PEDAGOGICAL USE OF COLOR Displacement and position vectors Torque (t) and angular momentum (L) vectors Velocity vectors (v) ជ Velocity component vectors Linear or rotational motion directions Force vectors (F) ជ Force component vectors Springs Acceleration vectors (a) ជ Acceleration component vectors Electric fields Capacitors Magnetic fields Inductors (coils) Positive charges + Voltmeters V Negative charges – Ammeters A Resistors Batteries and other DC power supplies Lightbulbs – + AC sources Switches Ground symbol Light rays Objects Lenses and prisms Images Mirrors CONVERSION FACTORS Length Speed m = 39.37 in = 3.281 ft in = 2.54 cm km = 0.621 mi mi = 280 ft = 1.609 km light year (ly) = 9.461 ϫ 1015 m angstrom (Å) = 10Ϫ10 m km/h = 0.278 m/s = 0.621 mi/h m/s = 2.237 mi/h = 3.281 ft/s mi/h = 1.61 km/h = 0.447 m/s = 1.47 ft/s Mass Force N = 0.224 lb = 105 dynes lb = 4.448 N dyne = 10Ϫ5 N = 2.248 ϫ 10Ϫ6 lb kg = 103 g = 6.85 ϫ 10Ϫ2 slug Work and energy slug = 14.59 kg Ϫ27 kg = 931.5 MeV/c J = 107 erg = 0.738 ft и lb = 0.239 cal u = 1.66 ϫ 10 cal = 4.186 J Time ft и lb = 1.356 J = 60 s Btu = 1.054 ϫ 103 J = 252 cal h = 600 s J = 6.24 ϫ 1018 eV day = 8.64 ϫ 10 s eV = 1.602 ϫ 10Ϫ19 J yr = 365.242 days = 3.156 ϫ 10 s kWh = 3.60 ϫ 106 J Volume Pressure L = 000 = 3.531 ϫ ft3 = 2.832 ϫ 10Ϫ2 m3 gal = 3.786 L = 231 in.3 cm3 10Ϫ2 ft3 atm = 1.013 ϫ 105 N/m2 (or Pa) = 14.70 lb/in.2 Pa = N/m2 = 1.45 ϫ 10Ϫ4 lb/in.2 lb/in.2 = 6.895 ϫ 103 N/m2 Angle Power 180Њ = rad rad = 5.730Њ 1Њ = 60 = 1.745 ϫ 10Ϫ2 rad hp = 550 ft и lb/s = 0.746 kW W = J/s = 0.738 ft и lb/s Btu/h = 0.293 W Essentials of College Physics Raymond A Serway Emeritus, James Madison University Chris Vuille Embry-Riddle Aeronautical University Australia · Brazil · Canada · Mexico · Singapore · Spain · United Kingdom · United States Physics Acquisitions Editor: Chris Hall Publisher: David Harris Vice President, Editor-in-Chief, Sciences: Michelle Julet Development Editor: Ed Dodd Editorial Assistant: Jessica Jacobs Technology Project Manager: Sam Subity Marketing Manager: Mark Santee Marketing Assistant: Michele Colella Marketing Communications Manager: Bryan Vann Project Manager, Editorial Production: Teri Hyde Creative Director: Rob Hugel Art Director: Lee Friedman Print/Media Buyer: Karen Hunt Permissions Editor: Bob Kauser Production Service: Joan Keyes, Dovetail Publishing Services, Inc Text Designer: Patrick Devine Photo Researcher: Jane Sanders Miller Copy Editor: Kathleen Lafferty Illustrator: Rollin Graphics, Progressive Information Technologies Cover Designer: Patrick Devine Cover Image: Adrian Weinbrecht/Photolibrary Cover Printer: Quebecor World/Dubuque Compositor: G&S Typesetters, Inc Printer: Quebecor World/Dubuque â 2007 by Raymond A Serway ExamViewđ and ExamView Pro® are registered trademarks of FSCreations, Inc Windows is a registered trademark of the Microsoft Corporation used herein under license Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc Used herein under license ALL RIGHTS RESERVED No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means — graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner — without the written permission of the publisher Printed in the United States of America 10 For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563 For permission to use material from this text or product, submit a request online at http://www.thomsonrights.com Any additional questions about permissions can be submitted by e-mail to thomsonrights@thomson.com © 2007 Thomson Learning, Inc All Rights Reserved Thomson Learning WebTutor™ is a trademark of Thomson Learning, Inc Thomson Higher Education 10 Davis Drive Belmont, CA 94002-3098 USA Library of Congress Control Number: 2005932024 ISBN 0-495-10619-4 The Foundation for Success Building the right course for you and your students is easy when you start with Serway and Vuille’s Essentials of College Physics! Because every course is as unique as its instructor—and its students—you need an approach tailored to your distinct needs No matter how you decide to execute your course, Essentials of College Physics, provides the proven foundation for success This accessible and focused text includes a broad range of engaging and contemporary applications that motivate student understanding of how physics works in the real world And with its extraordinary range of powerful teaching and learning resources, it’s easy for you to craft a course that fits your exact requirement with: WebAssign Focused homework management system using pedagogy and content from the book, including hints and feedback for students Access to the PhysicsNow™ student tutorial system—interactive, integrated learning technology that puts concepts in motion Premium book-specific content for audience response systems that lets you interact with your students directly from your own PowerPoint® lectures A multimedia presentation tool that lets you incorporate colorful images and clarifying animations into every lecture Whatever your goals are for you and your students, Essentials of College Physics features the content and the courseware to get you there—without the risk Preview We know that providing your students with a solid foundation in the basics is the key to student success and that means providing them with proven, time-tested content As you peruse the following pages of this PREVIEW, be sure to note the adjacent diagram indicating the different components of our integrated, interrelated program No matter what kind of course you want to deliver— whether you offer a more traditional text-based course, you’re interested in using or are currently using an online homework management system, or you are ready to turn your lecture into an interactive learning environment through an audience response system—you can be confident that proven content provides the foundation for each and every component iii The strength of Essentials of College Physics starts with the foundation Essentials of College Physics provides students with a clear and logical presentation of the basic concepts and principles of physics With the text as the foundation, coupled with extraordinary media integration, it’s easy to build a course that gives every student the maximum opportunity for success Briefer than the average college physics text, Essentials of College Physics comprehensively covers all the standard topics in classical and modern physics Instructors will notice a clean and clear dialogue with the student, the book’s uncluttered look and feel, and attention paid to language The authors’ clear, logical, relaxed, Vectors are denoted in boldand engaging face with arrows over them style facilitates This makes them easier quick compreto recognize hension 154 Chapter Rotational Motion and the Law of Gravity Exercise 7.3 (a) What are the angular speed and angular displacement of the disc 0.300 s after it begins to rotate? (b) Find the tangential speed at the rim at this time Answers (a) 10.6 rad/s; 1.58 rad (b) 0.472 m/s 7.4 CENTRIPETAL ACCELERATION v Figure 7.5a shows a car moving in a circular path with constant linear speed v Even though the car moves at a constant speed, it still has an acceleration To understand this, consider the defining equation for average acceleration: r O : a av ϭ : (a) Ꭽ vi r Ꭾ vf r vf Ϫ : vi O ac ϭ (b) Figure 7.5 (a) Circular motion of a car moving with constant speed (b) As the car moves along the circular path from Ꭽ to Ꭾ, the direction of its velocity vector changes, so the car undergoes a centripetal acceleration Ꭾ ⌬s vf ⌬u r tf Ϫ ti ϭ : ⌬v : ⌬t [7.14] : ⌬v ⌬s ϭ v r O (a) vf ⌬v vf Ϫ : vi where ⌬v ϭ vf Ϫ vi is the change in velocity When ⌬t is very small, ⌬s and ⌬u are : also very small In Figure 7.6b, : is apvf is almost parallel to : vi , and the vector ⌬v proximately perpendicular to them, pointing toward the center of the circle In : the limiting case when ⌬t becomes vanishingly small, ⌬v points exactly toward the center of the circle, and the average acceleration : a av becomes the instantaneous : acceleration : point in the same direction (in this a From Equation 7.14, : a and ⌬v limit), so the instantaneous acceleration points to the center of the circle The triangle in Figure 7.6a, which has sides ⌬s and r, is similar to the one formed by the vectors in Figure 7.6b, so the ratios of their sides are equal: : r [7.13] : a av ϭ vi v2 r To derive Equation 7.13, consider Figure 7.6a An object is first at point Ꭽ with velocity : vi at time t i and then at point Ꭾ with velocity : vf at a later time tf We assume that : vi and : vf differ only in direction; their magnitudes are the same (vi ϭ vf ϭ v) To calculate the acceleration, we begin with Equation 7.12, : Ꭽ [7.12] tf Ϫ ti The numerator represents the difference between the velocity vectors : vf and : vi These vectors may have the same magnitude, corresponding to the same speed, but if they have different directions, their difference can’t equal zero The direction of the car’s velocity as it moves in the circular path is continually changing, as shown in Figure 7.5b For circular motion at constant speed, the acceleration vector always points toward the center of the circle Such an acceleration is called a centripetal (center-seeking) acceleration