Physics Fundamentals by Vincent P. Coletta Loyola Marymount University University,, Los Angeles, CA Copyright © 2008 by Physics Curriculum & Instruction, Inc. www.PhysicsCurriculum.com All Rights Reserved Produced in the United United States of America
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CONTENTS
C
3–3 Circular Motion 3–4 Ref Refer eren ence ce Fr Fraames and Re Rellati tivve Mo Moti tion on
ontents Preface Why Study Physics? Goals of the Text Features Acknowledgements
Introduction Motion Matter Applications Mathematics Der ivations Study Objectives
Measurement and Units Use of Units Fundamental Quantities Base and Der ived Units SI System of Units Definition of the Second Definition of the Meter Names of Units Power s of Ten Conver sion of Units Consistency of Units Significant Figures Order-of-Magnitude Estimates
1 Description of Motion I–1 1–2 1–3 1–4 1–5 1–6
Trajector y of a Par ticle Speed Displacement Vector Algebra Components of Ve Vector s Velocity
2 Motion in a Straight Line 2–1 Acceler ation in One Dimension 2–2 2– 2 Linea Linearr Mo Moti tion on at Co Cons nsta tant nt Ac Acce cele lera rati tion on 2–3 Free Fall A Closer Look: Fr F ree Fall in Air *2–4 Gra rap phical Analysis of Linear Motion In Per spective: Ga G alileo Galilei
3 Motion in a Plane 3–1 Acceler ation on a Cur ve ved Path 3–2 Projectile Motion
4 Newton’s Laws of Motion
v v v vi viii
1 1 2 3 4 4 4
6 6 6 7 7 7 8 9 9 9 10 11 12
16 16 18 22 23 27 31
41 41 45 49 53 54 56
64 65 67
4–1 4–2 4–3 4–4 4–5 4–6 4–7 4–8 4– 8
Classical Mechanics Force Newton’s Fir st Law Mass Newton’s Second and Th Third Laws Force Laws The Concept of Force Appl Ap plic icat atio ions ns of Ne Newt wton on’’s La Laws ws of Mo Moti tion on
i 72 76
87 88 88 90 91 92 96 101 102
Friction tion and Other Applica Applications tions of 5 Fric Newton’s Laws
118
5–1 Friction 118 A Closer Look: Microscopic Description Description of Fr iction 124 5–2 Centripetal Force 125 A Closer Look: Micro Microscopi scopicc Description Description of Force 125 5–3 Center of Mass 127
6 Gravitation 6–1 Univer sal Gr avitation 6–2 Gra Gravvita tati tion onaal Att ttra ract ctiion of th the e Ea Earth rth *6–3 Noniner titial Reference Frames In Perspectiv Perspective: e: Origin Originss of the Theory of Univer sal Gr avitation In Per spective: Is I saac Newton
7 Energy 7–1 Wor k and Kinetic Ener gy 7–2 Grav Gravitati itational onal Potenti Potential al Energy; Energy; Cons Constant tant Gr avitational Force 7–3 Gravitational Potentia Potentiall Energy; Variabl Variable e Gr avitational Force 7–4 Spring Po Potenti tential al Energy Energy;; Cons Conservation ervation of Energy 7–5 7– 5 Co Cons nserva ervati tive ve an and d No Nonc ncon onse servat rvativ ive e Fo Forc rces es 7–6 Power A Closer Look: Th The Energy to Run *7–7 Ener gy of a System of Par titicles
8 Momentum 8–1 Impulse and Linear Momentum 8–2 Mome Momentum ntum of a System System of Particles; Particles; Conserv rvaation of Linear Momentum 8–3 Collisions and Kinetic Ener gy
9 Rotation 9–1 9–2 9–3 9– 3 9–4 9–5 *9–6
Description of Rotational Motion Torque Dyna Dy nami mics cs of Ro Rota tati tion on ab abou outt a Fi Fixe xed d Ax Axis is Rotational Kinetic Ener gy Angular Momentum Ener gy Analysis of Running
139 139 144 147 152 154
162 163 169 173 177 180 182 184 187
199 199 202 204
214 214 219 221 22 1 224 226 228
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CONTENTS
10 Static Equilibrium 10–1 Conditions for Static Equilibr iu ium 10–2 Center of Gr avity *10–3 Stress and Str ain
11 Fluids 11–1 11–2 11–3 *11–4 11–5 *11–6 *11–7
Proper ties of Fluids Pressure in a Fluid at Rest Archimedes’ Pr Pr inciple Surface Te Tension and Capillar ity Flui Fl uid d Dy Dyna nam mic ics;Be s;Bern rnou oulllli’i’s Equ quat atiion Viscosity Poiseuille’s Law
empe pera ratu turre an and d Ki Kine neti tic c Th Theo eory ry 12 Tem 12–1 12–2 12–3 *12–4 *12–5 12–6
Temperature Measurement Ideal Gas Law Kine neti ticTh cTheo eory;Mo ry;Mode dell of an Id Idea eall Gas Derivation of the Ideal Gas Law De Vapor Pressure and Humidity Ther mal Expansion
13 Heat 13–1 13–2 13–3 13–4 13–5
237 237 242 244
257 257 259 265 270 273 279 282
295 29 5 295 298 303 306 309 311
320 Definition of Heat Calor imetr y Radiation Convection Conduction
320 321 326 329 330
14 Thermodynamics
338
14–1 14–2 14–3 14–4 *14–5
Ther modynamic Systems Fir st Law of Th Ther modynamics Heat Engines and Refriger ator s Second Law of Th Ther modynamics Human Metabolism
15 Harmonic Motion 15–1 15–2 15–3 15–4 15–5
339 341 346 349 355
366
Simple Har monic Motion 366 Relations Rela tionship hip between between SHM and and Circular Circular M Motion otion 369 Mass and Spr ing 371 The Pendulum 374 Damped and Forced Oscillations 378
Waves; So S ound 16 Mechanical Wa 16–1 Description of Wa Waves 16–2 Wave Speed 16–3 Movi Moving ng Sources Sources and and Observers:The Doppler Effect 16–4 Po Power an and d In Inte ten nsit ity;th y;the e Dec eciibe bell Sc Scal ale e 16–5 Time Depende Dependence nce of the Displace Displacement ment of a Par ticle of the Medium 16–6 16 –6 Sup Superpo erposit sition ion of Wa Wave ves; s; Bea Beats; ts; Sta Standi nding ng Wa Wave vess A Closer Look: The Ear
386 387 392 395 399 404 405 418
17 The Electric Field 17–1 17–2 17–3 17–4
Electr ic Char ge Coulomb’s Law The Electr ic Field Fields Produced by by Continuous Continuous Distributions of Char ge 17–5 Field Lines
18 Electric Potential 18–1 18–2 18–3 *18–4
Electrical Pot Electrical Potentia entiall Energy Energy and and Electri Electricc Potent Potential ial Capacitance Dielectr ics The Oscilloscope
19 Electric Current 19–1 Electr ic Cur rent 19–2 Ohm’s Law 19–3 19 –3 El Elec ectri tricc Pow ower; er; Ba Batt tteri eries es an and d AC So Sour urce cess A Closer Look: Superconductivity *19–4 *19– 4 Elec Electric tric Current Current and Ohm’s Law on the Microscopic Level
20 Direct Current Circuits 20–1 20–2 20–3 *20–4 20–5
Descr iption of Circuits Kirchhoff ’s Rules Equivalent Resistance Multiloop Circuits Measureme Meas urement nt of Current, Po Potenti tential al Differenc Difference, e, and Resistance 20–6 RC Circuits A Closer Look: Elec Electrical trical Effects Effects in the Human Body 20–7 Elect 20–7 Electric ric Sh Shoc ockk an and d Ho Hous useh ehol old d El Elec ectri trici city ty
