.

Which bulb is brighter?

Bulb 1 Bulb 2

FIGURE 22.8 Two bulbs lit by the current discharging a capacitor.

FIGURE 22.10 The current I.

Eu

I

The current I is due to the motionof charges in the electric �eld.

We imagine an area across the wire throughwhich the charges move. In a time ∆t,charge ∆q moves through this area.

KNIG9721_03_chap_22.indd 705 28/09/13 2:23 PM

research-based pedagogy

Annotated Equations...

784 cha p t e r 24 Magnetic Fields and Forces

However, there is a force on a current-carrying wire that is perpendicular to a magnetic field, as shown in FigURe 24.37.

noTe ▶ The magnetic field is an external field, created by a permanent magnet or by other currents; it is not the field of the current I in the wire. ◀

The direction of the force on the current is found by considering the force on each charge in the current. We model current as the flow of positive charge, so the right-hand rule for forces applies to currents in the same way it does for moving charges. With your fingers aligned as usual, point your right thumb in the direction of the current (the direction of the motion of positive charges) and your index finger in the direction of B

u

. Your middle finger is then pointing in the direction of the force Fu

on the wire, as in FigURe 24.37c. Consequently, the entire length of wire within the magnetic field experiences a force perpendicular to both the current direction and the field direction, as shown in FigURe 24.37b.

If the length of the wire L, the current I, or the magnetic field B is increased, then the magnitude of the force on the wire will also increase. We can show that the mag-netic force on a current-carrying wire is given by

FigURe 24.37 Magnetic force on a current-carrying wire.

A DC power line near the equator runs east-west. At this location, the earth’s magnetic field is parallel to the ground, points north, and has magnitude 50 mT. A 400 m length of the heavy cable that spans the distance between two towers has a mass of 1000 kg. What direction and magnitude of current would be necessary to offset the force of gravity and “levitate” the wire? (The power line will actually carry a current that is much less than this; 850 A is a typical value.)

PRePaRe First, we sketch a top view of the situation, as in FigURe 24.38. The magnetic force on the wire must be opposite that of gravity. An application of the right-hand rule for forces shows that a current to the east will result in an upward force—out of the page.

solve The magnetic field is perpendicular to the current, so the magnitude of the magnetic force is given by Equation 24.10. To levitate the wire, this force must be opposite to the weight force but equal in magnitude, so we can write

mg = ILB

where m and L are the mass and length of the wire and B is the

Magnetic force on a power line

magnitude of the earth’s field. Solving for the current, we find

I =mg

LB=11000 kg2 19.8 m/s221400 m2 150 * 10-6 T2 = 4.9 * 105 A

directed to the east.

assess The current is much larger than a typical current, as we expected.

exAMpLe 24.11

FigURe 24.38 Top view of a power line near the equator.

Video Tutor demo

In many practical cases the wire will be perpendicular to the field, so that a = 90°. In this case,

Fwire = ILB (24.10)

If we rewrite Equation 24.10 as B = Fwire /IL, we can see that the unit for magnetic field, the tesla, can be defined in terms of other units:

1 T = 1 N

A # m

Length of wire inmagnetic �eld (m)

Angle between wireand magnetic �eld

Current in wire (A) Magnetic �eld (T)

Fwire = ILB sin aI

L

aBu

(24.9)

L

I

I

A wire is perpendicularto an externally createdmagnetic �eld.

If the wire carriesa current, the magnetic�eld will exert a forceon the wire.

(a)

(c)

(b)

The right-hand rule for forces applies. Your thumb should point in the direction of the current.

Fu

Fu

Bu

Bu

Bu

E

N

S

W

400 m

The �eld of the earth near theequator is parallel to theground and points to the north.

I

Bu

KNIG9721_03_chap_24.indd 784 03/10/13 1:54 PM

Streamlining use of Color...

Structured Problem Solving...

Active Learning... 10.4 Potential Energy 297

Stop to thINk 10.4 Rank in order, from largest to smallest, the gravitational potential energies of identical balls 1 through 4.