Its magnitude is given by ⌬u –vi (b) Figure 7.6 (a) As the particle moves from Ꭽ to Ꭾ, the direction of v i to its velocity vector changes from : : vf (b) The construction for determining the direction of the change in velocity ⌬: v , which is toward the center of the circle or ⌬v ϭ v ⌬s r [7.15] Substituting the result of Equation 7.15 into a av ϭ ⌬v/⌬t gives a av ϭ v ⌬s r ⌬t [7.16] But ⌬s is the distance traveled along the arc of the circle in time ⌬t, and in the limiting case when ⌬t becomes very small, ⌬s/⌬t approaches the instantaneous value Foundation ᭣ Important statements and definitions are set in boldface type or are highlighted with a background screen for added emphasis and ease of review Important equations are highlighted with a tan background iv The International System of units (SI) is used throughout the book The U.S customary system of units is used only to a limited extent in the problem sets of the early chapters on mechanics Essentials of College Physics provides a wealth of outstanding examples and problem sets to help students develop critical problem-solving skills and conceptual understanding ᭤ All worked Examples include six parts: Goal, Problem, Strategy, Solution, Remarks, and Exercise/Answer The “Solution” portion of every Example is presented in two-columns to enhance student learning and to help reinforce physics concepts In addition, the authors have taken special care to present a graduated level of difficulty within the Examples so students are better prepared to work the end-of-chapter Problems 8.4 Examples of Objects in Equilibrium 181 EXAMPLE 8.4 Locating Your Lab Partner’s Center of Gravity Goal Use torque to find a center of gravity Problem In this example, we show how to find the location of a person’s center of gravity Suppose your lab partner has a height L of 173 cm (5 ft, in) and a weight w of 715 N (160 lb) You can determine the position of his center of gravity by having him stretch out on a uniform board supported at one end by a scale, as shown in Figure 8.9 If the board’s weight wb is 49 N and the scale reading F is 3.50 ϫ 10 N, find the distance of your lab partner’s center of gravity from the left end of the board L L/2 F n O xcg w wb Figure 8.9 (Example 8.4) Determining your lab partner’s center of gravity Strategy To find the position x cg of the center of gravity, compute the torques using an axis through O Set the sum of the torques equal to zero and solve for x cg Solution Apply the second condition of equilibrium There is no torque due to the normal force : n because its moment arm is zero Solve for x cg and substitute known values: ⌺⌷ ϭ Ϫwx cg Ϫ wb(L/2) ϩ FL ϭ x cg ϭ FL Ϫ wb(L/2) w (350 N)(173 cm) Ϫ (49 N)(86.5 cm) ϭ ϭ 79 cm 715 N Remarks The given information is sufficient only to determine the x-coordinate of the center of gravity The other two coordinates can be estimated, based on the body’s symmetry Exercise 8.4 Suppose a 416-kg alligator of length 3.5 m is stretched out on a board of the same length weighing 65 N If the board is supported on the ends as in Figure 8.9, and the scale reads 880 N, find the x-component of the alligator’s center of gravity Answer 1.59 m 8.4 EXAMPLES OF OBJECTS IN EQUILIBRIUM Recall from Chapter that when an object is treated as a geometric point, equilibrium requires only that the net force on the object is zero In this chapter, we have shown that for extended objects a second condition for equilibrium must also be satisfied: the net torque on the object must be zero The following general procedure is recommended for solving problems that involve objects in equilibrium Math Focus 6.1 One-Dimensional Elastic Collisions The usual notation and subscripts used in the equations of one-dimensional collisions often obscure the underlying simplicity of the mathematics In an elastic collision, the rather formidable-looking Equations 6.10 and 6.11 are used, corresponding to conservation of momentum and conservation of energy, respectively In a typical problem, the masses and the initial velocities are all given, leaving two unknowns, the final velocities of the colliding objects Substituting the more common-looking variables, X ϭ v 1f and Y ϭ v f, together with the known quantities yields equations for a straight line (the momentum equation) and an ellipse (the energy equation) The mathematical solution then reduces to finding the intersection of a straight line and an ellipse Example: In a one-dimensional collision, suppose the first object has mass m1 ϭ 1kg and initial velocity v1i ϭ 3m/s, whereas the second object has mass m2 ϭ 2kg and initial velocity v2i ϭ Ϫ3m/s Find the final velocities for the two objects (For clarity, significant figure conventions are not observed here.) Solution: Substitute the given values and X ϭ v 1f and Y ϭ v f into Equations 6.10 and 6.11, respectively, and simplify, obtaining Ϫ3 ϭ X ϩ 2Y 27 ϭ X ϩ 2Y (1) Problem-Solving Strategy Objects in Equilibrium (2) Diagram the system Include coordinates and choose a convenient rotation axis computing the net torque on the object Equation (1) is that of a straight line, whereasfor Equation (2) describes an ellipse Solve Equation (1)2.forDraw X a free-body diagram of the object of interest, showing all external forces acting and substitute into Equation (2), obtaining 27 ϭon it For systems with more than one object, draw a separate diagram for each object (Most problems will have a single object of interest.) (Ϫ3 Ϫ 2Y)2 ϩ 2Y 2, which can be simplified to Y ϩ 2Y Ϫ ϭ In general, the quadratic formula must now be applied, but this equation factors, giving Y ϭ v f ϭ 1m/s or Ϫ3m/s Only the first answer, 1m/s, makes sense Substituting it into Equation (1) yields X ϭ v 1f ϭ Ϫ5m/s It is also possible to use Equation 6.10 together with the derived Equation 6.14 This situation, illustrated in Example 6.5, is equivalent to finding the intersection of two straight lines It’s easier to remember the equation for the conservation of energy than the special Equation 6.14, so it’s a good idea to be able to solve such problems both ways Foundation ᭡ New! Just-In-Time Math Tutorials! An emphasis on quantitative problem-solving is provided in the Math Focus boxes These boxes develop mathematical methods important to a particular area of physics, or point out a technique that is often overlooked Each Math Focus box has been placed within the applicable section of the text, giving students just-in-time support A complete Appendix provides students with additional math help applied to specific physics concepts v Building critical-thinking skills and conceptual understanding Essentials of College Physics includes time-tested as well as new pedagogy that adheres to the findings of physics education research to help students improve their conceptual understanding Chapter 11 Energy in Thermal Processes Gary Settles/Science Source/Photo Researchers, Inc 288 Photograph of a teakettle, showing steam and turbulent convection air currents A P P L I C AT I O N Cooling Automobile Engines A P P L I C AT I O N Algal Blooms in Ponds and Lakes The same process occurs when a radiator raises the temperature of a room The hot radiator warms the air in the lower regions of the room The warm air expands and, because of its lower density, rises to the ceiling The denser cooler air from above sinks, setting up the continuous air current pattern shown in Figure 11.9 An automobile engine is maintained at a safe operating temperature by a combination of conduction and forced convection Water (actually, a mixture of water and antifreeze) circulates in the interior of the engine As the metal of the engine block increases in temperature, energy passes from the hot metal to the cooler water by thermal conduction The water pump forces water out of the engine and into the radiator, carrying energy along with it (by forced convection) In the radiator, the hot water passes through metal pipes that are in contact with the cooler outside air, and energy passes into the air by conduction The cooled water is then returned to the engine by the water pump to absorb more energy The process of air being pulled past the radiator by the fan is also forced convection The algal blooms often seen in temperate lakes and ponds during the spring or fall are caused by convection currents in the water To understand this process, consider Figure 11.10 During the summer, bodies of water develop temperature gradients, with an upper, warm layer of water separated from a lower, cold layer by a buffer zone called a thermocline In the spring or fall, temperature changes in the water break down this thermocline, setting up convection currents that mix the water The mixing process transports nutrients from the bottom to the surface The nutrient-rich water forming at the surface can cause a rapid, temporary increase in the algae population ᭣ A wealth of interesting and relevant Applications reveals the role physics plays in our lives and in other disciplines These Applications are woven throughout the text narrative and are indicated with a margin note For biology and pre-med students, icons point the way to various practical and interesting Applications of physical principles to biology and medicine With this edition the authors