21 Magnetism 21–1 The Magnetic Field 21–2 Magn Magnetic etic Forces Forces on CurrentCurrent-Carrying Carrying Conductor s 21–3 21– 3 Mot Motion ion of a Po Point int Cha Charge rge in a Mag Magnet netic ic Fie Field ld 21–4 Magn Magnetic etic Field Fieldss Produ Produced ced by Elect Electric ric Curren Currents ts 21–5 Magnetic Fields Produced Produced by by Permanent Permanent Magnets *21–6 Magnetic Mater ials A Closer Look: Bi B iomagnetism
427 427 431 434 440 444
457 458 468 476 479
493 493 495 500 50 0 501 509
518 519 520 523 526 528 529 532 534 53 4
550 550 554 560 56 0 563 569 572 574
22 Electromagnetic Induction and AC Circuits 22–1 Far aday’s Law 22–2 Inductance *22–3 Alter nating Cur rent Circuits In Per sp spective: M ic ichael Far aday
588 589 597 603 616
CONTENTS
23 Light 23–1 23–2 23–3 23–4
Electromagnetic Wa Waves The Nature of Light The Propagation of Light Reflection and Refr action
24 Geometrical Optics 24–1 Plane Mir ror s 24–2 Spher ical Mir ror s 24–3 Lenses
The e Ey Eye e an and d Op Opti tica call Ins Instr trum umen ents ts* * 25 Th
628 629 632 638 644
662 663 665 676
698 69 8
25–1 25–2 25–3 25–4
The Human Eye 699 The Magnifier 710 The Microscope 713 The Telescope 716 In Perspective Perspective:: Structur Structure e of the Retina and Color Sensitivity 719 *25–5 Factor s Limiting Vi Visual Acuity 722
26 Wave Optics 26–1 26–2 26–3 26–4
Wave Proper ties of Light Interference Diffraction Polarization A Closer Look: M ag agic in the Sky
27 Relativity 27–1 27–1 27–2 27–3 27–4 27–5
Measur Meas urem emen entt ofTim ofTime; e; Ei Eins nste tein in’’s Pos ostu tula late tess Time Dilation Length Contr action Relative Velocity Relativistic Mass and Ener gy A Closer Look: Gener al al Relativity A Closer Look: Al Alber t Einstein
28 Quantum Concepts 28–1 Photons 28–2 Wave-Par ticle Duality 28–3 The Uncer ta tainty Pr inciple In Per sp spective: R ic ichard Feynman In Per sp spective: S te tephen Hawking
29 The Atom 29–1 29– 1 Atomic Atomic Spectra and and the Bohr Model Model of the Atom 29–2 29– 2 Wa Wave ve Properties Properties of Electron Electrons; s; Quan Quantum tum Mechanics 29–3 29– 3 Quan QuantumTheory tumTheory of Atomic Atomic Structure Structure and Spectra; X Rays A Closer Look: Laser s A Closer Look: S em emiconductor s
731 732 736 741 748 754
765 766 766 770 776 779 781 784 788
798 799 804 807 810 813
818 819 830 835 841 845
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30 Nuclear Physics and Elementary Particles 30–1 30–2 30–3 30–4 30–5
854
Nuclear Str ucture Radioactive Decay Nucl Nu clea earr Re Reaact ctiion onss; Fi Fiss ssio ion n and Fu Fusi sion on Biological Effects of Radiation Elementar y Par ticles In Per spective: Ma Mar ie Cur ie
854 861 871 877 880 886
Appendix Appe ndix A Re Revie view w of Mat Mathem hemati atics cs
895
A–1 A–2 A–3 A–4 A–5 A–6
Basic Oper ations Pow Po wer erss ofT ofTe en an and d Sc Scie ient ntiific Not otat atiion Logar ithms Algebr a Geometr y Tr igonometr y
895 896 898 899 903 905
Appendix B Gauss’s Law
906
B–1 Electr ic Flux B–2 Gauss’s Law and Ap Applications B–3 Der ivation of Gauss’s Law
906 907 911
Appendix C Models of Appendix of Electrical Electrical Conduction in Metals
913
Appe pend ndiix D Selected Isotopes
916
Appendix E Answ Appendix Answers ers to OddOddNumbered Problems
920
Index
931
P
reface
Why Study Physics? magine you have lived your entire life without being able to see the world in color. Imagine you can only see in black and white. Then imagine that someone gives you a way to see color for the first time. Before you experience color vision, however, you could not know what you were missing. missing. You would have only the word of others to imagine how wonderful it could be. Seeing the world without any understanding of physics is like seeing the world without color. It is being blind to much of the beauty, richness, and depth of the physical universe. A good course in physics provides the means to open this universe to you, to see the world with the insight that physics provides. More specifically, knowledge of physics allows you: To begin to appreciate the diverse phenomena of the world in a new, more unified way, to see a world governed by physical principles, and to understand how these principles serve as a foundation for understanding other sciences such as biology and chemistry. To be able to apply the principles of physics to the solution of problems and to understand understa nd how physica physicall principles have been used to solve enormous technical technical problems, opening up new vistas of experience of the physical universe undreamed of 50 or 10 100 0 years ago—space exploration, lasers, electron microscopes, computer memory chips, magnetic resonance imaging, and so on. To wonder about the mysteries of the physical universe that remain and the vistas that will unfold within your lifetime. You are very likely taking physics because it is a required course, and you may rightly regard it as a challenge, a means for realizing your professional goals. But if you can be open to some of the broader educational objectives, you may find your physics course to be a lasting, enriching experience, and you may even find that such an attitude enhances your chance for success.
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Goals of the Text Designed for a 1-year course in college physics or advanced high school physics, using algebra and trigonometry, this text is the product of more than 20 years of experience experie nce teaching college physics. For more than 10 years I have worked to devel develop op the best possible physics textbook. The following are some general goals that have guided my work: 1 Use the most direct, concise language possible to convey ideas. 2 Use illustrations and photographs as effectively as possible to aid understanding. 3 Improve the explanation of difficult concepts. 4 Introduce abstract physical concepts wherever possible by appealing to common experiences that illustrate the concepts. 5 Present applications of physical principles—to biology, modern technology, sports and other everyday activities—in a way that clearly distinguishes applications from physical principles. 6 Present derivations derivations in a way most likely to help, not hinder, understanding. Adapt both the style of deriv derivations ations and placement of deriv derivations ations to individual topics in
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such a way that the relationship of physical concepts is demonstrated in the clearest possible way. 7 Formulate new and interesting examples and problems, many drawn from reallife experiences, to make the course more interesting for both students and instructors.