Elastic Potential EnergyEnergy can also be stored in a compressed or extended spring as elastic (or spring) potential energy Us. We can find out how much energy is stored in a spring by using an external force to slowly compress the spring. This external force does work on the spring, transferring energy to the spring. Since only the elastic potential energy of the spring is changing, Equation 10.3 reads

∆Us = W (10.14)

That is, we can find out how much elastic potential energy is stored in the spring by calculating the amount of work needed to compress the spring.

FIGURE 10.16 shows a spring being compressed by a hand. In ◀◀ SECtIoN 8.3 we found that the force the spring exerts on the hand is Fs = -k ∆x (Hooke’s law), where ∆x is the displacement of the end of the spring from its equilibrium position and k is the spring constant. In Figure 10.16 we have set the origin of our coordinate system at the equilibrium position. The displacement from equilibrium ∆x is therefore equal to x, and the spring force is then -kx. By Newton’s third law, the force that the hand exerts on the spring is thus F = +kx.

As the hand pushes the end of the spring from its equilibrium position to a final position x, the applied force increases from 0 to kx. This is not a constant force, so we can’t use Equation 10.5, W = Fd, to find the work done. However, it seems reason-able to calculate the work by using the average force in Equation 10.5. Because the force varies from Fi = 0 to Ff = kx, the average force used to compress the spring is Favg =

12 kx. Thus the work done by the hand is

W = Favgd = Favgx = a1

2 kxbx =

1

2 kx2

This work is stored as potential energy in the spring, so we can use Equation 10.14 to find that as the spring is compressed, the elastic potential energy increases by

∆Us =1

2 kx2

Just as in the case of gravitational potential energy, we have found an expression for the change in Us, not Us itself. Again, we are free to set Us = 0 at any convenient spring extension. An obvious choice is to set Us = 0 at the point where the spring is in equilibrium, neither compressed nor stretched—that is, at x = 0. With this choice we have

1

2

3

4

v = 0

vu

Us =1

2kx2 (10.15)

Elastic potential energy of a spring displaced a distance x from equilibrium (assuming Us = 0 when the end of the spring is at x = 0)

x

Us

p.44

QUADRATIC

NotE ▶ Because Us depends on the square of the displacement x, Us is the same whether x is positive (the spring is compressed as in Figure 10.16) or negative (the spring is stretched). ◀

Fu

x = 0

x

x

Spring in equilibrium

As x increases, so does F.

FIGURE 10.16 The force required to compress a spring is not constant.

On each stride, the tendon stretches, storing about 35 J of energy.

Calf muscle

Achilles tendon

Spring in your step As you run, you lose some of your mechanical energy each time your foot strikes the ground; this energy is transformed into unrecoverable thermal energy. Luckily, about 35% of the decrease of your mechanical energy when your foot lands is stored as elastic potential energy in the stretchable Achilles tendon of the lower leg. On each plant of the foot, the tendon is stretched, storing some energy. The tendon springs back as you push off the ground again, helping to propel you forward. This recovered energy reduces the amount of internal chemical energy you use, increasing your efficiency.

KNIG9721_03_chap_10.indd 297 16/08/13 2:04 PM

Guided Practice...

10.6 Potential Energy

17.�Below we see a 1 kg object that is initially 1 m above the ground and rises to a height of 2 m.�Anjay and Brittany each measure its position but use a dif�ferent coordinate system to do so.�Fill in the table to show the initial and final gravitational potential ener�gies and � as�measured by �Anjay and Brittany�.�

18.�Three balls of equal mass are fired simultaneously with �equal�speeds�from the same height above the ground. Ball 1 is fired straight up,�ball 2 is fired straight down, and ball 3 is fired horizontally�. Rank in�order�, from lar�gest to smallest, their speeds �v�1�, �v�2�, and �v�3�as they hit�the ground.�Or�der:�

Explanation:�

19.�Below are shown three frictionless tracks. �A�block is released from rest at the position shown�on the left. �T�o which point does the block make it on the right before reversing direction and�sliding back? Point B is the same height as the starting position.�

A�B�

C�

A�B�

C�

A�B�

C�

Makes it to� Makes it to� Makes it to�

Anjay�

Ends here�

2 m� Starts here�

Brittany�

0�

0�

DU�

10-8 C H A P T E R �1�0�.�Ener�gy and �W�ork�

U�i� U�f� �U�Anjay�Brittany�

Ball 1�

Ball 3�

Ball 2�


ocus students...on their goals

FThe MCAT is being restructured to test competencies, not knowledge. Students will be required to reason, to do more than simply plug in numbers into equations. Of the hundreds of new end-of-chapter problems, many of these require students to reason using ratios and proportionality, to reason using real-world data, and to assess answers to see if they make physical sense.

Building on the book’s acclaimed real-world focus, even more applications from the living world have been added to text, worked examples, and end-of-chapter problems, giving students essential practice in applying core physical principles to new real-world situations.

inCrEASEd EmPhASiS on CritiCAl thinking And rEASoning

ExPAndEd lifE-SCiEnCE And BiomEdiCAl APPliCAtionS

Problems 349

mCat-Style Passage Problems

Kangaroo Locomotion

Kangaroos have very stout tendons in their legs that can be used to store energy. When a kangaroo lands on its feet, the tendons stretch, transform-ing kinetic energy of motion to elastic potential energy. Much of this energy can be transformed back into kinetic energy as the kangaroo takes another hop. The kangaroo’s peculiar hopping gait is not very efficient at low speeds but is quite efficient at high speeds.

Figure P11.68 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mL/s) per kg of body mass, allowing a direct comparison between the two species.

For humans, the energy used per second (i.e., power) is propor-tional to the speed. That is, the human curve nearly passes through the origin, so running twice as fast takes approximately twice as much power. For a hopping kangaroo, the graph of energy use has only a very small slope. In other words, the energy used per sec-ond changes very little with speed. Going faster requires very little additional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the neces-sary power is approximately the same. 68. | A person runs 1 km. How does his speed affect the total

energy needed to cover this distance? A. A faster speed requires less total energy. B. A faster speed requires more total energy. C. The total energy is about the same for a fast speed and a slow

speed. 69. | A kangaroo hops 1 km. How does its speed affect the total

energy needed to cover this distance? A. A faster speed requires less total energy. B. A faster speed requires more total energy. C. The total energy is about the same for a fast speed and a slow

speed. 70. | At a speed of 4 m/s, A. A running human is more efficient than an equal-mass

hopping kangaroo. B. A running human is less efficient than an equal-mass

hopping kangaroo. C. A running human and an equal-mass hopping kangaroo have

about the same efficiency. 71. | At approximately what speed would a human use half the

power of an equal-mass kangaroo moving at the same speed? A. 3 m/s B. 4 m/s C. 5 m/s D. 6 m/s 72. | At what speed does the hopping motion of the kangaroo

become more efficient than the running gait of a human? A. 3 m/s B. 5 m/s C. 7 m/s D. 9 m/s

FIGURE P11.68 Oxygen uptake (a measure of energy use per second) for a running human and a hopping kangaroo.

Human,running

Speed (m/s)0

Oxygen uptake (mL/kg # s)

2 4 6 8 10 12

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

Red kangaroo,hopping

StoP to thInk anSwERS

Chapter Preview Stop to Think: C. The work Christina does on the javelin is transferred into kinetic energy, so the javelin has 270 J of kinetic energy as it leaves her hand. As the javelin rises, some of its kinetic energy is transformed into gravitational potential energy, but the total energy remains constant at 270 J. Thus at its highest point, the javelin’s kinetic energy is 270 J - 70 J = 200 J.

Stop to Think 11.1: C. In each case, what you get is the potential-energy change of the box. Crane 2 lifts a box with twice the mass the same distance as crane 1, so you get twice as much energy with crane 2. How about what you have to pay? Crane 2 uses 20 kJ, crane 1 only 10 kJ. Comparing crane 1 and crane 2, we find crane 2 has twice the energy out for twice the energy in, so the efficiencies are the same.