have increased the number of life scienceoriented applications and end-of-chapter Problems to help motivate students to master the content Tip notations address common student misconceptions stu-the device picThe pressure at a and specific situations point in a fluid canin bewhich measured with Cool layer 5°–4°C in Figure 9.7b: an evacuated cylinder enclosing a light piston connected to a dents tured often follow unproductive paths spring that has been previously calibrated with known weights As the device is submerged in a fluid, the fluid down on the of the piston Approximately 100 Tippresses sections aretopfound in and thecompresses the spring until the inward force exerted by the fluid is balanced by the outward (a) Summer layering of water force exerted by the spring Let F be the magnitude of the force on margins, providing students with the help theythe piston and A the area of the top surface of the piston Notice that the force that compresses need to avoid common mistakes the spring is spread out over the entire area, motivating our formal definition of pressure: and misunderstandings Warm Layer 25°–22°C Figure 11.9 Convection currents are set up in a room warmed by a radiator 9.3 Density and Pressure 211 Thermocline 20°–10°C If F is the magnitude of a force exerted perpendicular to a given surface of area A, then the pressure P is the force divided by the area: Pϵ F A TIP 9.1 Force and Pressure Equation 9.7 makes a clear distinction between force and pressure Another important distinction is that force is a vector and pressure is a scalar There is no direction associated with pressure, but the direction of the force associated with the pressure is perpendicular to the surface of interest ᮤ Pressure [9.7] Because pressure is defined as force per unit area, it has units of pascals (newtons per square meter) The English customary unit for pressure is the pound per inch squared Atmospheric pressure at sea level is 14.7 lb/in2, which in SI units is (b) Fall and spring upwelling Pa 1.01from ϫ 10 Figure 11.10 (a) During the summer, a warm upper layer of water is separated a cooler lower layer by a thermocline (b) Convection currents during the spring or fall mix the As water canfrom cause Equation 9.7, the effect of a given force depends critically on weand see algal blooms the area to which it’s applied A 700-N man can stand on a vinyl-covered floor in regular street shoes without damaging the surface, but if he wears golf shoes, the metal cleats protruding from the soles can considerable damage to the floor With the cleats, the same force is concentrated into a smaller area, greatly elevating the pressure in those areas, resulting in a greater likelihood of exceeding the ultimate strength of the floor material Snowshoes use the same principle (Fig 9.8) The snow exerts an upward normal force on the shoes to support the person’s weight According to Newton’s third law, this upward force is accompanied by a downward force exerted by the shoes on the snow If the person is wearing snowshoes, that force is distributed over the very large area of each snowshoe, so that the pressure at any given point is relatively low and the person doesn’t penetrate very deeply into the snow ᭤ Applying Physics sections allow students to review concepts presented in a section Some Applying Physics examples demonstrate the connection between the concepts presented in that chapter and other scientific disciplines Foundation Applying Physics 9.1 vi Quick Quiz questions throughout the book provide students ample opportunity to assess their conceptual understanding Checkpoints ask simple questions based on the text to further reinforce key ideas © Royalty-Free/Corbis SI unit: pascal (Pa) Figure 9.8 Snowshoes prevent the person from sinking into the soft snow because the force on the snow is spread over a larger area, reducing the pressure on the snow’s surface Bed of Nails Trick After an exciting but exhausting lecture, a physics professor stretches out for a nap on a bed of nails, as in Figure 9.9, suffering no injury and only moderate discomfort How is this possible? Explanation If you try to support your entire weight on a single nail, the pressure on your body is your weight divided by the very small area of the end of the nail The resulting pressure is large enough to penetrate the skin If you distribute your weight over several hundred nails, however, as demonstrated by the professor, the pressure is considerably reduced because the area that supports your weight is the total area of all nails in contact with your body (Why is lying on a bed of nails more comfortable than sitting on the same bed? Extend the logic to show that it would be more uncomfortable yet to stand on a bed of nails without shoes.) Figure 9.9 (Applying Physics 9.1) Does anyone have a pillow? Several components from the text are enhanced in the PhysicsNow student tutorial program to reinforce material, including the dynamic Active Figures, which are animated diagrams from the text Labeled with the PhysicsNow icon, these figures come to life and allow students to visualize phenomena and processes that can’t be represented on the printed page ᭣ Over 40 of the text’s worked Examples are identified as Interactive Examples and labeled with the PhysicsNow icon As part of the PhysicsNow webbased tutorial system, students can engage in an interactive extension of the problem solved in the corresponding worked Example from the text This often includes elements of both visualization and calculation, and may also involve prediction and intuition building Students are guided through the steps needed to solve a problem type and are then asked to apply what they have learned to different scenarios INTERACTIVE EXAMPLE 4.7 Atwood’s Machine Goal Use the second law to solve a two-body problem Problem Two objects of mass m and m 2, with m Ͼ m 1, are connected by a light, inextensible cord and over a frictionless pulley, as in Active Figure 4.15a Both cord and pulley have negligible mass Find the magnitude of the acceleration of the system and the tension in the cord Strategy The heavier mass, m 2, accelerates downwards, in the negative y-direction Since the cord can’t be stretched, the accelerations of the two masses are equal in magnitude, but opposite in direction, so that a is positive and a is negative, and a ϭ Ϫa Each mass is acted : on by a force of tension T in the upwards direction and a force of gravity in the downwards direction Active Figure 4.15b shows free-body diagrams for the two masses Newton’s second law for each mass, together with the equation relating the accelerations, constitutes a set of three equations for the three unknowns — a 1, a , and T Solution Apply the second law to each of the two masses individually: T T m1 m2 m1 a1 m1g a2 m2 m2g (a) (b) ACTIVE FIGURE 4.15 (Example 4.7) Atwood’s machine (a) Two hanging objects connected by a light string that passes over a frictionless pulley (b) Free-body diagrams for the objects Log into to PhysicsNow at http://physics.brookscole.com/ecp and go to Active Figure 4.15 to adjust the masses of objects on Atwood’s machine and observe the resulting motion m 1a ϭ T Ϫ m 1g Substitute a ϭ Ϫa into the second equation, and multiply both sides by Ϫ1: m 2a ϭ ϪT ϩ m 2g Add the stacked equations, and solve for a1: (m ϩ m 2)a ϭ m 2g Ϫ m 1g a1 ϭ Substitute this result into Equation (1) to find T: Tϭ m 2a ϭ T Ϫ m 2g (1) (2) (3) m Ϫ m1 g m1 ϩ m m2mϩmm g 1 2 Remarks The acceleration of the second block is the same as that of the first, but negative When m gets very large compared with m 1, the acceleration of the system approaches g, as expected, because m is falling nearly freely under the influence of gravity Indeed, m is only slightly restrained by the much lighter m The acceleration of the system can also be found by the system approach, as illustrated in Example 4.10 An MCAT Test Preparation Guide is contained in the preface to help students prepare for the exam and reach their career goals The Guide outlines key test concepts and directed review activities from the text and the PhysicsNow student tutorial program to help students get up to speed Foundation ᭤ Also in the PhysicsNow student tutorial program are Coached Problems These engaging problems reinforce the lessons in the text by taking the same step-by-step approach to problem solving as found in the text Each Coached Problem gives students the option of breaking down a problem from the text into steps with feedback to ‘coach’ them toward the solution There are approximately three Coached Problems per chapter Once the student has worked through the problem, he or she can click “Try Another” to change the variables in the problem for more practice I.6 Index F Fahrenheit temperature scale, 250–251, 250 Faraday, Michael, 61, 394, 398, 521–522, 521 Faraday’s law of magnetic induction, 524 applications of, 526–527, 526, 527 minus sign in, 530–531, 530, 531 in motional emf, 527–529, 527, 528 statement of, 523–527, 524, 525 Farads, 425 Farnsworth, Philo, 763 Far point, 655, 655 Farsightedness, 655–658, 655 Femtometers, 735 Fermi, Enrico, 744, 760 Fermions, 770 Fermis, 735 Ferromagnetic materials, 513 Feynman, Richard, 693, 764 Feynman diagrams, 764–765, 