Paul Tipler Physics for Scientist (BookFi.org) PDF

Prefixes for Powers of 10* The Greek Alphabet Multiple Prefix Abbreviation Alpha  a Nu  n...

Prefixes for Powers of 10* The Greek Alphabet Multiple Prefix Abbreviation Alpha  a Nu  n Beta  b Xi  j 1024 yotta Y Gamma  g Omicron  o 1021 zetta Z 1018 exa E Delta  d Pi  p 1015 peta P Epsilon  e, e Rho  r 1012 tera T Zeta  z Sigma  s 109 giga G Eta  h Tau  t 106 mega M Theta u Upsilon  y 103 kilo k Iota i Phi  f 102 hecto h Kappa k Chi  x 101 deka da Lambda l Psi  c 10
1 deci d Mu m Omega  v 10
2 centi c 10
3 milli m 10
6 micro m 10
9 nano n 10
12 pico p 10
15 femto f Mathematical Symbols 10
18 atto a 10
21 zepto z  is equal to 10
24 yocto y
is defined by * Commonly used prefixes are in bold. All prefixes are pronounced with the  is not equal to accent on the first syllable.  is approximately equal to  is of the order of Terrestrial and Astronomical Data*  is proportional to  is greater than Acceleration of gravity g 9.81 m/s2  32.2 ft/s2 at Earth’s surface  is greater than or equal to Radius of Earth RE RE 6371 km  3959 mi  is much greater than Mass of Earth ME 5.97  10 kg 24 ! is less than Mass of the Sun 1.99  10 kg 30 " is less than or equal to Mass of the moon 7.35  10 kg 22 !! is much less than Escape speed 11.2 km/s  6.95 mi/s x change in x at Earth’s surface dx differential change in x Standard temperature and 0°C  273.15 K x absolute value of x pressure (STP) 1 atm  101.3 kPa  v S S magnitude of v Earth–moon distance† 3.84  108 m  2.39  105 mi Earth–Sun distance (mean)† 1.50  1011 m  9.30  107 mi n! n(n
1)(n
2)…1 Speed of sound in dry air (at STP) 331 m/s  sum Speed of sound in dry air 343 m/s lim limit (20°C, 1 atm) t → 0 t approaches zero Density of dry air (STP) 1.29 kg/m3 dx derivative of x with Density of dry air (20°C, 1 atm) 1.20 kg/m3 dt respect to t Density of water (4°C, 1 atm) 1000 kg/m3 #x partial derivative of x Heat of fusion of water (0°C, 1 atm) Lf 333.5 kJ/kg #t with respect to t Heat of vaporization of water Lv 2.257 MJ/kg x2 (100°C, 1 atm)  f(x)dx x1 definite integral x2 * Additional data on the solar system can be found in Appendix B and at  F(x) `  F(x2 )
F(x1 ) http://nssdc.gsfc.nasa.gov/planetary/planetfact.html. x1 † Center to center. Abbreviations for Units A ampere H henry nm nanometer (10
9 m) Å angstrom (10
10 m) h hour pt pint atm atmosphere Hz hertz qt quart Btu British thermal unit in inch rev revolution Bq becquerel J joule R roentgen C coulomb K kelvin Sv seivert °C degree Celsius kg kilogram s second cal calorie km kilometer T tesla Ci curie keV kilo-electron volt u unified mass unit cm centimeter lb pound V volt dyn dyne L liter W watt eV electron volt m meter Wb weber °F degree Fahrenheit MeV mega-electron volt y year fm femtometer, fermi (10
15 m) Mm megameter (106 m) yd yard ft foot mi mile mm micrometer (10
6 m) Gm gigameter (109 m) min minute ms microsecond G gauss mm millimeter mC microcoulomb Gy gray ms millisecond  ohm g gram N newton Some Conversion Factors Length Force–pressure 1 m  39.37 in  3.281 ft  1.094 yd 1 N  105 dyn  0.2248 lb 1 m  1015 fm  1010 Å  109 nm 1 lb  4.448 N 1 km  0.6214 mi 1 atm  101.3 kPa  1.013 bar  76.00 cmHg  14.70 lb/in2 1 mi  5280 ft  1.609 km Mass 1 lightyear  1 c # y  9.461  1015 m 1 u  [(10
3 mol
1)/NA] kg  1.661  10
27 kg 1 in  2.540 cm 1 tonne  103 kg  1 Mg 1 slug  14.59 kg Volume 1 kg weighs about 2.205 lb 1 L  103 cm3  10
3 m3  1.057 qt Energy–power Time 1 J  107 erg  0.7376 ft # lb  9.869  10
3 L # atm 1 h  3600 s  3.6 ks 1 kW # h  3.6 MJ 1 y  365.24 d  3.156  107 s 1 cal  4.184 J  4.129  10
2 L # atm 1 L # atm  101.325 J  24.22 cal Speed 1 eV  1.602  10
19 J 1 km/h  0.278 m/s  0.6214 mi/h 1 Btu  778 ft # lb  252 cal  1054 J 1 ft/s  0.3048 m/s  0.6818 mi/h 1 horsepower  550 ft # lb/s  746 W Angle–angular speed Thermal conductivity 1 rev  2p rad  360° 1 W/(m # K)  6.938 Btu # in/(h # ft2 # °F) 1 rad  57.30° Magnetic field 1 rev/min  0.1047 rad/s 1 T  104 G Viscosity 1 Pa # s  10 poise This page intentionally left blank SIXTH EDITION PHYSICS FOR SCIENTISTS AND ENGINEERS WITH MODERN PHYSICS Paul A. Tipler Gene Mosca W. H. Freeman and Company New York  PT: For Claudia GM: For Vivian Publisher: Susan Finnemore Brennan Executive Editor: Clancy Marshall Marketing Manager: Anthony Palmiotto Senior Developmental Editor: Kharissia Pettus Media Editor: Jeanette Picerno Editorial Assistants: Janie Chan, Kathryn Treadway Photo Editor: Ted Szczepanski Photo Researcher: Dena Digilio Betz Cover Designer: Blake Logan Text Designer: Marsha Cohen/Parallelogram Graphics Senior Project Editor: Georgia Lee Hadler Copy Editors: Connie Parks, Trumbull Rogers Illustrations: Network Graphics Illustration Coordinator: Bill Page Production Coordinator: Susan Wein Composition: Preparé Inc. Printing and Binding: RR Donnelly Library of Congress Control Number: 2007010418 ISBN-10: 0-7167-8964-7 (Extended, Chapters 1–41, R) ISBN-13: 978-0-7167-8964-2 ISBN-10: 1-4292-0132-0 (Volume 1, Chapters 1–20, R) ISBN-10: 1-4292-0133-9 (Volume 2, Chapters 21–33) ISBN-10: 1-4292-0134-7 (Volume 3, Chapters 34–41) ISBN-10: 1-4292-0124-X (Standard, Chapters 1–33, R) © 2008 by W. H. Freeman and Company All rights reserved. Printed in the United States of America Second printing W. H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com Contents in Brief 1 Measurement and Vectors / 1 PART I MECHANICS 2 Motion in One Dimension / 27 3 Motion in Two and Three Dimensions / 63 4 Newton’s Laws / 93 5 Additional Applications of Newton’s Laws / 127 6 Work and Kinetic Energy / 173 7 Conservation of Energy / 201 8 Conservation of Linear Momentum / 247 Thinkstock/Alamy 9 Rotation / 289 10 Angular Momentum / 331 R Special Relativity / R-1 11 Gravity / 363 12 Static Equilibrium and Elasticity / 397 13 Fluids / 423 PART II OSCILLATIONS AND WAVES 14 Oscillations / 457 15 Traveling Waves / 495 16 Superposition and Standing Waves / 533 PART III THERMODYNAMICS 17 Temperature and Kinetic Theory of Gases / 563 18 Heat and the First Law of Thermodynamics / 591 19 The Second Law of Thermodynamics / 629 20 Thermal Properties and Processes / 665 vii viii Contents in Brief PART IV ELECTRICITY AND MAGNETISM 21 The Electric Field I: Discrete Charge Distributions / 693 22 The Electric Field II: Continuous Charge Distributions / 727 23 Electric Potential / 763 24 Capacitance / 801 25 Electric Current and Direct-Current Circuits / 839 26 The Magnetic Field / 887 27 Sources of the Magnetic Field / 917 28 Magnetic Induction / 959 29 Alternating-Current Circuits / 995 30 Maxwell’s Equations and Electromagnetic Waves / 1029 PART V LIGHT 31 Properties of Light / 1055 32 Optical Images / 1097 33 Interference and Diffraction / 1141 PART VI MODERN PHYSICS: QUANTUM MECHANICS, RELATIVITY, AND THE STRUCTURE OF MATTER 34 Wave-Particle Duality and Quantum Physics / 1173 35 Applications of the Schrödinger Equation / 1203 36 Atoms / 1227 37 Molecules / 1261 38 Solids / 1281 39 Relativity / 1319 40 Nuclear Physics / 1357 41 Elementary Particles and the Beginning of the Universe / 1389 APPENDICES A SI Units and Conversion Factors / AP-1 B Numerical Data / AP-3 C Periodic Table of Elements / AP-6 Math Tutorial / M-1 Answers to Odd-Numbered End-of-Chapter Problems / A-1 Index / I-1 Contents Extended Preface xvii Physics Spotlight: About the Authors xxxii Linear Accelerators / 51 * optional material Summary 52 Problems 53 Chapter 1 Chapter 3 MEASUREMENT AND VECTORS / 1 MOTION IN TWO AND THREE 1-1 The Nature of Physics 2 DIMENSIONS / 63 1-2 Units 3 3-1 Displacement, Velocity, and Acceleration 64 1-3 Conversion of Units 6 3-2 Special Case 1: Projectile Motion 71 1-4 Dimensions of Physical Quantities 7 3-3 Special Case 2: Circular Motion 78 1-5 Significant Figures and Order of Magnitude 8 1-6 Vectors 14 Physics Spotlight: 1-7 General Properties of Vectors 14 GPS: Vectors Calculated While You Move / 82 Physics Spotlight: Summary 83 The 2005 Leap Second / 21 Problems 84 Summary 22 Problems 23 Chapter 4 NEWTON’S LAWS / 93 PART I MECHANICS 4-1 Newton’s First Law: The Law of Inertia 94 4-2 Force and Mass 95 4-3 Newton’s Second Law 97 Chapter 2 4-4 The Force Due to Gravity: Weight 99 MOTION IN ONE DIMENSION / 27 4-5 Contact Forces: Solids, Springs, and Strings 101 2-1 Displacement, Velocity, and Speed 28 4-6 Problem Solving: Free-Body Diagrams 104 2-2 Acceleration 35 4-7 Newton’s Third Law 109 2-3 Motion with Constant Acceleration 37 4-8 Problem Solving: Problems with Two 2-4 Integration 47 or More Objects 111 ix x Contents Physics Spotlight: Summary 194 Roller Coasters and the Need Problems 195 for Speed / 114 Chapter 7 Summary 115 Problems 116 CONSERVATION OF ENERGY / 201 7-1 Potential Energy 202 Chapter 5 7-2 The Conservation of Mechanical Energy 209 ADDITIONAL APPLICATIONS OF 7-3 The Conservation of Energy 219 NEWTON’S LAWS / 127 7-4 Mass and Energy 228 5-1 Friction 128 7-5 Quantization of Energy 231 5-2 Drag Forces 139 Physics Spotlight: 5-3 Motion Along a Curved Path 141 Blowing Warmed Air / 233 *5-4 Numerical Integration: Euler’s Method 147 5-5 The Center of Mass 149 Summary 234 Problems 236 Physics Spotlight: Accident Reconstruction— Chapter 8 Measurements and Forces / 158 CONSERVATION OF LINEAR Summary 159 MOMENTUM / 247 Problems 160 8-1 Conservation of Linear Momentum 248 8-2 Kinetic Energy of a System 254 8-3 Collisions 255 *8-4 Collisions in the Center-of-Mass Reference Frame 271 8-5 Continuously Varying Mass and Rocket Propulsion 273 Physics Spotlight: Pulse Detonation Engines: Faster (and Louder) / 277 Summary 278 Problems 279 Courtesy of Rossignol Ski Company Chapter 9 ROTATION / 289 Chapter 6 9-1 Rotational Kinematics: Angular Velocity WORK AND KINETIC ENERGY / 173 and Angular Acceleration 290 9-2 Rotational Kinetic Energy 292 6-1 Work Done by a Constant Force 174 9-3 Calculating the Moment of Inertia 294 6-2 Work Done by a Variable 9-4 Newton’s Second Law for Rotation 301 Force–Straight-Line Motion 179 9-5 Applications of Newton’s Second Law 6-3 The Scalar Product 182 for Rotation 303 6-4 Work–Kinetic-Energy Theorem—Curved 9-6 Rolling Objects 310 Paths 188 Physics Spotlight: *6-5 Center-of-Mass