Stop to Think 11.2: C. As the body uses chemical energy from food, approximately 75% is transformed into thermal energy. Also, kinetic energy of motion of the legs and feet is transformed into thermal energy with each stride. Most of the chemical energy is transformed into thermal energy.

Stop to Think 11.3: C. Samples 1 and 2 have the same thermal energy, which is the total kinetic energy of all the atoms. Sample 1

has twice as many atoms, so the average energy per atom, and thus the temperature, must be less.

Stop to Think 11.4: C. The radiator is at a higher temperature than the surrounding air. Thermal energy is transferred out of the system to the environment, so Q 6 0.

Stop to Think 11.5: A, D. The efficiency is fixed by the ratio of TC to TH. Decreasing this ratio increases efficiency; the heat engine will be more efficient with a hotter hot reservoir or a colder cold reservoir.

Stop to Think 11.6: A, D. The closer the temperatures of the hot and cold reservoirs, the more efficient the heat pump can be. (It is also true that having the two temperatures be closer will cause less thermal energy to “leak” out.) Any change that makes the two temperatures closer will allow the refrigerator to use less energy to run.

Stop to Think 11.7: B. In this case, kinetic energy is transformed into potential energy; there is no entropy change. In the other cases, energy is transformed into thermal energy, meaning entropy increases.

KNIG9721_03_chap_11.indd 349 23/08/13 9:53 AM

422 cha p t e r 13 Fluids

speed is faster in a larger tube because the center of the tube, where the flow is fastest, is farther from the “drag” exerted by the wall. As we’ve seen, the average speed is also proportional to R2. These two terms combine to give the R4 dependence.

Cardiovascular disease is a narrowing of the arteries due to the buildup of plaque deposits on the interior walls. Magnetic resonance imaging, which you’ll learn about in Chapter 24, can create exqui-site three-dimensional images of the internal structure of the body. Shown are the carotid arteries that supply blood to the head, with a dangerous narrowing—a stenosis—indi-cated by the arrow.

If a section of an artery has narrowed by 8%, not nearly as much as the stenosis shown, by what percentage must the blood-pressure difference between the ends of the narrowed section increase to keep blood flowing at the same rate?

reaSon According to Poiseuille’s equation, the pressure dif-ference ∆p must increase to compensate for a decrease in the artery’s radius R if the blood flow rate Q is to remain unchanged. If we write Poiseuille’s equation as

R 4 ∆p =8hLQ

p

conceptUal example 13.13 Blood pressure and cardiovascular disease

we see that the product R4∆p must remain unchanged if the artery is to deliver the same flow rate. Let the initial artery radius and pressure difference be Ri and ∆pi . Disease decreases the radius by 8%, meaning that Rf = 0.92Ri . The requirement

Ri 4 ∆pi = Rf

4 ∆pf

can be solved for the new pressure difference:

∆pf =Ri

4

Rf 4 ∆pi =

Ri 4

(0.92Ri)4 ∆pi = 1.4 ∆pi

The pressure difference must increase by 40% to maintain the flow.

aSSeSS Because the flow rate depends on R4, even a small change in radius requires a large change in ∆p to compensate. Either the person’s blood pressure must increase, which is dan-gerous, or he or she will suffer a significant reduction in blood flow. For the stenosis shown in the image, the reduction in radius is much greater than 8%, and the pressure difference will be large and very dangerous.

In Example 13.11 we examined blood flow through a capillary. Using the numbers from that example, calculate the pressure “drop” from one end of a capillary to the other.

PrePare Example 13.11 gives enough information to determine the flow rate through a capillary. We can then use Poiseuille’s equation to calculate the pressure difference between the ends.