764 Fiber optics, 592, 592 Fibrillation, 459 Fictitious forces, 160 Field forces, 61–62, 61 See also Electric fields; Magnetic fields Figure skating, 191–192, 191 Fine structure, 721 Fingerprints, dusting for, 492 First harmonic, 369, 370–372, 375 First law of motion, Newton’s, 62–63, 174–175 First law of planetary motion, Kepler’s, 166, 166 First law of thermodynamics, 300–309 adiabatic processes, 305–306, 305, 308t isobaric processes, 303–304, 308t isothermal processes, 307–308, 307, 308t isovolumetric processes, 306–307, 308t molar specific heats of gases, 302–304, 302t sign conventions in, 300–301 statement of, 300–301 Fission See Nuclear fission Fission fragments, 758 Flat mirrors, 599–601, 599, 600 Flat refracting surfaces, 610, 610, 611, 611 Floating, 218, 218, 220, 220 See also Buoyant forces Flow See Fluid dynamics Flow calorimeters, 296 Flow rate, 222 Fluid(s) See also Fluid dynamics Archimedes’s principle, 216–220, 217, 218, 219, 220 capillary action, 231, 231 contact angles, 231, 231 density and pressure in, 209–211, 210, 211 Pascal’s principle, 213–215, 214 pressure measurements of, 210, 211, 215–216, 215, 216 pressures of layers in, 213, 213 pressure variations with depth, 212–215, 212, 213, 214 surface effects of, 230–231, 230, 231 surface tension, 229–230, 229 Fluid dynamics, 220–226 Bernoulli’s equation, 223–226, 223, 224, 224, 225, 226 in blood vessels, 227, 227 equation of continuity, 221–223, 222, 226, 226 in garden hoses, 222–223, 223 golf balls and, 226–227, 227 in home plumbing, 228–229, 228 of ideal fluids, 221 in a pipe, 226, 226, 232, 232 Poiseuille’s law, 232–233, 232 Reynolds number, 234 sedimentation rate, 237, 237 streamline flow, 220–221, 221 through a viscous medium, 236–237, 236, 237 transport phenomena, 234–237, 235, 236, 237 turbulent flow, 221, 221, 227, 234 viscous flow, 221, 231–232, 232 f-number, 653–654 Focal length of lenses, 613, 613, 615 of mirrors, 603, 603 Focal points (foci) in ellipses, 166, 166 of lenses, 613, 613 of mirrors, 603, 603, 606 Food irradiation, 751 Foot-pounds, 91 Force(s), 61 action-reaction pairs, 68–69, 69 adhesive, 230–231, 230, 231 average, 125 buoyant, 216–220, 217, 218, 219, 220 in centripetal acceleration, 157–160, 157, 158, 159 cohesive, 230–231, 230, 231 color, 772 conservative, 96–97, 97, 103–104 contact vs field, 61–62, 61 Coulomb force, 413, 715, 736, 736 dissipative, 93 electric, 387–408, 390 charging by conduction, 389, 389 charging by induction, 389–390, 390 Coulomb’s law, 390–394, 392, 393 electric charge properties, 387–388, 388 electric field lines, 398–400, 399, 400 electric fields, 394–398, 394, 395, 397 electric flux, 402–404, 402, 403 Gauss’s law, 402–407, 404, 405, 406, 407 insulators and conductors, 388–390, 389, 390 problem-solving strategies for, 397 properties of, 390 fictitious, 160 friction, 77–81, 77, 78t fundamental electromagnetic, 62, 764, 765t, 772–773, 773 in electroweak theory, 772–773, 773 gravitational, 764, 765t strong, 62, 764, 765t, 772–773, 773 weak, 62, 764, 765t, 772–773, 773 gravitational, 62, 66–68, 66, 764, 765t in impulses, 125–127 of kinetic friction, 77–78 magnetic, 494–499 on a current-carrying conductor, 398, 496–499, 496, 497 direction of, 494–495, 494, 495 formula for, 494 gravitational force vs., 495–496, 498–499 magnitude of, 494, 496, 497 origin of, on a wire, 497 on a proton in Earth’s magnetic field, 495–496 right-hand rule number 1, 495, 495 between two parallel conductors, 507–509, 507 in Newton’s second law of motion, 63–66 nonconservative, 96–97, 97, 103–104, 104 normal, 69 nuclear, 736, 736 reaction, 68 restoring, 105, 327 of static friction, 77–78, 77, 78t units of, 63–64, 64t varying, 113–115, 113 wedge, 177 weight, 66–68 work and, 90–91, 113–115, 113 Forced convection, 287–288 Force platforms, 146 Force vibrations, 373–374, 373, 374 Fourth harmonic, 371 Frames of reference, 18 in general relativity, 688 inertial, 672–673, 676 lack of preferred, 676 relative velocity and, 53 Franklin, Benjamin, 387, 402 Franklin, Rosalind, 700, 700 Fraunhofer diffraction, 637–639, 637, 639 Free-body diagrams, 70 Freely falling objects, 33–35, 34, 161, 161t Freezing point of water, 248, 250, 250 Frequency, 328 angular, 333, 338 beat, 377, 377 cutoff, 695 of emitted photons, 717–718 of matter waves, 704 of radiation emitted by electron jumps, 715 refraction and, 583 in simple harmonic motion, 328, 332–334, 336 in standing waves, 369 of waves, 343–344, 369, 568, 583 Fresnel, Augustin, 637 Fresnel bright spots, 637, 637 Friction, 77–81 centripetal acceleration and, 158, 158 frictional work, 93–94 kinetic, 77–78, 77, 78t Newton’s third law and, 68–69 as nonconservative force, 97, 97 static, 77–78, 77, 78t viscosity as, 231–232, 232 Frictional work, 93–94 Fringes, 628–630, 628 Fundamental forces, 764–765 electromagnetic force, 62, 764, 765t, 772–773, 773 electroweak theory, 772–773, 773 gravitational, 764, 765t strong force, 62, 764, 765t, 772–773, 773 weak force, 62, 764, 765t, 772–773, 773 Fundamental frequency, 369, 370–373, 370, 375 Fused quartz, refraction through, 584 Fusion, nuclear, 686–687, 761–764, 763 Fusion reactors, 762–764, 763 G Galilean relativity, 672–673, 673 Galileo, 62, 338 Gamma decay, 745 Gamma rays, 569, 570 from gamma decay, 745 in irradiation of food and medical equipment, 751 in nuclear fusion, 762 penetrating power of, 739 Gases adiabatic processes, 305–306, 305, 308t Bernoulli’s principle for, 224 compressibility of, 205 diffusion of, 234–235, 235 expansion of, 266 ideal, 257–261, 258 ideal gas law, 259, 261 internal energy for, 264, 266 isobaric processes, 298–300, 298, 299, 303–304, 308t isothermal processes, 307–308, 307, 308t isovolumetric processes, 306–307, 308t kinetic theory of, 262–266, 262 Maxwell velocity distribution, 265, 265 molar specific heat at constant volume, 302–304, 302t moles of, 258 root-mean-square speed of, 264–265, 265, 265t speed of sound in, 357t work and, 297–300, 297 Gas thermometers, 248–250, 248, 249 Gauge pressure, 215 Gauss, 494 Index Gauss, Karl Friedrich, 402 Gaussian surfaces, 404, 406 Gaussian (cgs) system of measurement, 3, 3t, 4t See also Units Gauss’s law, 402–407, 404 electric flux and, 402–404, 402, 403 Gaussian surfaces, 404, 406 plane sheets and, 406–407, 406 spherical shells and, 404–405, 405 statement of, 161, 161, 403–404 Gay-Lussac’s law, 259 Geiger, Hans, 713, 713 Gell-Mann, Murray, 770 General relativity, 687–689, 687, 689 See also Relativity Generators, 531–535 alternating-current, 531–534, 531, 532, 557 changing magnetic flux in, 522–523 compared with motors, 534 direct-current, 532–533, 532 power delivered by, 557 Genetic damage, from radiation, 750 Geographic poles of the Earth, 493, 493 Geosynchronous orbit, 167–168 GFIs (ground fault interrupters), 480, 526, 526, 527 Glancing collisions, 137–140, 137, 139 Glass angle of refraction for, 583–584, 583, 586 Brewster’s angle for, 646 Pyrex®, 252, 252t Glaucoma testing, 130 Global warming, 256 Glomerulus, 235, 236 Gluons, 764, 765t, 772, 773, 773 Goddard, Robert, 140, 229 Gold, density of, 219 Golf balls, 226–227, 227 Goudsmit, Samuel, 721 Grand unification theory (GUT), 767, 773 Graphite, 502 Graphs acceleration from, 25–26, 25, 26 acceleration vs time, 28, 28 displacement from, 29 Feynman diagrams, 764–765, 764 position vs time, 21–22, 22, 23 PV diagrams, 298–300, 298, 299 sinusoidal curves on, 335–336, 335 slopes of, 21–22 stress–strain curves, 207, 207 temperature vs energy, 278–280, 279 velocity on, 21–22, 22 velocity vs time, 25–26, 25, 26 work on, 113–115, 113, 114 Gravitational acceleration, 33–35, 34 Gravitational constant, 160, 687 Gravitational force, 66 as a conservative force, 96 as fundamental force, 764, 765t general relativity and, 688 law of univeral gravitation and, 66, 66 magnetic force compared with, 495–496, 498–499 nonconservative forces and, 103–104, 104 weight and, 66–68 Gravitational lensing, 688, 689 Gravitational mass, 687 Gravitational potential energy, 97–104, 98, 98, 102, 103, 162–164 Gravitational torque, center of gravity and, 179–180, 180 Gravitational work, 98–99, 98, 163 Gravitons, 764, 765t Gravity, 160–165 See also Gravitational force acceleration of, 33–35, 34, 161–162, 161t center of, 179–181, 180, 181 on Ceres, 161–162 escape speed and, 164–165, 164, 265 in general relativity, 687–689, 687 gravitational constant, 160, 687 gravitational lensing, 688, 689 gravitational potential energy, 97–104, 98, 162 conservation of mechanical energy and, 101–103, 101, 102, 103 gravitational work and, 98–99, 98, 162–164 nonconservative forces and, 103–104, 104 reference levels for, 99–100, 99, 100 sign convention in, 162–163 statement of, 162 law of universal gravitation, 66, 160–162, 161 projectile motion and, 48–53, 48 action-reaction pairs in, 68 calculations of, 51–53, 51, 52 horizontal and vertical motions of, 49–50, 49 problem-solving strategies for, 50 work done by, 98–99, 98, 163 Grimaldi, Francesco, 577 Grounded objects, 389, 480, 481 Ground fault interrupters (GFIs), 480, 526, 526, 527 Ground state, 717, 724–725, 725t, 727–729, 727 Guitar strings, 345 GUT (grand unification theory), 767, 773 H Hadrons, 766–767, 766t, 770–772, 772, 772t Hahn, Otto, 686 Half-life, 739–741, 739, 742 Halogens, 725, 725t Hard magnetic materials, 492, 513 