Work 190 Spindizzy—Ultracentrifuges / 316 Physics Spotlight: Coasters and Baggage and Work Summary 317 (Oh My!) / 193 Problems 318  Contents xi Chapter 10 12-5 Stability of Rotational Equilibrium 407 ANGULAR MOMENTUM / 331 12-6 Indeterminate Problem 408 12-7 Stress and Strain 409 10-1 The Vector Nature of Rotation 332 10-2 Torque and Angular Momentum 334 Physics Spotlight: 10-3 Conservation of Angular Momentum 341 Carbon Nanotubes: Small and Mighty / 412 *10-4 Quantization of Angular Momentum 350 Physics Spotlight: Summary 413 Problems 414 As the World Turns: Atmospheric Angular Momentum / 353 Chapter 13 Summary 354 FLUIDS / 423 Problems 355 13-1 Density 424 Chapter R 13-2 Pressure in a Fluid 425 SPECIAL RELATIVITY / R-1 13-3 Buoyancy and Archimedes’ Principle 432 13-4 Fluids in Motion 438 R-1 The Principle of Relativity and the Constancy of the Speed of Light R-2 Physics Spotlight: R-2 Moving Sticks R-4 Automotive Aerodynamics: Ride with the Wind / 448 R-3 Moving Clocks R-5 R-4 Moving Sticks Again R-8 Summary 449 R-5 Distant Clocks and Simultaneity R-9 Problems 450 R-6 Relativistic Momentum, Mass, and Energy R-12 Summary R-15 PART II OSCILLATIONS AND Problems R-16 WAVES Chapter 11 Chapter 14 GRAVITY / 363 OSCILLATIONS / 457 11-1 Kepler’s Laws 364 11-2 Newton’s Law of Gravity 367 14-1 Simple Harmonic Motion 458 11-3 Gravitational Potential Energy 374 14-2 Energy in Simple Harmonic Motion 465 11-4 The Gravitational Field 378 14-3 Some Oscillating Systems 468 *11-5 Finding the Gravitational Field of a 14-4 Damped Oscillations 477 Spherical Shell by Integration 384 14-5 Driven Oscillations and Resonance 481 Physics Spotlight: Physics Spotlight: Gravitational Lenses: Moving to the Beat: A Window on the Universe / 386 Millennium Bridge / 486 Summary 387 Summary 487 Problems 388 Problems 488 Chapter 12 Chapter 15 STATIC EQUILIBRIUM TRAVELING WAVES / 495 AND ELASTICITY / 397 15-1 Simple Wave Motion 496 12-1 Conditions for Equilibrium 398 15-2 Periodic Waves 503 12-2 The Center of Gravity 398 15-3 Waves in Three Dimensions 509 12-3 Some Examples of Static Equilibrium 399 15-4 Waves Encountering Barriers 513 12-4 Static Equilibrium in an Accelerated Frame 406 15-5 The Doppler Effect 518 xii Contents Physics Spotlight: Physics Spotlight: All Shook Up: Sediment Basins Respirometry: Breathing and Earthquake Resonance / 524 the Heat / 619 Summary 525 Summary 620 Problems 527 Problems 622 Chapter 16 Chapter 19 SUPERPOSITION AND STANDING THE SECOND LAW OF WAVES / 533 THERMODYNAMICS / 629 16-1 Superposition of Waves 534 19-1 Heat Engines and the Second Law 16-2 Standing Waves 542 of Thermodynamics 630 *16-3 Additional Topics 550 19-2 Refrigerators and the Second Law of Thermodynamics 634 Physics Spotlight: 19-3 The Carnot Engine 637 Echoes of Silence: Acoustical Architecture / 554 *19-4 Heat Pumps 643 19-5 Irreversibility, Disorder, and Entropy 645 Summary 555 19-6 Entropy and the Availability of Energy 652 Problems 556 19-7 Entropy and Probability 653 PART III THERMODYNAMICS Physics Spotlight: The Perpetual Battle over Chapter 17 Perpetual Motion / 655 TEMPERATURE AND Summary 656 KINETIC THEORY OF GASES / 563 Problems 657 17-1 Thermal Equilibrium and Temperature 564 Chapter 20 17-2 Gas Thermometers and the Absolute THERMAL PROPERTIES AND Temperature Scale 566 PROCESSES / 665 17-3 The Ideal-Gas Law 569 17-4 The Kinetic Theory of Gases 574 20-1 Thermal Expansion 666 20-2 The van der Waals Equation and Physics Spotlight: Liquid–Vapor Isotherms 670 Molecular Thermometers / 584 20-3 Phase Diagrams 673 Summary 585 20-4 The Transfer of Heat 674 Problems 586 Physics Spotlight: Chapter 18 Urban Heat Islands: Hot Nights HEAT AND THE FIRST LAW OF in the City / 686 THERMODYNAMICS / 591 Summary 687 18-1 Heat Capacity and Specific Heat 592 Problems 688 18-2 Change of Phase and Latent Heat 595 18-3 Joule’s Experiment and the First Law PART IV ELECTRICITY AND of Thermodynamics 598 MAGNETISM 18-4 The Internal Energy of an Ideal Gas 601 Chapter 21 18-5 Work and the PV Diagram for a Gas 602 18-6 Heat Capacities of Gases 606 THE ELECTRIC FIELD I: DISCRETE CHARGE DISTRIBUTIONS / 693 18-7 Heat Capacities of Solids 611 18-8 Failure of the Equipartition Theorem 611 21-1 Charge 694 18-9 The Quasi-Static Adiabatic 21-2 Conductors and Insulators 697 Compression of a Gas 615 21-3 Coulomb’s Law 699  Contents xiii 23-4 Calculation of V for Continuous Charge Distributions 773 23-5 Equipotential Surfaces 781 23-6 Electrostatic Potential Energy 787 Physics Spotlight: Lightning—Fields of Attraction / 791 Summary 792 Problems 794 Chapter 24 CAPACITANCE / 801 24-1 Capacitance 802 24-2 The Storage of Electrical Energy 806 24-3 Capacitors, Batteries, and Circuits 810 NASA/Goddard Space Flight Center Scientific Visualization Studio 24-4 Dielectrics 817 24-5 Molecular View of a Dielectric 824 21-4 The Electric Field 704 Physics Spotlight: 21-5 Electric Field Lines 711 Changes in Capacitors— 21-6 Action of the Electric Field on Charges 714 Charging Ahead / 828 Physics Spotlight: Summary 829 Powder Coating—Industrial Static / 719 Problems 831 Summary 720 Chapter 25 Problems 721 ELECTRIC CURRENT AND Chapter 22 DIRECT-CURRENT CIRCUITS / 839 THE ELECTRIC FIELD II: CONTINUOUS 25-1 Current and the Motion of Charges 840 CHARGE DISTRIBUTIONS / 727 25-2 Resistance and Ohm’s Law 844 S 22-1 Calculating E from Coulomb’s Law 728 25-3 Energy in Electric Circuits 849 22-2 Gauss’s Law 738 25-4 Combinations of Resistors 854 S 22-3 Using Symmetry to Calculate E 25-5 Kirchhoff’s Rules 860 with Gauss’s Law 742 25-6 RC Circuits 868 22-4 Discontinuity of En 749 Physics Spotlight: 22-5 Charge and Field at Conductor Surfaces 750 Vehicle Electrical Systems: *22-6 The Equivalence of Gauss’s Law and Driven to Innovation / 874 Coulomb’s Law in Electrostatics 753 Summary 875 Physics Spotlight: Problems 877 Charge Distribution—Hot and Cold / 754 Chapter 26 Summary 755 THE MAGNETIC FIELD / 887 Problems 756 26-1 The Force Exerted by a Magnetic Field 888 Chapter 23 26-2 Motion of a Point Charge in a ELECTRIC POTENTIAL / 763 Magnetic Field 892 23-1 Potential Difference 764 26-3 Torques on Current Loops and Magnets 900 23-2 Potential Due to a System of 26-4 The Hall Effect 904 Point Charges 767 Physics Spotlight: 23-3 Computing the Electric Field Earth and the Sun— from the Potential 772 Magnetic Changes / 908 xiv Contents Summary 909 Summary 986 Problems 910 Problems 988 Chapter 29 ALTERNATING-CURRENT CIRCUITS / 995 29-1 Alternating Current in a Resistor 996 29-2 Alternating-Current Circuits 999 *29-3 The Transformer 1004 *29-4 LC and RLC Circuits without a Generator 1007 *29-5 Phasors 1010 *29-6 Driven RLC Circuits 1011 Physics Spotlight: The Electric Grid: Power to the People / 1019 Atlas Photo Bank/Photo Researchers, Inc. Summary 1020 Problems 1022 Chapter 27 Chapter 30 SOURCES OF THE MAXWELL’S EQUATIONS AND MAGNETIC FIELD / 917 ELECTROMAGNETIC WAVES / 1029 27-1 The Magnetic Field of Moving Point Charges 918 30-1 Maxwell’s Displacement Current 1030 27-2 The Magnetic Field of Currents: 30-2 Maxwell’s Equations 1033 The Biot–Savart Law 919 30-3 The Wave Equation for 27-3 Gauss’s Law for Magnetism 932 Electromagnetic Waves 1034 27-4 Ampère’s Law 933 30-4 Electromagnetic Radiation 1040 27-5 Magnetism in Matter 937 Physics Spotlight: Physics Spotlight: Wireless: Sharing the Spectrum / 1049 Solenoids at Work / 947 Summary 1050 Summary 948 Problems 1051 Problems 950 Chapter 28 PART V LIGHT MAGNETIC INDUCTION / 959 28-1 Magnetic Flux 960 Chapter 31 28-2 Induced EMF and Faraday’s Law 961 PROPERTIES OF LIGHT / 1055 28-3 Lenz’s Law 965 31-1 The Speed of Light 1056 28-4 Motional EMF 969 31-2 The Propagation of Light 1059 28-5 Eddy Currents 974 31-3 Reflection and Refraction 1060 28-6 Inductance 974 31-4 Polarization 1070 28-7 Magnetic Energy 977 31-5 Derivation of the Laws of Reflection *28-8 RL Circuits 979 and Refraction 1077 *28-9 Magnetic Properties of Superconductors 983 31-6 Wave–Particle Duality 1079 Physics Spotlight: 31-7 Light Spectra 1080 The Promise of Superconductors / 985 *31-8 Sources of Light 1081  Contents xv Physics Spotlight: 34-5 Electrons and Matter Waves 1181 Optical Tweezers and Vortices: 34-6 The Interpretation of the Wave Function 1185 Light at Work / 1088 34-7 Wave–Particle Duality 1187 Summary 1089 34-8 A Particle in a Box 1189 Problems 1090 34-9 Expectation Values 1193 34-10 Energy Quantization in Other Systems 1196 Chapter 32 Summary 1198 OPTICAL IMAGES / 1097 Problems 1199 32-1 Mirrors 1097 Chapter 35 32-2 Lenses 1108 APPLICATIONS OF THE *32-3 Aberrations 1121 SCHRÖDINGER EQUATION / 1203 *32-4 Optical Instruments 1122 35-1 The Schrödinger Equation 1204 Physics Spotlight: 35-2 A Particle in a Finite Square Well 1206 Eye Surgery: 35-3 The Harmonic Oscillator 1208 New Lenses for Old / 1131 35-4 Reflection and Transmission of Summary 1132 Electron Waves: Barrier Penetration 1211 35-5 The Schrödinger Equation in Problems 1134 Three Dimensions 1217 Chapter 33 35-6 The Schrödinger Equation for INTERFERENCE AND DIFFRACTION / 1141 Two Identical Particles 1220 Summary 1223 33-1 Phase Difference and Coherence 1142 Problems 1224 33-2 Interference in Thin Films 1143 33-3 Two-Slit Interference Pattern 1145 Chapter 36 33-4 Diffraction Pattern of a Single Slit 1149 ATOMS / 1227 *33-5 Using Phasors to Add Harmonic Waves 1152 36-1 The Atom 1228 33-6 Fraunhofer and Fresnel Diffraction 1159 36-2 The Bohr Model of the Hydrogen Atom 1229 33-7 Diffraction and Resolution 1160 36-3 Quantum Theory of Atoms 1234 *33-8 Diffraction Gratings 1162 36-4 Quantum Theory of the Hydrogen Atom 1236 Physics Spotlight: 36-5 The Spin–Orbit Effect and Fine Structure 1241 Holograms:Guided Interference / 1165 36-6 The Periodic Table 1244 36-7 Optical Spectra and X-Ray Spectra 1251 Summary 1166 Summary 1255 Problems 1167 Problems 1257 Chapter 37 PART VI MODERN PHYSICS: QUANTUM MECHANICS, MOLECULES / 1261 RELATIVITY, AND THE 37-1 Bonding 1261 STRUCTURE OF MATTER *37-2 Polyatomic Molecules 1269 37-3 Energy Levels and Spectra of Diatomic Molecules 1271 Chapter 34 Summary 1278 WAVE–PARTICLE DUALITY AND Problems 1279 QUANTUM PHYSICS / 1173 34-1 Waves