Features Organization The overall organization organization of this text is very traditional. traditional. The followi following ng departures from tradition are intended to improve unity and coherence: a separate chapter on universal gravitation placed just after chapters 4 and 5 on Newton’s laws and applications; a single chapter treating all mechanical waves, including sound, in an integrated way; an introduction to wave optics that begins with a qualitative overview of the wave properties of light, showing how diffraction and interference are related before each is discussed separately and quantitatively. quantitatively. To allow the reader to quickly locate specific topics, I have made frequent use of subsection headings within sections of a chapter.
Explanations The text offers particularly good explanations of many difficult concepts, including instantaneouss speed, relati instantaneou relative ve motion, universal gravitation, gravitation, energy, Archimedes’ Archimedes’prinprinciple, surface tension and capillarity, entropy, the eye and visual acuity, measurement of time in relativity, and wave-particle duality. A completely original feature is an elementary, quantitative discussion of optical coherence. The treatment of electricity and magnetism is unusually thorough and effective.
Applications Numerous applications of physics to biology, technology, sports, and everyday life help motivate motiv ate student interest. Every effor effortt is made to distingu distinguish ish applications from fundamental physical principles. For example, many applications are presented in examples and problems. Each half of the book contains one extended biophysical biophysical application: application: in Chapter Chapter1 11 the physics of fluids is applied to the human circulatory system, and in Chapter 25 optics is applied to the human eye. These unusually detailed detailed biophysical applications applications are chosen for the richness of the results that follow from simple physical principles.
Illustrations and Photographs Great care and meticulous attention to detail has been given to the development of fullcolor art that would realize the enormous potential of pictures to teach physics. The text contains approximately 1100 drawings and over 400 photographs, nearly all of which were planned as the manuscript was written, so that words and pictures work together to convey ideas. Illustrations accompanying end-of-chapter problems are particularly plentiful in mechanics, where they serve to ease the student toward increasingly abstract thinking. Three-dimensional perspective drawings are used extensively, especially in the chapter on magnetism. In the chapters on optics, unusually careful ray diagrams are provided, for example, to show chromatic aberration and image formation by a microscope. Illustrations often accompany examples. These illustrations are placed within the body of an example for easy reference. Often an example contains two illustrations, one relating to the formulation of the question, and a second relating to the solution (a free body diagram, for example).
Preface
Examples Over 300 worked examples guide the student first to the solution of elementary problems and then to the solution of conceptually and/or mathematically more complex problems. A general problem-solving strategy strategy is outlined in a special section preceding the problem set in Chapter 1. This strategy is then reinforced in the solution of examples throughout the book. Particular attention is given to solution of “word problems” in kinematics. In Chapter 2 I introduce the technique of translating questions formulated in words to questions expressed in symbols. For example, the question “If a speed of 70 m/s is needed for a plane to leave the ground, how long a runway is required?” becomes “Find x when v = 70 m/s. m /s.” This kind of translation from words to symbols is surprisingly effective in helping students overcome their difficulty with word problems.
Questions and Problems The focus of student effort effort in a physics course is on problem solving. Therefore Therefore I have tried to make the over 2000 end-of-chapter questions and problems a strong feature in this text. They serve to build understanding of physical principles and to stimulate student interest in applications of physics to a wide variety of subjects, including biology and sports. Many reviewers have praised the originality and effectiveness of the problems. The questions encourage students to build their qualitative, qualitative, conceptual understanding of physics. Answers to odd-numbered questions are provided at the end of the questions section in each chapter. Problems are rated in difficulty by the number of stars appearing next to them: those with no stars are easiest, one-star problems are more difficult, and two-star problems are most difficult. Answers to odd-numbered problems problems are provided at the end of the book.
Historical Insights Historical background is provided in introducing certain topics, for example, universal gravitation, electromagnetic waves, and atomic theory. These are areas in which history provides insight into the meaning of physical concepts by showing how these concepts evolved. evolved. A secondary goal is to provide insight into the process of discovery discovery in physics, revealing it as a human activity. In Perspective essays give additional historical material.
Essays Two kinds of essays are provided: 9 In Perspective historical essays and1 and 12 Closer Look essays that involve physical concepts or applications. Both kinds of essays are intended to stimulate students to think about ideas beyond what is required for the course. The In Perspective essays are mainly short biographies of physicists who have made some of the most important discoveries in physics: Galileo, Newton, Faraday, Einstein, Feynman, Hawking, and Curie. These are more than just a few paragraphs; they offer enough depth to humanize their subjects and sometimes to help understand what motivated motiva ted their discoveries. The Closer Look essays are discussions of physical principles and applications that encourage the student to think about subjects likely to arouse interest. For example, “Magic in the Sky” describes rare atmospheric optical effects such as the glory and Fata morgana. “Energy to Run” explains, in terms of energy principles, why it is so much easier to ride a bicycle than it is to run at the same speed. “Electrical Effects in the Human Body” provides the biophysical basis for understanding why an electric shock that produces only a small electric current inside the body can nevertheless be lethal. “Biomagnetism” describes how magnetotectic bacteria have evolved in such a
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way as to take advantage of the earth’s magnetic field. “Structure of the Retina and Color Sensitivity” describes the biophysics of the human eye. “General Relativity” shows how simple questions about relative motion led to a profound theory with amazing astronomical implications.