Harmonic motion, simple Hooke’s law and, 328–330 pendulum motion and, 337–339, 337 position, velocity, and acceleration with time, 334–337, 335 sinusoidal curves, 335–336, 335 uniform circular motion compared to, 331–334, 332 velocity with position, 330–331, 330, 332 Harmonic oscillator equations, 329, 336–337 Harmonic series in air columns, 374–376, 374, 376 in stretched strings, 369, 370–373, 370 Hearing cochlear implants, 380 decibel level, 359–361, 360t frequency response curves for, 379, 379 human ears, 378–380, 379 insect ears, 380 OSHA noise-level regulations, 361 protecting, 360 threshold of, 359–360, 379, 379 Hearts electrical activity in, 458–460, 458, 459, 460 electromagnetic pumps for artificial, 498, 498 Heat, 272–273 blackbody radiation, 693–694, 693, 694 calorimetry, 276–278 conduction of, 283–285, 283, 284, 284t convection of, 287–289, 287, 288 converting caloric to mechanical energy, 273–274, 273 energy transfer through, 109, 275 home insulation and, 285–287, 286t internal energy and, 272–274 latent, 278–283, 279t mechanical equivalent of, 273 molar specific, 302–304, 302t specific heat, 274–276, 274t, 302–304, 302t thermal radiation, 289–291, 289, 290 units of, 273 Heat engines Carnot cycle, 313–316, 314 cyclic processes in, 309–310, 309 Kelvin–Planck formulation of the second law, 312–313 refrigerators and heat pumps, 311–312, 311 I.7 reversible and irreversible processes, 313, 313 thermal efficiency of, 310 Heat pumps, 311, 311 Heisenberg, Werner, 707 Heisenberg’s uncertainty principle, 707–708, 707, 765 Helium discovery of, 715 electronic configuration of, 724 in fusion reactions, 762, 763–764 isotopes of, 504 modified Bohr theory applied to, 719–720 Henry, Joseph, 521 Henrys, 536 Herschel, William, 568 Hertz, 333 Hertz, Heinrich, 562–563, 563, 568, 578 Higgs boson, 773 High-voltage power lines, 560–561, 561 Home insulation, 285–287, 286t Home plumbing, 228–229, 228 Hooke’s law, 105, 327–331 acceleration and, 329 pendulum motion and, 338 spring constants, 105, 206, 327–329, 328 velocity as a function of position, 330–331, 330 Hoops, moments of inertia for, 187, 187t Horsepower, 111 Household circuits, 479–481 fuses and circuit breakers, 470, 479, 479, 481 ground-fault interrupters, 480, 526, 526, 527 high-voltage, 479–480, 480 rms voltage in, 549 safety and, 480–481, 481 Hubble Space Telescope, 662, 664, 664 Huygens, Christian, 577 Huygens’ principle, 588–590, 588, 589 Hydraulic lifts, 214–215, 214 Hydraulic press, 213–215, 214 Hydroelectric power plants, 531, 532 Hydrogen Bohr model of, 715–718, 715, 716, 717, 718 emission spectrum of, 714, 714 energy level diagram for, 717–718, 717, 718 isotopes of, 3, 687, 737, 762–764 quantum mechanics and, 720–723, 720, 721, 721t, 723 Hydrogen-like atoms, 719 Hydrometers, 244, 244 Hydrostatic equilibrium, 260–261 Hydrothermal vents, 326 Hyperopia (farsightedness), 655–658, 655 I ICDs (implanted cardioverter defibrillators), 460, 460 Ice, 257, 257, 278 Ice point, 248, 250, 250 Ideal absorbers, 290 Ideal gases Boltzmann’s constant for, 261 in comet collisions, 282 ideal gas law, 259, 261 kinetic theory of, 262–266, 262 molecular gases as, 262 moles of, 258 pressure of, 263 properties of, 257 in submerging a balloon, 260–261 Ideal reflectors, 290 Ideal transformers, 560 Image distance, 599–600, 599 Image point, of concave mirrors, 602, 602 Images from combinations of lenses, 619–621, 620 from flat refracting surfaces, 610, 610 on front and back sides of mirrors, 604, 609 in mirrors, 599–600, 599, 605, 606–608 I.8 Index Images (Continued ) from spherical refracting surfaces, 608–611, 609, 610, 611 from thin lenses, 615, 616 Impedance, 554–556, 555t, 558 Impending motion, 78 Implanted cardioverter defibrillators (ICDs), 460, 460 Impulse, 125 Impulse approximation, 131 Impulse–momentum theorem, 125–127 Incidence, angle of, 580, 580, 590, 645–646, 646 Included angles, 177 Incoherent light sources, 627 Index of refraction, 582–585 phase changes on reflection and, 632–634, 632, 633 polarizing angle and, 646 total internal reflection and, 590–592, 590, 591, 592 for various substances, 582t Induced current, 524, 524 Induced emf back emf, 534–535, 534, 538 Faraday’s law and, 523–527, 524, 525 in generators, 531–534, 532 Lenz’s law and, 524–527, 525, 530–531, 530 magnetic flux and, 521–523, 521, 522 motional emf, 527–529, 527, 528, 528 RL circuits, 538–540, 538 self-inductance, 535–537, 535 sparks and, 536 Induced polarization, 438–439, 438 Induced voltages Faraday’s law of induction, 523–527, 524, 525 ground fault interrupters, 526, 526, 527 induced emf, 521–523, 521, 522 Lenz’s law, 524–527, 525, 530–531, 530 motional emf, 527–529, 527, 528 Inductance, 536–537 Induction charging by, 389–390, 390 Faraday’s law, 523–527, 524, 525 of magnetism, 491 Inductive reactance, 551–552, 556 Inductors, 538 in alternating-current circuits, 551–552, 551, 552 energy stored in, 539, 557 power loss in, 556 in RL circuits, 538, 538 Inelastic collisions, 130–131 Inertia, 63 moment of, 184–189, 184, 185, 186, 187t, 188 Inertial electrostatic confinement, 763 Inertial frames of reference, 672–673, 676 Inertial mass, 687 Infrasonic waves, 355 Injuries, 126, 127–128 Instantaneous acceleration, 25–26, 25, 26, 28, 48 Instantaneous angular acceleration, 150 Instantaneous angular speed, 148 Instantaneous centripetal acceleration, 155 Instantaneous speed, 22 Instantaneous thrust, 141 Instantaneous velocity, 22–23, 23, 47 Insulation, 285–287, 286t Insulators, electrical, 388–390 in capacitors, 435–439, 435, 436, 437, 438 charging by induction and, 389–390, 390 resistivities and, 452, 452t Intensity, 359 of electromagnetic waves, 566–568 of light in cameras, 653 of polarized light, 644–645, 644 of sound waves, 358–363, 360t Intensity level, 359 Interference conditions for, 627–628 constructive, 346, 346, 367, 629, 629, 633 destructive, 346, 347, 367, 629, 633, 638 imperfections in lenses and, 634–635, 634 from Lloyd’s mirror, 631–632, 632 nature of light and, 577 Newton’s rings, 634–635, 634, 635 nonreflective coatings, 635, 635 overview of, 346–347, 346, 347 positions of bright and dark fringes, 630–631 of sound waves, 367–368, 367, 368, 376–378, 377 in television signals, 630 in thin films, 632–636, 633, 634, 635, 636 wavelength measurement by, 631 in a wedge-shaped film, 636, 636 Young’s double-slit experiment, 628–631, 628, 629, 630 Interferometers, Michelson, 674, 674 Internal combustion engines, 309, 309n Internal energy, 272 heat and, 109, 272–274 human metabolism and, 319–321, 320t molar specific heats and, 302–304, 302t for monatomic gases, 264, 266, 301 Internal resistance, 465–466, 465 Inverse-square law Coulomb’s law and, 401 of gravity, 160 of spherical waves, 361, 361 Inverse trigonometric functions, 11, 44 Iodine, as radioactive tracer, 751 Ionic solutes, in neural transmission, 483 Ionization energy, 717, 725t Ionizing radiation, damage from, 750–751, 750t See also Radiation Ions, in magnetic fields, 503–504, 503, 504 Iris, 654–655, 654 I2R loss, 457 Irradiation of food and medical equipment, 751 Irreversible processes, 313 Isobaric processes, 298–300, 298, 299, 303–304, 308t Isothermal processes, 307–308, 307, 308t, 313–316, 314 Isotopes, 734 of carbon, 743–747 of hydrogen, 3, 687, 737, 762–764 natural abundances of, 734 as radioactive tracers, 751 separating by mass spectrometers, 504, 504 Isovolumetric (isochoric) processes, 306–307, 308t J Jets, vertical loops by, 159–160, 159 Joule, James, 272 Joules, 91, 95, 273 Junction rule, 473–475, 473, 474 K Kaons, 766t, 769 Keck telescopes, Mauna Kea, 663 Kelvin–Planck formulation of the second law of thermodynamics, 312–313 Kelvins, 249 Kelvin temperature scale, 249–251, 249, 250, 276 Kepler, Johannes, 165 Kepler’s laws of planetary motion, 165–168, 166 Kidney dialysis, 235, 236, 498, 498 Kilocalories, 121, 273 Kilograms, Kilowatt-hours, 111, 457 Kinematics, 18 See also Motion Kinematics velocity equation, 64 Kinetic energy, 94–97, 95 from alpha decay, 742 average, 264 conservation of mechanical energy and, 101 in elastic vs inelastic collisions, 130–132 of ideal gases, 263–266 in relativistic mechanics, 683 rotational, 189–190, 189, 190 temperature and, 264–266 work–energy theorem and, 94, 95–97, 95, 97 Kinetic friction, 77–78, 77, 78t Kinetic theory of gases, 262–266, 262 Kirchhoff’s rules, 473–474, 473, 474 L Lambda baryons, 766t, 769 Laminar flow, 220–221, 221 Land, E H., 643 Lasers coherent light from, 628 in fusion reactors, 763 intensity of, 568 production of, 729 surgical and industrial uses of, 728–729, 729 Latent heat, 278 of condensation, 278n of fusion, 278, 279t, 280 phase changes and, 278–283, 279 of solidification, 278n of vaporization, 278, 279t, 280 Lateral magnification, 599, 661 Laue, Max von, 698 Laue patterns, 699, 699 Law of conservation of baryon number, 767–768 Law of conservation of lepton number, 768–769 Law of conservation of strangeness, 769–770, 769 Law of refraction, 583–585, 583, 589–590, 589 Law of universal gravitation, 66, 160–162, 161 Laws of motion, 61–76 See also Motion applications of, 69–76 forces in, 61–62, 61 Kepler’s laws of planetary motion, 165–168, 166 Newton’s first law, 62–63, 174–175 Newton’s second law, 63–68, 63–68, 64, 65, 66, 70–71, 184 Newton’s third law, 68–69, 