and Particles 1174 Chapter 38 34-2 Light: From Newton to Maxwell 1174 SOLIDS / 1281 34-3 The Particle Nature of Light: Photons 1175 38-1 The Structure of Solids 1282 34-4 Energy Quantization in Atoms 1180 38-2 A Microscopic Picture of Conduction 1286 xvi Contents 38-3 Free Electrons in a Solid 1289 Chapter 40 38-4 Quantum Theory of NUCLEAR PHYSICS / 1357 Electrical Conduction 1296 40-1 Properties of Nuclei 1357 38-5 Band Theory of Solids 1297 40-2 Radioactivity 1362 38-6 Semiconductors 1299 40-3 Nuclear Reactions 1370 *38-7 Semiconductor Junctions and Devices 1301 40-4 Fission and Fusion 1372 38-8 Superconductivity 1305 Summary 1383 38-9 The Fermi–Dirac Distribution 1309 Problems 1384 Summary 1313 Problems 1315 Chapter 41 ELEMENTARY PARTICLES AND THE Chapter 39 BEGINNING OF THE UNIVERSE / 1389 RELATIVITY / 1319 41-1 Hadrons and Leptons 1390 39-1 Newtonian Relativity 1320 41-2 Spin and Antiparticles 1393 39-2 Einstein’s Postulates 1321 41-3 The Conservation Laws 1396 39-3 The Lorentz Transformation 1322 41-4 Quarks 1400 39-4 Clock Synchronization and Simultaneity 1330 41-5 Field Particles 1403 39-5 The Velocity Transformation 1336 41-6 The Electroweak Theory 1404 39-6 Relativistic Momentum 1340 41-7 The Standard Model 1404 39-7 Relativistic Energy 1341 41-8 The Evolution of the Universe 1406 39-8 General Relativity 1348 Summary 1409 Summary 1351 Problems 1410 Problems 1352 Appendix A SI UNITS AND CONVERSION FACTORS / AP-1 Appendix B NUMERICAL DATA / AP-3 Appendix C PERIODIC TABLE OF ELEMENTS / AP-6 MATH TUTORIAL / M-1 ANSWERS TO ODD-NUMBERED END-OF-CHAPTER PROBLEMS / A-1 INDEX / I-1 NASA Preface The sixth edition of Physics for Scientists and Engineers offers a completely integrated text and media solution that will help students learn most effectively and will enable professors to customize their classrooms so that they teach most efficiently. The text includes a new strategic problem-solving approach, an integrated Math Tutorial, and new tools to improve conceptual understanding. New Physics Spotlights feature cutting-edge topics that help students relate what they are learn- ing to real-world technologies. The new online learning management system enables professors to easily cus- tomize their classes based on their students’ needs and interests by using the new interactive Physics Portal, which includes a complete e-book, student and instruc- tor resources, and a robust online homework system. Interactive Exercises in the Physics Portal give students the opportunity to learn from instant feedback, and give instructors the option to track and grade each step of the process. Because no two physics students or two physics classes are alike, tools to help make each physics experience successful are provided. KEY FEATURES ! NEW PROBLEM-SOLVING STRATEGY The sixth edition features a new problem-solving strategy in which Examples follow a consistent Picture, Solve, and Check format. This format walks students through the steps involved in analyzing the problem, solving the problem, and then checking their answers. Examples often include helpful Taking It Further sections which present alternative ways of solving problems, interesting facts, or additional information regarding the concepts presented. Where appropriate, Examples are followed by Practice Problems so students can assess their mastery of the concepts. xvii xviii Preface In this edition, the problem-solving steps are again juxtaposed with the neces- sary equations so that it’s easier for students to see a problem unfold. After each problem statement, students are asked Example 3-4 Rounding a Curve to Picture the problem. Here, the problem is N A car is traveling east at 60 km/h. It rounds a curve, and 5.0 s later it is traveling north at analyzed both conceptually and visually. 60 km/h. Find the average acceleration of the car. PICTURE We can calculate the average acceleration from its definition, a av  ¢v /¢t. To do S S In the Solve sections, each step of the solution is S S S this, we first calculate ¢v , which is the vector that when added to vi , results in vf. vf presented with a written statement in the left-hand W E SOLVE column and the corresponding mathematical ¢v S aav  S 1. The average acceleration is the change in velocity divided by the equations in the right-hand column. S elapsed time. To find aav , we first find the change in velocity: ¢t vi S S S S S 2. To find ¢v , we first specify vi and vf. Draw vi and vf (Figure 3-7a), and draw the vector addition diagram (Figure 3-7b) corresponding to vf  vi $ ¢v : S S S S vf  vi $ ¢v S S S 3. The change in velocity is related to the initial and final (a) velocities: vf
vi 60 km/h jn
60 km/h in S S aav   S 4. Substitute these results to find the average acceleration: ^ ¢t 5.0 s j 1h 1000 m ^ 5. Convert 60 km/h to meters per second: 60 km/h    16.7 m/s i 3600 s 1 km vf
vi 16.7 m/s jn
16.7 m/s in S S aav   S Check reminds students to make sure their results 6. Express the acceleration in meters per second squared: ¢t 5.0 s vf ∆v are accurate and reasonable. 