Acknowledgements The publication of an introductory physics textbook is a major undertaking, involving involving the efforts of many people, all of whom deserve thanks for their work. First, I wish to thank the thousands of students who over the years have used this text in manuscript form and helped it take its final form. Their patience with a manuscript having cosmetically rough illustrations and few photographs will benefit others who will learn physics from the finished book. Next I wish to express my gratitude for the efforts of the many reviewers who have taken the time to look at this book as it was being developed and who strongly influenced every feature of this book. Thanks to: Stanley Bashkin, University University of Arizona Jay S. Bolemon, University of Central Florida Louis H. Cadwell, Providence College George Caviris, S.U.N.Y., Farmingdale Robert W. Coakley, University of Southern Maine Lawrence B. Coleman, University of California, Davis Lattie F. Collins, East Tennessee State University John Cooper, Auburn University University Donald A. Daavettila, Michigan Technological Technological University University Miles J. Dresser, Washington State University, Pullman Henry Fenichel, University of Cincinnati Donald R. Franceschetti, Memphis State University Philip W. Gash, California State University, Chico Bernard S. Gerstman, Florida International University Barry Gilbert, Rhode Island College Joe S. Ham, Texas Texas A & M University University Paul Happem, Philadelphia College of Pharmacy & Science Hugh Hudson, University of Huston Richard Imlay, Louisiana State University Lawrence A. Kappers, University of Connecticut, Connecticut, Storrs Paul L. Lee, California State University, Northridge Donald H. Lyons, University of Massachusetts, Boston Rizwan Mahmoo, Slippery Rock University Robert H. March, University of Wisconsin, Madison
Preface
James J. Merkel, University of Wisconsin, Eau Claire Roger L. Morehouse, California State Polytechnic University, Pomona J. Ronald Mowery, Mowery, Harrisburg Area Community College Darden Powers, Baylor University Wayne F. Reed, Tulane University Donald E. Rehfuss, San Diego State University Joseph Josep h A. Schae Schaefer fer,, Loras College College Cindy Schwarz, Vassar College Joseph Shinar, Iowa State University Donald L. Sprague, Western Washington Washington University Fred J. Thomas, Sinclair Community College Martha R. Weller, Middle Tennessee State University John G. Willis, Indiana University Richard L. Wolfson, Middlebury College Lonnie L. VanZandt, Purdue University University George O. Zimmerman, Boston University The production of this book actually began years ago when I began using parts of the manuscript in my classes. Over the years, I was assisted in preparing the manuscript by dozens of student workers. I wish to thank all of them, especially Lorena Flores and Susanne Thomasson, who, after using the manuscript as students, each assisted me for 3 years—typing, drafting art, and laying out pages. The cheerful work and encouragement of all those students meant a lot to me at a time when the book was far from completion. Professor Martha Weller Weller from Middle Ten Tennessee nessee State Univers University ity deserves special thanks for her work on the solutions manual. Faced with the enormously tedious job of not only solving every problem in the book, but also communicating that solution in a form that would be helpful to students, she surpassed all expectations and produced solutions that are carefully detailed and insightful. Her solutions teach principles of physics and will be a strong aid to all who use them. Thanks to my mentor, Professor Gerald Jones of the University of Notre Dame, who years ago convinced me of the need for a better college physics text and who was a model for me of what a physics professor should be. I wish to thank my colleagues in physics and other disciplines who have been supportive, supporti ve, in particul particular ar Professor Emeritus Hanford Weckbach, S.J., who contributed so graciously of his time and knowledge of physics demonstrations and equipment, Professor John Bulman, who read several of the essays and made helpful suggestions, and Professor Madhu Amar, who helped me with some of the photographs and even provided one mole of gold for a picture. Thanks also to my friend and former colleague, Dr. William Kaune, President of EMF Factors, who provided helpful technical information. Thanks to Erianne Aichner for the many ways she has helped me over the years. She has been much more than a secretary. She has been a true friend, gladly going beyond the call of duty to help, and most importantly offering her continued encouragement. Thanks also to Janice Meichtry for her help with the steady stream of Federal Express packages that came through her office during production.
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Thanks to my friends who have been so supportive, especially Sandy Patterson, Sarah de Haras, and Richard Harris. Thanks to my family, Mary, Paul, John, David, Annemarie, Catherine, Michelle, Tiffany, Melanie, Taylor, and Ryan, who have been both supportive and understanding of the demands of the book. Finally, thanks to my parents, who instilled in me the love of knowledge and logical thinking that made this book possible, and to whom I dedicate this book.
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Introduction
Stonehenge
W
hy can some insects walk on water? What causes the beautiful beautiful colors in a soap bubble or an oil film? Is time travel in a time machine a scientific possibility? If you
have ever wondered about such questions, you possess the most basic motivation for the study of physics: curiosity about physical phenomena.The phenomena. The origins of physics began with human curiosity in a prescientific age long ago.Two fundamental problems stimulated late d that curiosity: curiosity: the nature of motion and the composition of matter. matter.
Motion Observing the stars was important in many early societies, for both practical and mystical mystic al reasons. In Egypt astronomers astronomers were able to predict the annual flooding of the Nile, which coincided with the first appearance each spring of the star Sirius. Astrology, a system of beliefs begun by the Babylonians and later developed by the Greeks, held that our personalities are affected by the position of the planets relative to the stars at the instant we are born. Ancient astronomers observed and charted the heavens. In England an early civilization produced Stonehenge, an arrangement of huge stones, which may have been used as a primitive observatory observatory 1500 years before the birth of Christ. Observation ultimately led to the attempt to organize astronomical data. In the second century, century, the Greek philosopher Ptolemy developed a system for describing the motion of the sun, moon, and planets about a stationary earth. Although earlier Greek astronomers had suggested that the earth moves about the sun, this idea was lost in antiquity, and Ptolemy’s model was generally accepted until the middle of the sixteenth century. Then, in1543, in 1543, the Polish astronomer and mathematician Nicolaus Copernicus published De Revolutionibus, in which he challenged the Ptolemaic description of the universe and proclaimed that all the planets, including the earth, revolve about the sun.
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Introduction
In the early seventeenth century, Galileo Galilei built one of the first telescopes and used it to observe the heavens. He is probably best known for his defense of the Copernican system and his ensuing controversy with the Catholic Church. Of even greater significance for the development of physics, however, was Galileo’s study of the nature of motion. He defined mathematicall mathematically y precise concepts with which to describe motion and performed simple experiments that led him to formulate the law of inertia. Galileo was aware of the potential of the powerful new ideas he introduced. In Two New Sciences he wrote: The theorems set forth in this brief discussion, if they come into the hands of other investigators, will continually lead to wonderful new knowledge. It is conceivable that in such a manner a worthy treatment may be gradually extended to all the realms of nature.
Experimental and theoretical studies by many scientists led to a fundamental understanding of motion motion by 1687 1687,, when the book Philosophiae Naturalis Principia Mathematica was published in England. This monumental work by Isaac Newton expounded his system for explaining both celestial and terrestrial motion. Today this branch of physics, covered in the first 10 chapters of this book, is called “classical mechanics.” In his own time, the scientific effect* of Newton’s ideas was to provide a complete solution to the problem of understanding planetary motion. In historical perspective, however, Newton’s work assumes even more importance, in that it is the basis for later physical theories. For example, investigations into the nature of electric and magnetic phenomena are built upon classical mechanics.
Matter The other ancient problem of physics was the relationship between bulk matter and the microscopic microscop ic particles of which it is composed. About 400 B.C. the Greek philosopher Democritus speculated that all matter consist of indivisible particles which he called “atoms.” What we call atoms today are not indivisible. But the possibility of finding the subatomic particles that truly are the basic building blocks of matter remains an intriguing question that has been only partially answered. Physicists continue to search for the fundamental particles. They also seek a unified understanding of the multiplicity of particles that have emerged from that search. The general trend in our study of physics will be toward an increasingly microscopic view, since many of the questions that arise in a study of macroscopic phenomena have their answer on the atomic or molecular level. For example, we shall study classical mechanics—a mechanics—a macroscopic view—in Chapters Chapters 1 to 10 and then apply these concepts on the microscopic level to explain temperature and heat. Our study of electricity and magnetism (Chapters 17 through 22) will involve involve a description of the electron and proton, the basic charged particles within the atom. Chapters 29 and 30 will complete our gradual transition from a macroscopic description of matter to a particle description with a study of atoms, nuclei, and elementary particles.
*Newton’s work had great influence on other areas of thought. Newtonian mechanics revealed a “clockwork universe,” a world of intricate but orderly motion. This picture of the universe as an ordered whole influenced religious, philosophical, and political ideas.