68, 69 Lawson’s criterion, 763 Length approximate values of measured, 2–3, 2t proper, 681–682 in relativistic mechanics, 675 units of, 1, 735 Length contraction, 681–682, 681 Lenses aberrations, 621–622, 621, 622 camera, 653, 653 checking for imperfections in, 634–635, 634 combinations of, 619–621, 620, 660–662, 660 in compound microscopes, 660–662, 660 concave lenses, 613, 614 converging, 613–614, 613, 617–618, 617, 621, 621 convex, 613, 614 to correct vision, 655–658, 655, 656 diverging, 613–614, 613, 618–619, 619 in diving masks, 616 in eyes, 654, 654 focal point and focal length in, 613, 613, 615 gravitational, 689 image properties from, 610–611, 610 nonreflective coatings on, 635, 635 power measured in diopters, 657 ray diagrams for, 615–616, 616 sign conventions for, 615–616, 615, 615t, 621 simple magnifiers, 658–660, 658 in telescopes, 662–664, 662, 663, 664 thin-lens equation, 614–615 Lens maker’s equation, 615 Lenz’s law, 524 Faraday’s law and, 530–531, 530 overview of, 524–527, 525 self-inductance and, 535–536, 535 Index Lepton number, 768–769 Leptons, 764, 766t, 767 Leucippus, Lever arms, 176, 176 Lift, on airplane wings, 227–228, 227 Light coherent, 627, 628–632, 628, 630, 632 colors of, 586–587, 586, 587 diffraction, 636–642 discovery of, 577 Fraunhofer, 637–639, 637, 639 Fresnel bright spots, 637, 637 gratings, 640–642, 640, 641, 698 order number in, 640–642 resolution in patterns, 664–666, 664, 665, 666 single-slit, 638–639, 638, 639 dispersion of, 585–587, 586, 587 dual nature of, 577–578, 703–706, 705 as electromagnetic wave, 565 evolution of the eye and, 570 fiber optics, 592, 592 Huygens’ principle, 588–590, 588, 589 interference conditions for, 627–628 constructive, 346, 346, 367, 629, 629, 633 destructive, 346, 347, 367, 629, 633, 638 imperfections in lenses and, 634–635, 634 from Lloyd’s mirror, 631–632, 632 nature of light and, 577 Newton’s rings, 634–635, 634, 635 nonreflective coatings, 635, 635 overview of, 346–347, 346, 347 positions of bright and dark fringes, 630–631 in thin films, 632–636, 633, 634, 635, 636 wavelength measurement by, 631 in a wedge-shaped film, 636, 636 Young’s double-slit experiment, 628–631, 628, 629, 630 photoelectric effect, 577–578, 695–698, 695, 696, 696t, 697 polarization of, 642–647, 643, 644, 646, 647 radiation pressure of, 566, 566 rainbows, 587, 587 ray approximation, 578, 578 reflection angle of, 580, 580 double images, 580 double reflections, 580–581, 580 fiber optics, 592, 592 Huygens’ principle and, 588–590, 589 interference patterns from, 631–632, 632 nonreflective coatings, 635, 635 overview of, 347–348, 347, 348, 566, 578–581, 579, 580 phase changes on, 632–633, 632, 633 polarization by, 645–647, 646 red eyes in flash photographs, 580 seeing the road on a rainy night, 579, 579 specular vs diffuse, 579, 579 total internal reflection, 590–592, 590, 591, 592 refraction, 581–585 at air-water boundary, 591–592, 591, 611, 611 angle of, 581–585, 581, 582, 583 atmospheric, 612, 612 chromatic aberration in, 621–622, 622 flat refracting surfaces, 610, 610, 611, 611 Huygens’ principle and, 588–590, 589 images formed at spherical surfaces, 608–611, 609, 610, 611 index of, 582–584, 582t, 632–634, 646 spectrum of, 568–570, 569, 570 speed of fixed value in free space, 673–674, 673, 675 luminiferous ether explanation, 673–674, 673 Michelson–Morley experiment, 674, 674 permeability and permittivity of free space and, 565 value of, 1, 565, 673 variation with medium, 582n, 584 total internal reflection, 590–592, 590, 591, 592 visible, 569, 570 Lightbulbs current in, 446 failures in, 457 in parallel connection, 468–469, 468, 471 in series connection, 467 symbols for, 427, 427 three-way, 471, 471 Light-colored clothing, 290 Lightning rods, 402 Lightning strikes, magnetic fields and, 498 Limiting angle of resolution, 664, 665–667 Linear accelerators, 419 Linear density, wave speed and, 345 Linearly polarized waves, 643, 643 Linear momentum, 124 Liquid-drop model, 759 Liquids See also Fluids compressibility of, 205, 209 speed of sound in, 357, 357t, 358 surface effects of, 230–231, 230, 231 surface tension in, 229–230, 229 thermal expansion of, 256–257, 257 Lithium, electronic configuration of, 724 Lloyd’s mirror, 631–632, 632 Load, compressibility and, 208 Load resistance, 465–466 Logarithms, 359 Loma Prieta earthquake (1989), resonance in, 373–374 Longitudinal waves, 341–342, 342, 357 Loop rule, 473–475, 473, 474 Loudspeaker operation, 498, 498 Luminiferous ether, 673–674, 674 Lyman series, 715, 717 M Magnet(s), 491–493 attraction and repulsion in, 491–492 cutting, 491 Earth as, 493, 493 electromagnets, 510–512, 510, 512, 513 individual atoms as, 512, 512 permanent, 513 soft vs hard, 492, 513 steering, 510, 510 superconducting, 455–456, 456, 494 Magnetic bacteria, 493 Magnetic domains, 513, 513 Magnetic fields, 494 around antennas, 564, 564, 565 bacteria and, 493 of current loops and solenoids, 509–512, 509, 510, 512, 522–523, 522 of the Earth, 493, 493, 495–496, 498–499, 509 electromagnetic waves and, 566 energy stored in, 539–540 field lines in, 492–493, 492, 493 induced emf from changing, 521–523, 521, 522 Lenz’s law, 524–527, 525, 530–531, 530 lightning strikes and, 498 of long, straight wires, 505–507, 505, 506 magnitude and direction of, 492, 494–495, 495, 497 Maxwell’s predictions on, 561–562 motional emf, 527–529, 527, 528 motion of charged particles in, 502–504, 502, 503, 504 notation for, 496 quantum states and, 720, 722 separation of radiation in, 738, 738 sizes of, 494 I.9 torque on a current loop in, 499–502, 499, 501 of twisted wires, 510 Magnetic resonance imaging (MRI), 752, 752 Magnetism, 491–513 See also Magnetic fields; Magnets attraction and repulsion in, 491–492, 507–508, 507 declination, 493 dusting for fingerprints and, 492, 492 electric motors and, 502, 502 electromagnetic pumps and, 498, 498 Faraday’s law of magnetic induction, 523–527, 524, 525 Lenz’s law, 524–527, 525, 530–531, 530 lightning strikes and, 498 loudspeaker operation, 498, 498 magnetic domains, 512–513, 512, 513 magnetic flux, induced emf from, 522–523, 522, 523 magnetic forces, 494 direction of, 494–495, 494, 495 formula for, 494 gravitational force vs., 495–496, 498–499 magnitude of, 494, 496, 497 origin of, on a wire, 497 on a proton in Earth’s magnetic field, 495–496 right-hand rule number 1, 495, 495 between two parallel conductors, 507–509, 507 magnetic moment, 500–501 magnetic poles, 493, 493 monopoles, 562 solenoids, 510–512, 510, 512, 536–537 Magnetite, 491, 493 Magnification angular, 659–660, 662–664 in combinations of lenses, 619–621, 620 in compound microscopes, 660–662, 660, 661 in concave mirrors, 602 in convex mirrors, 608 enlargement compared with, 600 in flat mirrors, 599–600 in lenses, 614, 617–619, 617, 618 of refracting surfaces, 609 in simple magnifiers, 658–660, 658 in telescopes, 662–664, 663, 664 Magnifying lenses, 658–660, 658 Malus’s law, 644 Manometers, 215–216, 215, 216 Marsden, Ernest, 713, 713 Masonry, thermal conduction through, 285 Mass approximate values of measured, 2–3, 2t atomic, 735 center of, 180–181 determination from Kepler’s laws, 166–167 determination from Newtonian gravitation, 161–162 gravitational, 687 inertial, 687 mass-to-charge ratio, 503–504, 503t, 504 molar, 258 moment of inertia and, 184 of neutrinos, 744 Newton’s first law and, 63 Newton’s second law and, 63–66 of subatomic particles, 391t, 734–735, 734t units of, 1–2, 2t, 63, 64t, 735 Mass–energy equivalence equation, 684, 684n Mass number, 734, 735, 744 Mass spectrometers, 503–504, 503t, 504 Mass-to-charge ratio, 503–504, 503t, 504 Math Focus common logarithms, 359 finding constants, 30 modeling physics with straight lines, 256 one-dimensional elastic collisions, 135 quadratic formula, 31 rms current, 548 I.10 Index Math Focus (Continued ) systems of equations, 71–27 torque and supplementary angles, 177 two-dimensional collisions, 138 Matter dark, 205, 775 dual nature of, 703–706, 705 fundamental particles of, 3, radiation damage in, 750–751, 750t states of, 204–205, 204, 205 wave frequency, 704 Maxima, in diffraction, 640–642 Maxwell, James Clerk, 561–562, 568, 577 Maxwell velocity distribution, 265, 265 Measurement See also Units of current and voltage, 449–450, 449 significant figures in, 5–8 uncertainty in, 5–6 unit conversions, Mechanical energy See Conservation of mechanical energy Mechanical equilibrium, torque and, 178 Mechanical equivalent of heat, 273 Mechanical waves, energy transfer through, 110 Medical applications apnea monitors, 526–527 cardiac pacemakers, 459 defibrillators, 434–435, 444 electrocardiograms, 458–460, 458, 459, 460 fiber optics, 592, 592 implanted cardioverter defibrillators, 460, 460 irradiation of medical equipment, 751 of lasers, 728 magnetic resonance imaging, 752, 752 positron emission tomography, 765 of radiation, 750–752, 750t, 752 radioactive tracers, 751 sphygmomanometers, 216, 216 of ultrasound, 355–356, 356 Meitner, Lise, 686 Melting points, 279t, 454 Mendeleev, Dmitri, 724 Mercury (element) adhesive forces in, 230, 230 in barometers, 215, 215 in thermometers, 247–248, 247 Mercury (planet), orbit of, 688 Mesons eightfold way and, 770, 770 properties of, 766, 766t quark color in, 772, 772 quark composition in, 771, 