3.4 m/s2 in $ 3.4 m/s 2 jn vi CHECK The eastward component of the velocity decreases from 60 km/h to zero, so we Taking It Further suggests a different way to expect a negative acceleration component in the x direction. The northward component of (b) approach an Example or gives additional the velocity increases from zero to 60 km/h, so we expect a positive acceleration component in the y direction. Our step 6 result meets both of these expectations. FIGURE 3-7 information relevant to the Example. TAKING IT FURTHER Note that the car is accelerating even though its speed remains constant. A Practice Problem often follows the solution of an PRACTICE PROBLEM 3-1 Find the magnitude and direction of the average acceleration Example, allowing students to check their vector. understanding. Answers are included at the end of the chapter to provide immediate feedback. PROBLEM-SOLVING STRATEGY A boxed Problem-Solving Strategy is included in Relative Velocity almost every chapter to reinforce the Picture, Solve, and PICTURE The first step in solving a relative-velocity problem is to identify Check format for successfully solving problems. and label the relevant reference frames. Here, we will call them reference frame A and reference frame B. SOLVE 1. Using vpB  vpA $ vAB (Equation 3-9), relate the velocity of the moving S S S object (particle p) relative to frame A to the velocity of the particle relative to frame B. 2. Sketch a vector addition diagram for the equation vpB  vpA $ vAB. Use S S S the head-to-tail method of vector addition. Include coordinate axes on the sketch. 3. Solve for the desired quantity. Use trigonometry where appropriate. CHECK Make sure that you solve for the velocity or position of the moving object relative to the proper reference frame. ! NEW INTEGRATED MATH TUTORIAL This edition has improved mathematical support for students who are taking cal- culus concurrently with introductory physics or for students who need a math review. The comprehensive Math Tutorial reviews basic results of algebra, geometry, trigonometry, and calculus, links mathematical concepts to physics concepts in the text, provides Examples and Practice Problems so students may check their understanding of mathematical concepts.  Preface xix Example M-13 Radioactive Decay of Cobalt-60 The half-life of cobalt-60 (60Co) is 5.27 y. At t 0 you have a sample of 60Co that has a mass equal to 1.20 mg. At what time t (in years) will 0.400 mg of the sample of 60Co have decayed? PICTURE When we derived the half-life in exponential decay, we set N >N 0  1>2. In this example, we are to find the time at which two-thirds of a sample remains, and so the ratio N >N 0 will be 0.667. SOLVE N 1. Express the ratio N >N 0 as an exponential function:  0.667  e
lt N0 N0 2. Take the reciprocal of both sides:  1.50  elt N ln 1.50 0.405 3. Solve for t: t  l l ln 1.5 ln 1.5 4. The decay constant is related to the half-life by l  (ln2)>t1>2 t t   5.27 y  3.08 y ln 2 1>2 ln 2 (Equation M-70). Substitute (ln2)>t1>2 for l and evaluate the time: CHECK It takes 5.27 y for the mass of a sample of 60Co to decrease to 50 percent of its initial mass. Thus, we expect it to take less than 5.27 y for the sample to lose 33.3 percent of its mass. Our step-4 result of 3.08 y is less than 5.27 y, as expected. PRACTICE PROBLEMS 27. The discharge time constant t of a capacitor in an R C circuit is the time in which the ca- pacitor discharges to e
1 (or 0.368) times its charge at t 0. If t  1 s for a capacitor, at what time t (in seconds) will it have discharged to 50.0% of its initial charge? 28. If the coyote population in your state is increasing at a rate of 8.0% a decade and con- tinues increasing at the same rate indefinitely, in how many years will it reach 1.5 times its current level? M-12 INTEGRAL CALCULUS Integration can be considered the inverse of differentiation. If a f(t) function f(t) is integrated, a function F(t) is found for which f(t) is the derivative of F(t) with respect to t. THE INTEGRAL AS AN AREA UNDER A CURVE; fi DIMENSIONAL ANALYSIS The process of finding the area under a curve on the graph il- lustrates integration. Figure M-27 shows a function f(t). The area of the shaded element is approximately fi ¢ti, where fi is evaluated anywhere in the interval ¢ti. This approximation is highly accurate if ¢ti is very small. The total area under some stretch of the curve is found by summing all the area elements it covers and taking the limit as each ¢ti approaches zero. This limit is called the integral of f over t and is written f dt area  lim a i ¢tiS 0 i fi¢ti M-74 t1 t2 t3 ti t t1 t2 The physical dimensions of an integral of a function f(t) are found by multiplying the dimensions of the integrand (the func- F I G U R E M - 2 7 A general function f(t). The area of the shaded tion being integrated) and the dimensions of the integration element is approximately fi¢ti, where fi is evaluated anywhere in variable t. For example, if the integrand is a velocity function the interval. See Math Tutorial for more In addition, margin notes allow students to easily see the links between physics information on concepts in the text and math concepts. Differential Calculus Example 8-12 Collisions with Putty Conceptual PEDAGOGY TO ENSURE Mary has two small balls of equal mass, a ball of plumber’s putty and a one of Silly Putty. ! CONCEPTUAL NEW She throws the ball of plumber’s putty at a block suspended by strings shown in Figure 8-20. The ball strikes the block with a “thonk” and falls to the floor. The block subsequently UNDERSTANDING swings to a maximum height h. If she had thrown the ball of Silly Putty (instead of the plumber’s putty), would the block subsequently have risen to a height greater than h? Silly Putty, unlike plumber’s putty, is elastic and would bounce back from the block. Student-friendly tools have been added to allow PICTURE During impact the change in momentum of the ball – block system is zero. The for better conceptual understanding of physics. greater the magnitude of the change in momentum of the ball, the greater, the magnitude of the change in momentum of the block. Does magnitude of the change in momentum of the ball increase more if the ball bounces back than if it does not? New Conceptual Examples are SOLVE introduced, where appropriate, to help The ball of plumber’s putty loses a large fraction of The block would swing to a greater students fully understand essential its forward momentum. The ball of Silly Putty would lose all of its forward momentum and then height after being struck with the ball of Silly Putty than it did after being v physics concepts. These Examples use the gain momentum in the opposite direction. It would undergo a larger change in momentum than did the struck with the ball of plumbers putty. Picture, Solve, and Check strategy so that ball of plumber’s putty. FIGURE 8-20 students not only gain fundamental CHECK The block exerts a backward impulse on the ball of plumber’s putty to slow the ball to a stop. The same backward impulse on the ball of Silly Putty would also bring it to a stop, conceptual understanding but must and an additional backward impulse on the ball would give it momentum in the backward direction. Thus, the block exerts the larger backward impulse on