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Introduction
Applications Although the questions we ask in physics are typically motivated by curiosity rather than by practical consideration, discoveries in physics have often had a dramatic impact on technology. This in turn has had very obvious and pervasive effects on modern society. For example, our entire electronic technology began with fundamental questions about the nature of electricity and magnetism. Early experiments used simple, largescale equipment. Today we have sophisticated electromagnetic communications systems and small, powerful computers utilizing tiny integrated circuits. These technologies are changing the way we live. The discovery of high-temperature superconductors in 1987 may lead to further change—practical electric cars, 300-mph magnetically levitated trains, smaller and more powerful computers using superconducting components,, and controlle components controlled d fusion as an abundant new source of energy. energy. An educated person in this high-tech age should have some knowledge of the principles of physics underlying the new technologies, if only to make the technologies less mysterious. A knowledge of physics is important for professional competence in many fields, since physics serves as a foundation for other sciences. For example, principles of quantum mechanics and atomic physics are used in chemistry to understand many biological processes, including nerve conduction. Thus a knowledge of physics is essentiall for chemist essentia chemistss and biologi biologists sts and also for physici physicians, ans, dentists, engineers, geologist, architects, and physical therapists. Aside from the very practical reasons for knowing some physics, there can be an esthetic value. Our appreciation of the world around us is enhanced when we view phenomena with the eyes of a physicist. Admittedly this is an acquired taste, and not everyone who takes a physics course will agree. But you may find pleasure in seeing physical principles applied to your environment—in understanding, for example, why you are pushed outward in a car as you turn a corner, or why a spinning baseball curves, or why the sky is blue. Many of the examples and problems in this text describe applications of physics to everyday life. There are also more lengthy descriptions of applications, many involving biological systems. Newton’s laws of motion, applied to the flow of fluids, are used to
Eighteenth-century equipment used to study electricity.
A modern integrated circuit containing hundreds of thousands of electrical components.
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Introduction
understand the human circulatory system. Principles of electricity are used to explain household electricity and electric shock. Optical principles are applied both to the human eye and to the microscope. Quantum physics is used to understand lasers. Nuclear physics is applied to carbon dating of ancient archeological specimens. Essays on various applications of physics appear throughout the text under the heading “A Closer Look.” The topics of essays are not commonly part of an introductory course and are included only to stimulate your interest. The text also contains “In Perspective” Perspecti ve” essays that give brief biographical biographical sketches of physicist physicistss who have made some of the most important discoveries in physics.
Mathematics Mathematics has an important role in the study of physics because the laws of physics are written in the language of mathematics; that is, they are expressions of precise relationships, set in a conceptual framework. As Galileo said nearly 400 years ago, Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and reads the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures… Without these one wanders wanders about in a dark labyrinth.
Thus there are certain mathematical prerequisites for a study of physics, mainly highschool algebra and trigonometry. This text does not require a knowledge of calculus. Appendix A gives a brief review review of the math you will need in your study of physics.
Derivations Some physical laws are more fundamental than others. Derivations in the text show how the more fundamental laws lead to secondary ones, which are then applicable to particular kinds of problems. Although students students often find deriv derivations ations unappealing, unappealing, they are an important part of physics. A physics book is not an encyclopedia. It certainly does not deal with all the detailed manifestations of physical law that occur in nature. Instead it provides a coherent description of fundamental physical laws and demonstrates the unity of physics—the relationship of physical laws—through derivations. There is another, very practical reason for supplying derivations in a text, rather than simply describing results. If you thoroughly understand a derivation, you will also understand when the derived equation may be used. Obviously the intelligent use of equations requires that you know where they are applicable. Thus you should at least be aware of the assumptions made in the text when equations are derived.
Study Objectives You should have two objectives in studying physics: (1) to obtain a unified understanding of the fundamental principles of physics , their areas of applicability, and their interrelationships, and (2) to develop the ability to solve practical problems using these principles. The two goals are complementary, and it is impossible to achieve one without the other.
Introduction
When the answer to a problem is provided, it is sometimes possible to “solve” the problem by a trial-and-error process of formula juggling devoid of any real understanding. If you have no idea of why the principle used should apply, obtaining a correct numerical answer will not be of much value. Therefore the time you spend working on specific problems should be preceded by a careful reading of the text and lecture notes, so that you thoroughly understand the concepts. A first course in physics is usually a great challenge and is often undertaken with considerable fear and anxiety. You may find it difficult to understand some of the concepts and impossible to solve certain problems. This is to be expected. It is definitely possible to learn from your mistakes in physics, and so it is important not to become discouraged. Like learning a new athletic skill or learning to play a musical instrument, learning physics requires practice. If you continue to work hard, your understanding will grow. You will find that you are able to understand many phenomena with a relatively small number of concepts. It can be very satisfying to see that the workings of both nature and technology can be explained in terms of just a few basic laws. It can also be satisfying to use physical laws to predict the outcome of a laboratory experiment and then verify your prediction by making measurements. In this book I attempt to explain in the clearest possible way some of the mysteries of the physical universe. It is my hope that you will learn from it, and at the end of your physics course you will be able to look back on it as a positive experience.
5
Return to Table of Contents
Measurement and Units
A microscopic motor, motor, viewed through an electron microscope. microscope. At the center is the rotor,, the part of the motor that turns. rotor The rotor diameter is 100 microns, microns, or 0.1 millimeters, millimeters, about the thickness of a human hair.
Use of Units
S
uppose you are driving with a friend and your gas tank is nearly empty.When you ask your friend how far far it is to the nearest gas station, she responds,“About responds,“About 3,” with
no indication of whether she means 3 blocks or 3 miles or perhaps some other measure of distance. Such a response is not helpful.Your friend gives you no information at all unless she gives the numerical value of the distance and the unit of length in terms of which that distance distance is measured—blocks, measured—blocks, miles, whate whatever ver.. As this example illustrates, illustrates, it is important to express the numerical value of a quantity in terms of some unit. Distance or length may be expressed expressed in units such as met meters, ers, fee feet, t, mile miles, s, or kilometers.Tim kilometers.Time e may be expressed expressed in units units of seconds, seconds, hours, days, or years. Speed may may be expressed expressed in units of miles per hour, hour, kilome kilometers ters per hour, hour, meters per second, second, and so on. Alwa Always ys remember remember to include the unit in expressing the numerical value of any physical quantity.. Without the unit the number tity number is meaningless.
Fundamental Quantities All physical quantities can be defined in terms of a very small number of fundamental physical quantities. All the quantities studied in the first three chapters of this book can be defined in terms of just two fundamental quantities: length and time. For example, the speed of an object is defined as the distance traveled by the object divided by the elapsed time. In Chapter 4 we shall need to introduce a third fundamental quantity quantity,, mass, which is measured in units such as kilograms or grams.
6
Measurement and Units
We define the fundamental quantities by defining how we measure them. For instance, the length of an object is defined by comparing the object with multiples of some standard length, say, a meter. When we say that a basketball player is 2 meters tall, we mean that 2 vertical meter sticks, one on top of the other, will just reach from the floor to the top of the player’s head. The time of any event is defined by measurement of the event’s event’s time on a clock, using standard units of time—ho time—hours, urs, minutes, and seconds. We shall return to certain subtle questions concerning measurement of time in Chapter 27 when we study Einstein’s theory of relativity.