771t Metabolic rate, 320–321, 320t Metabolism, 319–321, 320t Metal detectors in airports, 558 Metals, work functions of, 696, 696t Metastable states, 728, 728 Meters, Metric units, 1–3, 3t, 4t See also Units Michelson, Albert A., 674 Michelson–Morley experiment, 674, 674 Micrometers, 568 Microscopes compound, 660–662, 660, 666–667 electron, 705–706, 705 magnification of, 661 x-ray, 706 Microwaves, 569, 569, 645, 774–775 Millikan, Robert, 388 Millikan oil-drop experiment, 396 Minima, in diffraction, 637, 639 Mirages, 612, 612 Mirror equation, 603 Mirror reflection, in elementary particles, 772 Mirrors, 599–608 aberrations, 621–622, 621, 622 concave, 601–603, 602, 603, 606–607 convex, 603–606, 604, 605, 608 day and night settings on rearview, 601, 601 flat, 599–601, 599, 600 front vs back sides of, 604 Lloyd’s, 631–632, 632 mirror equation, 603 ray diagrams for, 604–606, 605 reversibility of light rays and, 606 side-view, 606, 606 sign conventions for, 604, 604t Mnemonics ELI the ICE man, 553n SOHCAHTOA, 11n Moderators, 761, 761 Molar mass, 258, 264–265 Molar specific heats, 302–304, 302t Moles, 258 Moment of inertia, 184 in batons, 185–186, 185, 186 conservation of angular momentum and, 191 for extended objects, 186–189, 187t, 188 formula for, 184–185, 184 in physical pendulums, 339 Momentum, 124–141 in alpha decay, 742 angular, 190–193, 191 in aerial somersaults, 192, 192 conservation of, 166, 191 in figure skating, 191–192, 191 forces on, 190 Kepler’s second law and, 166 spin, 512 in a spinning stool, 192–193, 192 archer on frictionless ice, 129–130, 129 ballistic pendulums and, 132–133, 133 conservation of, 128–130 angular, 166, 191 ballistic pendulums and, 132–133, 133 in elastic collisions, 130–131, 134–137, 134 in perfectly inelastic collisions, 131–134, 131, 133 relativity and, 683 statement of, 128–130, 128, 129 in elastic collisions, 130–131, 134–137, 134, 136 in electromagnetic waves, 566 in glancing collisions, 137–140, 137, 139 impulse–momentum theory, 125–127 in inelastic collisions, 130–134, 131, 133 linear, 124 in Newton’s second law of motion, 124 in nuclear reactions, 749 of photons, 684–685, 703 recoil, 129–130, 129 relativistic, 682–683 rocket propulsion, 140–141, 140 uncertainty principle and, 707–708, 707 Monopoles, electric, 562 Monopoles, magnetic, 491, 562 Moon, helium-3 mining on, 764 Morley, Edward W., 674 Moseley, Henry G J., 726 Moseley plots, 726, 726 Motion of fluids, 220–226 Bernoulli’s equation, 223–226, 223, 224, 224, 225, 226 in blood vessels, 227, 227 equation of continuity, 221–223, 222, 226, 226 in garden hoses, 222–223, 223 golf balls and, 226–227, 227 in home plumbing, 228–229, 228 of ideal fluids, 221 in a pipe, 226, 226, 232, 232 Poiseuille’s law, 232–233, 232 Reynolds number, 234 sedimentation rate, 237, 237 streamline flow, 220–221, 221 through a viscous medium, 236–237, 236, 237 transport phenomena, 234–237, 235, 236, 237 turbulent flow, 221, 221, 227, 234 viscous flow, 221, 231–232, 232 laws of, 61–82 applications of, 69–76 forces in, 61–62, 61 Kepler’s laws of planetary motion, 165–168, 166 Newton’s first law, 62–63, 174–175 Newton’s second law, 63–68, 64, 65, 66, 124, 184 Newton’s third law, 68–69, 68, 69 in one dimension, 18–36 acceleration, 24–26, 24, 25, 26 constant acceleration in, 28–32, 28, 29t, 30, 31, 32 displacement, 18–19, 19 freely falling objects, 33–35, 34 motion diagrams, 26–27, 27 problem-solving strategies for, 29 quadratic formula, 31 velocity, 19–23, 21t, 22 pendulum, 337–339, 337, 339 periodic, 328–330, 328 planetary, Kepler’s laws of, 165–168, 166 projectile, 48–53, 48 action-reaction pairs in, 68 calculations of, 51–53, 51, 52 horizontal and vertical motions of, 49–50, 49 problem-solving strategies for, 50 rotational angular acceleration, 147, 149–150, 183–189, 183, 184 angular frequency, 333 angular momentum, 190–193, 190, 191, 192 angular speed, 147–149, 148 basic equations of, 150–151, 150t center of gravity and, 179–181, 180, 181 centripetal acceleration, 154–160, 154, 155, 157, 158, 159 under constant angular acceleration, 150–151 Kepler’s laws, 165–168, 166, 167t kinetic energy in, 189–190, 189, 190 moment of inertia, 184–189, 184, 185, 186, 187t, 188 Newtonian gravitation and, 160–165, 161, 164t relation between angular and linear quantities, 151–154, 152 right-hand rule for, 156–157, 157 rotational equilibrium, 178–179, 178, 181–183, 182, 183 sign conventions in, 149–150 simple harmonic motion compared to, 331–334, 332 tangential acceleration, 152 tangential speed, 152, 152, 156 torque, 174–178, 174, 175, 176, 177 under zero torque, 184 simple harmonic Hooke’s law and, 105, 328–330 pendulum motion and, 337–339, 337 position, velocity, and acceleration with time, 334–337, 335 sinusoidal curves, 335–336, 335 uniform circular motion compared to, 331–334, 332 velocity with position, 330–331, 330, 332 in two dimensions projectile motion, 48–53, 48, 49, 51, 52 relative velocity, 53–55, 53, 54 vector quantities in, 47–48, 47 Motional emf, 527–529, 527, 528, 528 Motion diagrams, 26–27, 27 Motors, electric, 502, 502, 534–535, 534 Mount Palomar telescopes (California), 663, 667 Moving frames of reference, 53 MRI (magnetic resonance imaging), 752, 752 Index Müller, K Alex, 455 Multimeters, 449, 450 Multiplication significant figures in, of vectors by scalars, 42 Muons, 678–679, 679, 766–767, 766t Musical instruments guitar fundamentals, 345, 371–372, 371 harmonic series, 369, 370–372, 370 pipe organs, 374–375, 374 sour notes, 377–378 tuning, 370, 377 Myopia (nearsightedness), 656, 656, 658 N Nanocoulombs, 391 Nanometers, 568 Natural convection, 287, 287 Natural logarithms, 476 Natural radioactivity, 747, 747 Near point, 655, 655, 658–660, 658 Nearsightedness, 656, 656, 658 Ne’eman, Yuval, 770 Negative acceleration, 24 Negative charges discovery of, 387–388, 388 electric field lines and, 399, 399, 401, 401 Negative vectors, 34, 42 Neon signs, 714 Neptunium, decay series starting with, 747, 747t Neurons, 481–484, 482, 483 Neutrinos, 744, 762, 766t, 767 Neutron number, 734, 741 Neutrons charge and mass of, 734–735, 734t decay of, 768–769 discovery of, 748 in nuclear reactors, 760–761, 760 properties of, 3, Newton, Isaac, 160, 165 Newtonian focus, 663, 663 Newton-meters, 90, 91, 175 Newtons, 63–64 Newton’s first law of motion, 62–63, 174–175 Newton’s law of universal gravitation, 66 Newton’s rings, 634–635, 634, 635 Newton’s second law of motion, 63–68 accelerating objects and, 73–74 gravitational force and, 66, 66 momentum and, 124 problem-solving strategies for, 70–71 rotational analog of, 174, 183–184, 183 statement of, 63, 124 units of force and mass in, 63–66, 64, 64t, 65 weight and, 66–68 Newton’s third law of motion, 68–69, 68, 69 Nichrome wire, resistance of, 452–453, 457 Night vision, 291 Nitrogen, Maxwell speed distribution for, 265 Noble gases, electronic configuration for, 724–725, 725t Nodes, in standing waves, 369, 369 Noise-level regulations, 361 Nonconservative forces, 96–97, 97, 103–104, 104 Nonohmic materials, 451 Nonreflective coatings, 635, 635 Normal force, 69 North pole, of magnets, 491, 493 Notation for alternating current source, 547 for antiparticles, 765 for circuit elements and circuits, 427, 427, 451, 549t for electric potential difference, 425 for electrons, 744 for inductors, 538, 538 for limits, 22 for magnetic fields, 496 for resistors, 427, 427, 451 scientific, for self-induced emf, 535, 535 for shells and subshells, 721t for vector quantities, 10, 19, 41, 65 Nuclear bombs, 760 Nuclear fission, 758–761 energy from, 686, 759–760 nuclear reactors, 760–761, 760, 761 sequence of events in, 758–759, 759 Nuclear force, 736 Nuclear fusion, 686–687, 761–764, 763 Nuclear magnetic resonance, 752, 752 Nuclear physics, 734–752 binding energy, 737, 738 decay processes, 741–747, 742, 744 medical applications of radiation, 750–752, 750t, 752 natural radioactivity, 747, 747 nuclear reactions, 747–750, 747t nuclear stability, 736, 736 properties of atomic nuclei, 734–736, 734t, 735, 736 Q values, 749 radioactivity, 738–741, 738, 739 Nuclear reactions, 747–750 Nuclear reactors, 760–761, 760, 761 Nucleons, 734 See also Neutrons; Protons Nucleus, atomic, 713, 713 binding energy in, 737, 738 charge and mass in, 734–735, 734t density of, 735 size of, 735 stability of, 736, 736t, 764 strong force in, 62, 764, 764, 765t, 772–773, 773 O Object distance, 599–600, 599 Occupational radiation exposure limits, 751 Ocean levels, rising, 256 Oersted, Hans, 505, 521 Ohm, Georg Simon, 451 Ohmic materials, 451, 451 Ohms, 450, 551 Ohm’s law, 450–451, 450, 451, 554 Omega-minus particles, 770, 771–772 Onnes, H Kamerlingh, 455 Open-circuit voltage, 465 Optical fibers, 592, 592 Optical instruments, 653–667 cameras, 425–426, 580, 621, 653–654, 653 compound microscopes, 660–662, 660, 666–667 eyes, 654–658, 654, 655, 656, 666 resolution of single-slit and circular apertures, 664–667, 664, 665, 666 simple magnifier, 658–660, 658 telescopes, 662–664, 662, 663, 664 Orbital magnetic quantum number, 720 Orbital quantum number, 720 Orbits de Broglie wavelengths and, 715–716 geosynchronous, 167–168 Kepler’s laws on, 165–168, 166, 167t Order number, 629, 640–642 Order-of-magnitude estimates, 9–10 Origin, in coordinate systems, 10–11, 10, 11 Oscillating