the Silly-Putty ball. In ac- evaluate their answers. cord with Newton’s third law, the impulse of a ball on the block is equal and opposite to the impulse of the block on the ball. Thus, the Silly-Putty ball exerts the larger forward impulse on the block, giving the block a larger forward change in momentum. xx Preface New Concept Checks enable students to check their conceptual ✓ CONCEPT CHECK 3-1 understanding of physics concepts while they read chapters. Answers Figure 3-9 is a motion diagram of are located at the end of chapters to provide immediate feedback. Concept the bungee jumper before, during, Checks are placed near relevant topics so students can immediately and after time t6 , when she mo- mentarily come to rest at the low- reread any material that they do not fully understand. est point in her descent. During the part of her ascent shown, she New Pitfall Statements, identified by exclamation points, help students is moving upward with increas- ing speed. Use this diagram to de- avoid common misconceptions. These statements are placed near termine the direction of the the topics that commonly cause confusion, so that students can jumper’s acceleration (a) at time t6 immediately address any difficulties. and (b) at time t9. where U 0 , the arbitrary constant of integration, is the value of the potential energy at y  0. Because only a change in the potential energy is defined, the actual value of U is not important. For example, if the gravitational potential energy of the Earth – skier system is chosen to be zero when the skier is at the bottom of the hill, its value when the skier is at a height h above that level is mgh. Or we could choose the potential energy to be zero when the skier is at point P halfway down the ski slope, in which case its value at any other point would be mgy, where y is the height of the skier above point P. On the lower half of the slope, the potential energy would then be negative. ! We are free to choose U to be zero at any convenient reference point. ! Physics Spotlight NEW PHYSICS SPOTLIGHTS Blowing Warmed Air Physics Spotlights at the end of appropriate Wind farms dot the Danish coast, the plains of the upper Midwest, and hills from California to Vermont. Harnessing the kinetic energy of the wind is nothing new. chapters discuss current applications of physics Windmills have been used to pump water, ventilate mines,* and grind grain for centuries. and connect applications to concepts described Today, the most visible wind turbines run electrical generators. These turbines transform kinetic energy into electromagnetic energy. Modern turbines range in chapters. These topics range from wind farms widely in size, cost, and output. Some are very small, simple machines that cost under $500/turbine, and put out less than 100 watts of power.† Others are complex to molecular thermometers to pulse detonation behemoths that cost over $2 million and put out as much as 2.5 MW>turbine.‡ All engines. of these turbines take advantage of a widely available energy source — the wind. The theory behind the windmill’s conversion of kinetic energy to electromag- netic energy is straightforward. The moving air molecules push on the turbine blades, driving their rotational motion. The rotating blades then turn a series of gears. The gears, in turn, step up the rotation rate, and drive the rotation of a gen- erator rotor. The generator sends the electromagnetic energy out along power lines. But the conversion of the wind’s kinetic energy to electromagnetic energy is not 100 percent efficient. The most important thing to remember is that it cannot be 100 percent efficient. If turbines converted 100 percent of the kinetic energy of the air into electrical energy, the air would leave the turbines with zero kinetic energy. A wind farm converting the kinetic energy of That is, the turbines would stop the air. If the air were completely stopped by the the air to electrical energy. (Image Slate.) turbine, it would flow around the turbine, rather than through the turbine. So the theoretical efficiency of a wind turbine is a trade-off between capturing the kinetic energy of the moving air, and preventing most of the wind from flow- ing around the turbine. Propeller-style turbines are the most common, and their theoretical efficiency at transforming the kinetic energy of the air into electromag- netic energy varies from 30 percent to 59 percent.§ (The predicted efficiencies vary because of assumptions made about the way the air behaves as it flows through and around the propellers of the turbine.) So even the most efficient turbine cannot convert 100 percent of the theoretically available energy. What happens? Upstream from the turbine, the air moves along straight streamlines. After the turbine, the air rotates and is turbulent. The rotational component of the air’s movement beyond the turbine takes energy. Some dissipation of energy occurs because of the viscosity of air. When some of the air slows, there is friction between it and the faster moving air flowing by it. The turbine blades heat up, and the air itself heats up.° The gears within the turbine also convert kinetic energy into thermal energy through friction. All this thermal energy needs to be accounted for. The blades of the turbine vibrate individually — the energy associated with those vibrations cannot be used. Finally, the turbine uses some of the electricity it generates to run pumps for gear lubrication, and to run the yaw motor that moves the turbine blades into the most favorable position to catch the wind. In the end, most wind turbines operate at between 10 and 20 percent efficiency.# They are still attractive power sources, because of the free fuel. One turbine owner explains, “The bottom line is we did it for our business to help control our future.”** * Agricola, Gorgeus, De Re Metallic. (Herbert and Lou Henry Hoover, Transl.) Reprint Mineola, NY: Dover, 1950, 200–203. † Conally, Abe, and Conally, Josie, “Wind Powered Generator,” Make, Feb. 2006, Vol. 5, 90 – 101. ‡ ”Why Four Generators May Be Better than One,” Modern Power Systems, Dec. 2005, 30. § Gorban, A. N., Gorlov, A. M., and Silantyev, V. M., “Limits of the Turbine Efficiency for Free Fluid Flow.” Journal of Energy Resources Technology, Dec. 2001, Vol. 123, 311 – 317. ° Roy, S. B., S. W. Pacala, and R. L. Walko. “Can Large Wind Farms Affect Local Meteorology?” Journal of Geophysical Research (Atmospheres), Oct. 16, 2004, 109, D19101. # Gorban, A. N., Gorlov, A. M., and Silantyev, V. M., “Limits of the Turbine Efficiency for Free Fluid Flow.” Journal of Energy Resources Technology, December 2001, Vol. 123, 311 – 317. ** Wilde, Matthew, “Colwell Farmers Take Advantage of Grant to Produce Wind Energy.” Waterloo-Cedar Falls Courier, May 1, 2006, B1$.  