Solve The measured volume flow rate leaving the heart was given as 5 L/min = 8.3 * 10-5 m3/s. This flow is divided among all the capillaries, which we found to number N = 3 * 109. Thus the flow rate through each capillary is

Qcap =Qheart

N=

8.3 * 10-5 m3/s

3 * 109 = 2.8 * 10-14 m3/s

Solving Poiseuille’s equation for ∆p, we get

∆p =8hLQcap

pR 4=

8(2.5 * 10-3 Pa # s)(0.001 m)(2.8 * 10-14 m3/s)

p(3 * 10-6 m)4 = 2200 Pa

If we convert to mm of mercury, the units of blood pressure, the pressure drop across the capillary is ∆p = 16 mm Hg.

aSSeSS The average blood pressure provided by the heart (the average of the systolic and diastolic pressures) is about 100 mm Hg. A physiology textbook will tell you that the pressure has decreased to 35 mm by the time blood enters the capillaries, and it exits from capillaries into the veins at 17 mm. Thus the pressure drop across the capillaries is 18 mm Hg. Our calculation, based on the laws of fluid flow and some simple estimates of capillary size, is in almost perfect agreement with measured values.

example 13.14 pressure drop along a capillary

KNIG9721_03_chap_13.indd 422 01/08/13 11:39 AM

10.4 Potential Energy 297

Stop to thINk 10.4 Rank in order, from largest to smallest, the gravitational potential energies of identical balls 1 through 4.

Elastic Potential EnergyEnergy can also be stored in a compressed or extended spring as elastic (or spring) potential energy Us. We can find out how much energy is stored in a spring by using an external force to slowly compress the spring. This external force does work on the spring, transferring energy to the spring. Since only the elastic potential energy of the spring is changing, Equation 10.3 reads

∆Us = W (10.14)

That is, we can find out how much elastic potential energy is stored in the spring by calculating the amount of work needed to compress the spring.

FIGURE 10.16 shows a spring being compressed by a hand. In ◀◀ SECtIoN 8.3 we found that the force the spring exerts on the hand is Fs = -k ∆x (Hooke’s law), where ∆x is the displacement of the end of the spring from its equilibrium position and k is the spring constant. In Figure 10.16 we have set the origin of our coordinate system at the equilibrium position. The displacement from equilibrium ∆x is therefore equal to x, and the spring force is then -kx. By Newton’s third law, the force that the hand exerts on the spring is thus F = +kx.

As the hand pushes the end of the spring from its equilibrium position to a final position x, the applied force increases from 0 to kx. This is not a constant force, so we can’t use Equation 10.5, W = Fd, to find the work done. However, it seems reason-able to calculate the work by using the average force in Equation 10.5. Because the force varies from Fi = 0 to Ff = kx, the average force used to compress the spring is Favg =

12 kx. Thus the work done by the hand is

W = Favgd = Favgx = a1

2 kxbx =

1

2 kx2

This work is stored as potential energy in the spring, so we can use Equation 10.14 to find that as the spring is compressed, the elastic potential energy increases by

∆Us =1

2 kx2

Just as in the case of gravitational potential energy, we have found an expression for the change in Us, not Us itself. Again, we are free to set Us = 0 at any convenient spring extension. An obvious choice is to set Us = 0 at the point where the spring is in equilibrium, neither compressed nor stretched—that is, at x = 0. With this choice we have

1

2

3

4

v = 0

vu

Us =1

2kx2 (10.15)

Elastic potential energy of a spring displaced a distance x from equilibrium (assuming Us = 0 when the end of the spring is at x = 0)

x

Us

p.44

QUADRATIC

NotE ▶ Because Us depends on the square of the displacement x, Us is the same whether x is positive (the spring is compressed as in Figure 10.16) or negative (the spring is stretched). ◀

Fu

x = 0

x

x

Spring in equilibrium

As x increases, so does F.

FIGURE 10.16 The force required to compress a spring is not constant.

On each stride, the tendon stretches, storing about 35 J of energy.

Calf muscle

Achilles tendon

Spring in your step As you run, you lose some of your mechanical energy each time your foot strikes the ground; this energy is transformed into unrecoverable thermal energy. Luckily, about 35% of the decrease of your mechanical energy when your foot lands is stored as elastic potential energy in the stretchable Achilles tendon of the lower leg. On each plant of the foot, the tendon is stretched, storing some energy. The tendon springs back as you push off the ground again, helping to propel you forward. This recovered energy reduces the amount of internal chemical energy you use, increasing your efficiency.

KNIG9721_03_chap_10.indd 297 16/08/13 2:04 PM


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