Base and Derived Units The units used to express fundamental quantities are called base units, and the units used to express all other quantities are called derived units. Thus meters, feet, seconds, and hours are all base units, since they are used to measure the two fundamental quantities length and time. The units miles per hour and meters per second are examples of derived units. Base units are further characterized as being either primary or secondary. For each fundamental quantity, one base unit is designated the primary unit and all other units for that quantity are secondary. For measuring time, the second is the primary base unit, and minutes, hours, days, and so on are all secondary base units.
SI System of Units For consistency and reproducibility of experimental results, it is important that all scientists use a standard system of units. The Système International (SI) is the system now used in most scientific work throughout the world. This system uses primary base units of meters, kilograms, and seconds for measurements of length, mass, and time respectively. In this book we shall use SI units primarily. Occasionally, however, in the early chapters, we shall also use the British system, in which length is measured in feet and force in pounds, since some of these units will be more familiar to you than the corresponding SI units.
Definition of the Second The primary SI unit of time is the second (abbre (abbreviated viated s). Before 1960 the second was defined as a certain fraction of a day; that is, the second was defined as a fraction of the time required for one rotation of the earth. According to this definition, there are 86,400 seconds in a day day..* A difficulty with this standard is that the earth’ earth’ss rate of rotation is not constant, and so a day is not a constant, reproducible standard of time. The earth’ss rotational rate experiences small random fluctuations from day to day. In addiearth’ tion there are seasonal variations and a gradual slowing down over the years. To take these facts into account, the second was defined, before 1960, as 1/86,400 of an average day during the year 1900.
*1 day 24 hours,1 hour
60 minutes, and1 minute
60 s. So1 day
(24) (60) (60) s
86,400 s.
7
8
Measurement and Units
Like the other devices shown here, an atomic clock (bottom) is used to measure time.
We now use a more precise and reproducible standard to define the second—a standard consistent with the earlier definition. The second is now defined in terms of the radiation emitted by cesium atoms. Radiation is a periodic wave phenomenon. The time per cycle, called the period, is characteristic of the radiation’s source. The second is defined to be 9,192,631,770 periods of radiation emitted by cesium atoms under certain conditions. The device used to measure time with cesium radiation is a large and elaborate device called an atomic clock. Atomic clocks are extremely accurate. Two Two of them will agree with one another to within 1 part in 10 101 13. An atomic clock is maintain maintained ed by the National Institute of Standards and Technology Technology.. Secondary units of time, such as minutes (min) and hours (h), are defined in terms of the second (1 min 60 s,1 h 60 min 3600 s).
Definition of the Meter The primary SI unit of length is the meter (abbreviated m). Originally the meter was defined as one ten-millionth (10 –7) of the distance from the earth’s equator to the North Pole. Later the meter was redefined to be the distance between two lines engraved on a certain bar made of a platinum-iridium alloy and carefully preserved in a French laboratory. The distance between the engraved lines was consistent with the older, less precise definition. Copies of the standard meter bar were distributed throughout the world.
9
Measurement and Units
In 1960 the meter was redefined as a certain multiple of the wavelength of the orange light emitted by krypton atoms under certain conditions. This newer atomic definition was again made consistent with the older definitions. The most recent definition definition of the mete meterr was made in 1983. By that time measuremeasurements of the speed of light had become so precise that their accuracy was limited by the precision of the krypton standard meter. The speed of light in a vacuum is a fundamental constant of nature. And since time could be measured on an atomic clock with much greater precision than distance could be measured, it made sense to turn the definition of the unit of length around, defining it in terms of speed and time. As of 1983 the meter is defined to be the distance traveled by light in a vacuum during a time interval of 1/299,792,458 second. So now, by definition, the speed of light is 299,792,458 m/s.
Names of Units Some derived derived units in the SI system are given no special name. An example is the unit of speed, m/s. Other derived units are given given special names. An example is the SI unit of force, the newton (abbreviated N), defined as 1 kg-m/s 2. The names of some SI derived units and their definitions are given on the inside front cover of this book.
Powers Pow ers of Ten Units that are powers-of-ten multiples of other units are often convenient to use, and so we use certain prefixes to denote those multiples. For example, centi- means a factor of10 –2, milli- means a factor of10 –3, and kilo- means a factor of 10 +3. Thus 1 centimeter centimeter (cm) 10 –2 m, 1 millimeter (mm) (mm) 10 –3 m, and 1 kilometer (km) 10+3 m. The most commonly used powers-of-ten prefixes are listed on the inside front cover of this book.
Conversion of Units It is often necessary to convert units from one system to another. For example, you may need to convert a distance given in miles to units of meters. To do this, you can use the conversio conv ersion n factor 1 mile = 1609 meters. A table of useful conversi conversion on factors is given on the inside front cover of this book.
EXAMPLE 1
Astronomical Distance
The star Sirius is about 8 light-years from earth. A light-year (abbreviated LY) is a unit of distance—the distance light travels in 1 year. One LY equals approximately 10 16 m. Express the distance to Sirius in meters. SOLUTION
Sinc Si ncee th thee ra rati tio o
1016 m
equa eq uals1, ls1, we ca can n mu mult ltip iply ly 1 LY
the equation expressing distance in light-years by this factor without changing the equation. We then cancel units of lightyears and find the distance in meters. 10 m 1 LY 16
distance
8 LY
8 1016 m
10
Measurement and Units
EXAMPLE 2
Speed in SI Units
Express a speed of 60 miles per hour (mi/h) in meters per second. speed SOLUTION We use the conversion factors 1 mi 1609 m and1 h 3600 s, expressed as ratios, in such a way that when we multiply by these ratios we can cancel out miles and hours, leaving units of meters per second.
60
mi
h m
1609 m
1h
1 mi
3600 s
27 s
Consistency Consist ency of Units In solving problems, we shall often use equations expressing relationships between various physical quantities. quantities. Algebraic symbols such as x and t are used to represent the physical quantities. Whenever we solve for the value of one quantity by substituting numerical values for other quantities in an equation, it is important to include the units along with the numerical values. The units are carried along in the calculation and treated as algebraic quantities. We then obtain from the calculation both the numerical answer and the correct units. Using units in this way will alert you when you make certain common errors. For example, consider the following equation from Chapter 2: x
1 2
at 2
where x represents distance, a represents acceleration, and t represents time. Suppose we wish to calculate x at time t 5 s, given an acceleration a 4 m/s2. We substitute these values into the equation and find:
1 m x 4 2 (5 s)2 2 s
1 m (4)(5)2 2 2 s
50 m
(s2)
We obtain our answer in meters, a correct unit for distance. Suppose we had mistakenly written the equation as x 12 at , forgetting the exponent 2 on the t. When we substitute values into this incorrect equation, we obtain units for x of
m s
2
m (s) s
which are clearly incorrect units for a distance. These incorrect units reveal that we have made some kind of mistake—either we have used an incorrect equation or we have substituted a quantity with incorrect units into a correct equation. Of course, getting the units to come out correctly is no guarantee that you have not made some other kind of error. But at least it allows you to eliminate some kinds of errors.