Preface xxi ! PHYSICS PORTAL NEW www.whfreeman.com/physicsportal Physics Portal is a complete learning management system that includes a com- plete e-book, student and instructor resources, and an online homework system. Physics Portal is designed to enrich any course and enhance students’ study. All Resources in One Place Physics Portal creates a powerful learning environment. Its three central components—the Interactive e-Book, the Physics Resources library, and the Assignment Center —are conceptually tied to the text and to one another, and are easily accessed by students with a single log-in. Flexibility for Teachers and Students From its home page to its text content, Physics Portal is fully customizable. Instructors can customize the home page, set course announcements, annotate the e-book, and edit or create new exercises and tutorials. xxii Preface Interactive e-Book The complete text is integrated with the following: Conceptual animations Interactive exercises Video illustrations of key concepts Study resources include Notetaking and highlighting Student notes can be collectively viewed and printed for a personalized study guide. Bookmarking for easy navigation and quick return to important locations. Key terms with links to definitions, Wikipedia, and automated Google Search Full text search for easy location of every resource for each topic Instructors can customize their students’ texts through annotations and supple- mentary links, providing students with a guide to reading and using the text.  Preface xxiii Physics Resources For the student, the wide range of resources focuses on interactivity and concep- tual examples, engaging the student and addressing different learning styles. Flashcards Key terms from the text can be studied and used as self-quizzes. Concept Tester—Picture It Students input values for variables and see resulting graphs based on values. Concept Tester—Solve It Provides additional questions within interactive animations to help students visualize concepts. Applied Physics Videos Show physics concepts in real-life scenarios. On-line quizzing Provides immediate feedback to students and quiz results can be collected for the instructor in a gradebook. xxiv Preface Assignment Center Homework and Branched-Tutorials for Student Practice and Success The Assignment Center manages and automatically grades homework, quizzes, and guided practice. All aspects of Physics Portal can be assigned, including e-book sections, simulations, tutorials, and homework problems. Interactive Exercises break down complex problems into individual steps. Tutorials offer guidance at each stage to ensure students fully understand the problem-solving process. Video Analysis Exercises enable students to investigate real-world motion. Student progress is tracked in a single, easy-to-use gradebook. Details tracked include completion, time spent, and type of assistance. Instructors can choose grade criteria. The gradebook is easily exported into alternative course management systems. Homework services End-of-chapter problems are available in WebAssign and on Physics Portal.  Preface xxv Integrated Easy to Use Customizable MEDIA AND PRINT SUPPLEMENTS FOR THE STUDENT Student Solutions Manual The new manual, prepared by David Mills, professor emeritus at the College of the Redwoods in California, provides solutions for selected odd-numbered end-of-chapter problems in the textbook and uses the same side-by- side format and level of detail as the Examples in the text. Volume 1 (Chapters 1–20, R) 1-4292-0302-1 Volume 2 (Chapters 21–33) 1-4292-0303-X Volume 3 (Chapters 34–41) 1-4292-0301-3 Study Guide The Study Guide provides students with key physical quantities and equations, misconceptions to avoid, questions and practice problems to gain further understanding of physics concepts, and quizzes to test student knowledge of chapters. Volume 1 (Chapters 1–20, R) 0-7167-8467-X Volume 2 (Chapters 21–33) 1-4292-0410-9 Volume 3 (Chapters 34–41) 1-4292-0411-7 Physics Portal On-line quizzing Multiple-choice quizzes are available for each chapter. Students will receive immediate feedback, and the quiz results are collected for the instructor in a grade book. Concept Tester Questions Flashcards xxvi Preface FOR THE INSTRUCTOR Instructor’s Resource CD-ROM This multifaceted resource provides instructors with the tools to make their own Web sites and presentations. The CD contains illustrations from the text in.jpg format, Powerpoint Lecture Slides for each chapter of the book, i-clicker questions, a problem conversion guide, and a complete test bank that includes more than 4000 multiple-choice questions. Volume 1 (Chapters 1–20, R) 0-7167-8470-X Volume 2 (Chapters 21–33) 1-4292-0268-8 Volume 3 (Chapters 34–41) 1-4292-0267-X Answer Booklet with Solution CD Resource This book contains answers to all end-of-chapter problems and CD-ROMs of fully worked solutions for all end-of- chapter problems. Solutions are available in editable Word files on the Instructor’s CD-ROM and are also available in print. Volume 1 (Chapters 1–20, R) 0-7167-8479-3 Volume 2 (Chapters 21–33) 1-4292-0457-5 Volume 3 (Chapters 34–41) 1-4292-0461-3 Transparencies 0-7167-8469-6 More than 100 full color acetates of figures and tables from the text are included, with type enlarged for projection. FLEXIBILITY FOR PHYSICS COURSES We recognize that not all physics courses are alike, so we provide instructors with the opportunity to create the most effective resource for their students. Custom-Ready Content and Design Physics for Scientists and Engineers was written and designed to allow maximum customization. Instructors are invited to create specific volumes (such as a five- volume set), reduce the text’s depth by selecting only certain chapters, and add additional material. To make using the textbook easier, W. H. Freeman encourages instructors to inquire about our custom options. Versions Accomodate Common Course Arrangements To simplify the review and use of the text, Physics for Scientists and Engineers is available in these versions: Volume 1 Mechanics/Oscillations and Waves/Thermodynamics (Chapters 1–20, R) 1-4292-0132-0 Volume 2 Electricity and Magnetism/Light (Chapters 21–33) 1-4292-0133-9 Volume 3 Elementary Modern Physics (Chapters 34–41) 1-4292-0134-7 Standard Version (Chapters 1-33, R) 1-4292-0124-X Extended Version (Chapters 1-41, R) 0-7167-8964-7 Acknowledgments We are grateful to the many instructors, students, colleagues, and friends who have contributed to this edition and to earlier editions. Anthony J. Buffa, professor emeritus at California Polytechnic State University in California, wrote many new end-of-chapter problems and edited the end-of- chapter problems sections. Laura Runkle wrote the Physics Spotlights. Richard Mickey revised the Math Review of the fifth edition, which is now the Math Tutorial of the sixth edition. David Mills, professor emeritus at the College of the Redwoods in California, extensively revised the Solutions Manual. We received in- valuable help in creating text and checking the accuracy of text and problems from the following professors: Thomas Foster Jerome Licini Paul Quinn Southern Illinois University Lehigh University Kutztown University Karamjeet Arya Dan Lucas Peter Sheldon San Jose State University University of Wisconsin Randolph-Macon Woman’s College Mirley Bala Texas A&M University—Corpus Christi Laura McCullough Michael G. Strauss Michael Crivello University of Wisconsin, Stout University of Oklahoma San Diego Mesa College Jeannette Myers Brad Trees Carlos Delgado Francis Marion University Ohio Wesleyan University Community College of Southern Nevada Marian Peters George Zober David Faust Appalachian State University Yough Senior High School Mt.