Measurement and Units
Significant Figures When you measure any physical quantity, there is always some uncertainty in the measured value. For example, if you measure the dimensions of a desk with a meter stick marked with smallest divisions of millimeters, your measurements measurements may be accurate to the nearest millimeter but not to the nearest tenth of a millimeter. When you state the dimensions, you could explicitly indicate the uncertainty in your measurements. For example, you might measure the length of a desk to the nearest millimeter (or tenth of a centimeter) and express the desk’s length as 98.6 0.1 cm. This means that you believe the length to be between 98.5 cm and 98.7 cm. In this text, we shall not explicitly indicate the uncertainty in a measured value. We shall, however, imply this uncertainty by the way we express a value. Saying that the length of the desk is 98.6 cm means that we have some confidence in the three measured digits, in other words, confidence that the true length differs from this number by no more than 0.1 cm. We say that there are three significant figures in this measurement. If you say that the length is 98.60 cm, giving four significant figures, you are implying implyin g that your measurement measurement is accurat accuratee to four significant figures, in other words, that the uncertainty is no more than 0.01 cm. Since your measurement does not have this degree of precision, it would be misleading to state the result in this way. The measured length is 98.6 cm, not 98.60 cm. Sometimes the number of significant figures is unclear. For example, if we say a certain distance is 400 m, are the two zeroes significant figures or are they included just to indicate the location of the decimal point? Do we mean that the uncertainty in distance is 1 meter? Using powers-of-ten notation avoids such ambiguity. For example, if we say the distance is 4.00 102 m, we give three significant figures, meaning that the uncertainty in distance is 0.01 102 m, or1 m. But if we say the distance is 4.0 102 m, we give two significant figures, meaning that the uncertainty is 0.1 102 m, or 10 m. Often it is tempting to state a result you have calculated with too many significant figures, simply because this is the way the numerical value appears on your calculator. For example, suppose you wish to calculate the area of a desk top. You measure a length of 98.6 cm and a width of 55.2 cm. You compute the rectangular area by multiplying these two numbers. Your calculator reads 5442.72. But each of your measurements is accurate to only three significant figures, and so the product is also accurate to only three significant figures. Thus you should round off the calculator reading and state the area as 5440 cm 2 or, better yet, 5.44 103 cm2. Now suppose you had measured the width of the desk with less precision than the length—measuring only to the nearest centimeter, so that the result is 55 cm. The length is known to three significant figures, but the width is known to only two significant figures. The less precise measurement is the limiting factor in the precision with which you can calculate the area. When two or more numbers are multiplied or divided, the final answer should be given to a number of significant figures equal to the smallest number of significant figures in any of the numbers used in the calculation. So, when you multiply a length of 98.6 cm times a width of 55 cm, do not state the area as 5423 cm 2, as indicated on your calculator. Rather, round off to two significant figures and state the area as 5400 cm 2 or as 5.4 103 cm2. When numbers are added or subtracted, the uncertainty in the calculated value is limited by the number having the greatest uncertainty. Thus, when you add or subtract, the number of decimal places retained in the answer should equal the smallest number of decimal places in any of the quantities you add or subtract. For example, the sum12.25 m 0.6 m 44 m should not be written as 56.85 m but rather should be rounded off to 57 m.
11
12
Measurement and Units
Often numbers that appear in equations do not represent measured values and so are not subject to the rules for significant figures. For example, the numerical factor 1 1 2 appears in the equation x at . This number is exact. There is no uncertainty in its 2 2 value, and it places no limitation on the number of significant figures to which x can be calculated. If, for example, values for a and t are known to 3 significant figures, x may be calculated to 3 significant figures.
Order-of-Magnitude Order -of-Magnitude Estimates It is often useful to estimate a number to the nearest power of ten. Such an estimate is called an order-of-m order-of-magnitude agnitude estimate . Estimating is appropriate either when the available data do not permit any greater accuracy or when you don’t need to know the number with any greater accuracy. Estimates can also be useful in checking the results of a more careful calculation, simply because it is so easy to calculate when you are working only with powers of ten. For example, suppose we want to estimate the number of high schools in the United States. We could begin by estimating the country’s country’s high school age population. population. Since high school takes 4 years and an average lifetime is roughly 80 years, we might estimate that one person in 20 of the 200 million or so people in the country is of high school age. This gives a high-school-aged high-school-aged population of about 10 million, or 10 7. Of course this estimate is not very accurate, since not all age groups are equally represented in the population, and certainly not everyone of high school age is in high school. But 107 high school students is a reasonable order-of-magnitude estimate. Next we estimate that the average high school has an enrollment on the order of 10 3. This means that the number of high schools in the United States is on the order of 107 /103 10 4.
Problems Standards Stan dards of Length and Time
Unit Conversi Conversion on
1 Two atomic clocks keep almost exactly the same time,
4 How many picosecond picosecondss are in 1 h?
but one runs faster than the other by1 part in 10 . How long would you have to wait before the clocks’ readings differed differed by 1 s? 1799 9 the legal standard of length in France was 2 Before 179 the foot of King Louis XIV. Since the king could not personally measure the length of everything with his foot, what was needed to make this standard unit of measure at all useful? was redefined as the distance traveled 3 In 1983 the meter was by li light ght in a va vacuu cuum m dur during ing a ti time me int interv erval al of 1/299,792,458 s, so that now the speed of light is exactly 299,792,458 m/s. Why wasn’t the number rounded off so that the speed could be exactly 300,000,000 m/s?
5 How many volts are in 30 megavolts?
13
6 How many milliamps are in 0.2 amp? 7 A picture has dimensions of 20 cm by 30 cm. Find the
area in m2. 8 A rectangular metal plate has dimensions of 8 cm by 5 cm by 3 mm. Find the plate’s volume in m 3. 9 A football field is 100 yards long. Express this length in meters. 10 A room has dimensions of 5 m by 4 m. How many square yards of carpet are required to carpet the room? 11 Express the speed of light in units of mi/s. 12 You are driving on the Autobahn in Germany at a speed of 180 km/h. Express your speed in mi/h.
Measurement and Units
Consistency of Units
Order-of-Magnitude Estimates
13 In the following equations, t is time in s,
v
is velocity in
m/s, and a is acceleration in m/s : v
at
v
26 Estimate the number of heartbeats in an average life-
a2
t
v
at
2
Which of these equations is consistent with the units? m, v is velocity in m/s, and a is acceleration in m/s2: v
2ax
a2t 2
v
x
time. 27 Estimate the total time you will spend during your
14 In the following equations, t is time in s, x is distance in
2
24 Estimate the total volume of water on earth. 25 Estimate the total volume of the earth’s atmosphere.
2
v
xa t
Which of the equations is consistent with the units? 15 If you calculate v2 / a, where v is in m/s and a is in m/s2, what units will your answer have?
Significant Figures 16 How many significant figures are in each of the follow-
ing numbers: (a) 25.673; (b) 2200; (c) 2.200 103; (d) 3005; (e) 0.0043; (f) 4.30 10–3? 17 How many significant figures are in each of the following in g nu numb mber ers: s: (a (a)) 165 65;; (b (b)) 50 500; 0; (c (c)) 5. 5.00 00 102; –3 (d) 40,001; (e) 0.0070; (f) 7.000 10 ? 18 Round off each number in Problem 16 to two signifisignificant figures. 19 Round off each of the following quantities to three significant figures: (a) 5782 m; (b) 2.4751 105 s; (c) 3.822 10–3 kg; (d) 0.06231 m. 20 A nickel has a radius of 1.05 cm and a thickness of 1.5 mm. Find its volume in m 3. 21 A rectangular plot of land has dimensions of 865 m by 2234 m. How many acres is this? (1 acre 43,560 square feet.) 22 Find the sum of the following distances: 4.65 m, 31.5 cm, 52.7 m. 23 Find the sum of the following masses: 21.6 kg, 230 kg, 55 g.
lifetime waiting for traffic lights to change from red to green. 28 Estimate the total time you will spend during your lifetime waiting in line at the grocery store. 29 Estimate the total number of pediatricians in the United States. 30 Estimate the total number of teachers of college English composition courses in the United States. 31 Estimate the surface area of a water reservoir that is 10 m deep and big enough to supply the water needs of the Los Angel Angeles es area for1 year year.. 32 (a) Estimate the maximum traffic capacity in one direction on an interstate highway in units of cars per minute. (b) Estimate how long it would take to evacuate a city of 1 million on one interstate highway. highway. 33 Estim Estimate ate the numbe numberr of M&Ms needed to fill a 1-lit -liter er 3 3 (10 (1 0 cm ) bottle. 34 Suppose you are a visitor on another planet and observe the setting sun. You notice that your little finger, which is 1 cm wide, just covers the sun when you extend your arm out and hold your finger1 m away from your eyes. The bottom edge of the sun begins to dip belo below w the horizon, and 5 minutes later the sun completely disappears. Estimate the length of a day on the planet.
13
I
n Perspective
N-Rays, N-Ra ys, Pol Polywater ywater,, and Cold Fusion
Most non-scientists believe that science
type of radiation. Blondlot named his rays
ally unmasked as ordinary water containing
advances advan ces inex inexorabl orably—fa y—facts cts lead leading ing to
“N-rays” after Nancy, the city in which he
certain impurities. This simple conclusion
theory, leading to further facts that allow
was working. He turned out paper after
took nearly 7 years to reach! That much
refinement of the theory,and so on. It may
paper on the subject and became quite
time was required before all the research-
appear that simple adherence to a cook-
famous, drawing many well-known scien-
ers who had failed to reproduce the exper-
book like “scientific method” is a surefire
tists into the ranks of his supporters and
iment were finally believed.
route to success—good scientific law, law, like a
giving birth to an entire school of N-ray
good cake, coming from careful measure-
research.
Our third example is of still more recent vintage. In April 1989, chemis chemists ts Stanley
ment and mixing of the right ingredients
Reports of failures to confirm Blondlot’s
Pons and Martin Fleischmann called a press
under just the right conditions.The history
findings began to appear, but defenders of
conference to announce the discovery of
of science, however, teaches otherwise.
Blondlot offered critiques of the challen-
an amazing new process called “cold fusion.”
Sometimes a scientist’s insight leads to a
gers’ experimental methods and powers of
Fusion is the combining of light atomic
brilliant and unexpected discovery, for
observation. Finally, in late 1904, Blondlot
nuclei to form heavier nuclei and is the
example, Einstein’s theory of relativity. relativity. And
was visited by the American Robert Wood,
process by which the sun generates energy.
sometimes what appears at first to be a
professor of physics at Johns Hopkins Uni-
The process was believed to require sun-
revolutionary discovery turns out to be a
versity. Through some clever sleight of
like conditions of extremely high tempera-
disappointing mistake.
hand,Wood fooled Blondlot into claiming
ture in order to overcome the electrical
Such mistakes are not always easy to
to observe N-rays under conditions in
repulsion between the positively charged
recognize. An erroneous claim of an im-
which, given Blondlot’s own theories, they
nuclei and get them close enough together
portant discovery can arise from a desire
could not possibly have appeared. When
so that they could fuse and release energy.
to interpret facts in a way that confirms a
Wood described his trick in a letter to
Huge research efforts around the world
scientist’s own theories. It can be difficult
Nature,
have been devoted to controlling fusion in
for one to refute such a claim by attempt-
was the beginning of the end for N-rays.
a prestigious scientific journal, it
enormously large and expensive machines,
ing to reproduce an experiment because
Our second example dates back only to
producin pro ducingg high tempe temperatur ratures es (Fig (Fig.. A).
no two experiments are ever performed
the late 1960s. In In those years, a Soviet sci-
Although Althou gh stead steadyy progr progress ess has been made,
under exactly the same conditions. The
entist studying the properties of water
these machines are not yet energy efficient;
scientist who claims to have observed a
discovered what he claimed to be a poly-
that is, they do not generate as much
new effect can always say to another scien-
merized form of water.This so-called poly-
energy as is needed to operate them.
tist who has repeated the experiment and
water, which had been produced by long
Pons and Fleischmann claimed to have
not seen the effect: “But you have not
and repeated heating of the water in an
bypassed the usual way of creating fusion at
carried out my experiment in exactly the
elaborate glassware apparatus, was ob-
high temperatures by producing cold fusion
way I did. You did not use reagents reagents from
served to be a clear, plastic-like material.
in a small beaker containing heavy (deu-
the same source; you did not observe long
The discovery sent shock waves through
terium-rich) water and a palladium coil
enough or carefully enough; your instru-
the scientific community and was given
carrying electricity electricity (Fig. B).This process, process, if it
ments were faulty….”
apocalyptic coverage in the press, which
had actually worked, would have provided
Our first example occurred occurred long ago, in
claimed with some scientific support that
virtually limitless low-cost energy and would
1903—before, you might think, we knew
the clumping of the water molecules into
have solved the world’s energy problems.
as much as we know today. today. In that year year,, the
this undrinkable form could, if not con-
Not surprisingly, surprisingly, gover government nment and indus-
French scientist Rene Blondlot, who had
tained, eventually spread to all the water in
try were anxious to invest in this work,
been working with the newly discovered
the world. The supposed polywater, after
and other scientists around the world were
X-rays,, claimed to have found another new X-rays
careful caref ul measurement measurement and analy analysis, sis, was fin-
eager to reproduce the cold fusion effect.
I
n Perspective
Fig. A Inside the Princeton fusion reactor.
Fig. B Cold fusion apparatus.
However, very few of the many labs that repeated the “cold fusion” experiment found any evidence that fusion was taking place. Pons and Fleischmann attacked their critics and maintained their claim. Lack of positive experimental results by others eventually took its toll. The general consensus today is that, whatever Pons and Fleischmann may have have observed, it was not fusion. Like the proponents of N-rays and polywater before them, Pons and Fleischmann had been too caught up in visions of a grand discovery, and had abandoned the openness required to successfully probe the secrets of nature.
Fig.C Fi g.C Enormous energy is displayed displayed in a solar flare, seen during a solar eclipse.