charges, electromagnetic waves from, 563–564, 564 OSHA noise-level regulations, 361 Osmosis, 235 Overdamped oscillators, 340, 340 Overtones, 369, 370–371, 375 Oxygen consumption, metabolic rate and, 320, 320t Ozone, 570 P Pacemakers, 459 Pain threshold, 359–360, 379, 379 Paintings, x-ray studies of, 699 I.11 Parabolic trajectories See Projectile motion Parallel connections capacitors in, 427–429, 428, 429, 432–433, 432, 471 lightbulbs in, 468–469, 468, 471 resistors in, 468–473, 468, 469, 471, 472 Parallel plate capacitors, 425–427 design of, 424–425, 424 dielectrics in, 435, 435, 437–438 electric fields in, 407, 407 properties of, 425–427, 426 Parent nucleus, 741 Particle accelerators, 420 Particle physics See Elementary particles Pascal, Blaise, 213 Pascals, 206, 211 Pascal’s principle, 213–215, 214 Paschen series, 715, 717 Path difference, 629, 630 Pauli, Wolfgang, 721, 744 Pauli exclusion principle, 722, 723–725, 724t, 725t, 771–772 Pendulum movement, 337–339 ballistic, 132–133, 133 in clocks, 338 measuring the gravitational constant from, 339 periodic motion of, 337–339, 337 physical pendulum, 339, 339 in prospecting, 338–339 resonance in, 373, 373 time dilation and, 679–680 Penzias, Arno A., 774, 774 Perfectly elastic collisions, 134 Perfectly inelastic collisions, 131–134, 131, 133 Period(s) orbital, 166 in pendulum motion, 338, 339, 679–680 in simple harmonic motion, 328, 332–334, 336 Periodic motion, 328–330, 328 Periodic table, 724–725, 725t Permanent magnets, 513 See also Magnets Permeability of free space, 505, 565 Permittivity of free space, 404, 565 Perpetual motion machines, 316 PET (positron emission tomography), 765 Phase angle, for series circuits, 555–556, 555t Phase changes in comet collisions, 282–283 latent heat and, 278–283, 279 from mechanical energy, 281–283 power output and, 557 on reflection from higher refractive index, 632, 632 on reflection from thin films, 633, 633 sublimation, 278 temperature vs energy during, 278–281, 279 of water, 278–281, 279, 279t Phasor diagrams, for RLC circuit, 553–554, 553, 554 Phasors, 553 Photocells, 698 Photoelectric effect, 577–578, 695–698, 695, 696, 696t, 697 Photoelectrons, 695–698, 695 Photons characteristic x-rays and, 726–727, 726 Compton effect, 701–703, 701 from electron jumps, 717–718, 718 in electroweak theory, 772–773, 773 as elementary particle, 764, 765t energy of, 578, 696, 703 in gamma decay, 745 momentum of, 684–685, 703 from particle–antiparticle annihilation, 765 photoelectric effect and, 577–578, 696–697, 696t, 697 stimulated absorption process, 727–728, 727 stimulated emission process, 728, 728 virtual, 764, 765 wavelength of, 703 I.12 Index Physical pendulums, 339, 339 Piano tuners, 377–378 Piezoelectric effect, 355, 355 Pions, 766, 766t Pipe organs, 374–375, 374 Pipes bursting from thermal expansion, 257 fluid dynamics in, 226, 226, 232, 232 standing waves in, 374–376, 374, 376 Planck’s constant, 578, 694 Planck’s theory, 694, 694 Plane of polarization, 643 Plane polar coordinates, 11, 11 Planetary motion, Kepler’s laws of, 165–168, 166 Plane waves, 362–363, 362, 564–565, 565 Plasma (state of matter), 204, 205, 763 Plasma confinement time, 763 Plasma ion density, 763 Platinum resistance thermometers, 454–455 Point sources, of sound waves, 361–363 Poise (unit), 232 Poiseuille, J L., 232 Poiseuille’s law, 232–233, 232 Polar coordinate system, 11–12, 11 Polarity of capacitors, 437 of induced emf, 524–526 of stereo speakers, 368 Polarization, 438 of electric charges, 390 of light waves, 642–647, 643, 644, 646, 647 of microwaves, 645 in molecules, 438, 438 by reflection, 645–647, 646 by scattering, 647, 647 by selective absorption, 643–645, 644 in sunglasses, 646–647 Polarizers, 643–645, 644 Polarizing angle, 646, 646 Polaroid, 643 Polaroid sunglasses, 646–647 Poles, magnetic, 491, 493 Polonium, 738 Population inversion, 728 Position vs time graphs, 21–22, 22, 23, 28 Positive charges discovery of, 387, 388 electric field lines and, 399–400, 399, 400 Positron emission tomography (PET), 765 Positrons, 738, 745, 762, 765 Potassium ions, 483–484 Potential(s) See also Electric potential action, 481, 483–484, 483 equipotentials, 424, 424 stopping, 695 Potential difference See Electric potential; Voltage Potential energy, 97–109 conservation of mechanical energy and, 101 conservative forces and, 98 elastic, 105–106 electrical, 413–417, 413, 414, 414 gravitational, 97–104, 98, 98, 102, 103, 162– 164 spring, 104–109, 105, 107, 108 Pounds, 64 Power, 456 in alternating-current circuits, 556–558 average, 111, 112–113, 557 from Carnot engines, 315 delivered to a resistor, 456 electrical energy and, 456–458 from fission reactors, 760–761, 760, 761 from fusion reactors, 763 of a lens, 657 long-distance transmission of, 560–561, 561 overview of, 110–113, 112 in transformers, 560–561, 561 wave intensity and, 359 Power factor, 557 Prefixes, unit, 3t Presbyopia, 656 Pressure absolute, 215 of an ideal gas, 263 atmospheric, 211, 212, 215 average, 211 bed of nails trick, 211, 211 blood, 216, 216 fluid speed and, 224–225, 224, 225 gauge, 215 measurements of fluid, 210, 211, 215–216, 215, 216 molecular model for, 262–264, 262 Pascal’s principle, 213–215, 214 radiation, 566, 566 standard temperature and pressure, 259 variation with depth, 212–215, 212, 213, 214 Pressure waves, 342, 342 Primary coils, 521, 521 Primary winding, 559–560, 559 Principal axis, of concave mirrors, 602, 602 Principle of equivalence, 688 Principle of relativity, 675, 678 Prism spectrometer, 586–587, 586, 587 Probability electron clouds and, 723, 723 entropy and, 318–319, 318t, 319 in radioactive decay, 741 Schrödinger’s wave function and, 706 Problem-solving strategies, 12–14 for accelerated motion, 29 for alternating current, 555 applying Kirchhoff’s rules to a circuit, 474 calculating electric forces and fields, 397 for calorimetry with phase changes, 280 for complex capacitor combinations, 431–432 for conservation of mechanical energy, 101–102 for electric potential, 421 for energy methods and rotation, 189–190 for forces that cause centripetal acceleration, 157–158 for Newton’s second law, 70–71 for objects in equilibrium, 181–182 for one-dimensional collisions, 135 for projectile motion, 50 for relative velocity, 53 simplifying circuits with resistors, 471–472 for thin-film interference, 635 for two-dimensional collisions, 138–139 Projectile motion, 48–53, 48 action-reaction pairs in, 68 calculations of, 51–53, 51, 52 horizontal and vertical motions of, 49–50, 49 problem-solving strategies for, 50 Projection angles, 49, 50 Proper length, 681–682 Proper time, 678 Protein structure, from x-ray diffraction, 700 Proton–proton cycle, 761–762 Protons in atoms, 3, charge and mass of, 391, 391t, 734–735, 734t in Earth’s magnetic field, 495–496 in solenoids, 511 stability of, 767, 773 Pupils, 654, 654 PV diagrams, 298–300, 298, 299 Pyrex® glass, 252, 252t Pythagorean theorem, 11, 13–14, 139, 155 Q QCD (quantum chromodynamics), 772 QRS pulse, 459 Quadratic formula, 31 Quantum chromodynamics (QCD), 772 Quantum mechanics atomic transitions and lasers, 727–729, 727, 728, 729 Bohr atomic model and, 715–720, 715, 716, 717, 718 characteristic x-rays, 726–727, 726 correspondence principle, 719 electron clouds, 723, 723 hydrogen atom and, 720–723, 720, 721, 721t, 723 Pauli exclusion principle, 722, 723–725, 724t, 725t positrons in, 738, 745, 762, 765 principal quantum numbers, 694, 717–718, 720–721, 721t Quantum numbers for hydrogen atom, 721t orbital, 720, 721t orbital magnetic, 720, 721t principal, 694, 717–718, 720–721, 721t of quarks, 771, 771t shells and subshells and, 720–721, 721t, 724, 724t spin magnetic, 721–723, 721 strangeness, 769–770, 769 Quantum physics, 693–708 See also Quantum mechanics blackbody radiation, 693–694, 693, 694 Compton effect, 701–703, 701 correspondence principle, 719 dual nature of light and matter, 703–706, 705 electron microscopes, 705–706, 705 hydrogen atom and, 720–723, 720, 721, 721t, 723 photocells and, 698 photoelectric effect, 695–698, 695, 696, 696t, 697 Planck’s theory, 694, 694 uncertainty principle, 707–708, 707 wave equation for hydrogen, 720–723, 720, 721, 721t, 723 wave function, 706 x-ray diffraction, 698–699, 698, 699 Quantum states in Bohr model, 717, 719–720 energy and, 694 ground state, 717, 724–725, 725t, 727–729, 727 for hydrogen atoms, 721–723, 721t Pauli exclusion principle and, 722, 723–725, 724t, 725t spin and, 721–723, 721 Quantum tunneling, 761 Quarks, 770–772 charges on, 388n color in, 771–772, 772 as fundamental particles, 3, 764 properties of, 771, 771t Queckensted test, 244 Q values, 749, 758, 762 R Rad (radiation absorbed dose), 750–751 Radians, 11, 147–149, 147, 147, 333, 337 Radiation blackbody, 693–694, 693, 694, 775, 775 cosmic background, 774–775 medical applications of, 750–752, 750t, 752 around nuclear reactors, 761 occupational exposure limits, 751 radiation pressure of light, 566, 566 thermal, 289–291, 289, 290 thermometers, 290, 290 units of, 750–751 Radioactive dating, 745, 746–747 Radioactivity, 738–752 alpha decay, 741–743, 742 beta decay, 743–745, 744 decay constants and half-lives, 739–741, 739 decay processes, 741–747, 742, 744 discovery of, 738 gamma decay, 745 natural vs artificial, 747, 747 nuclear reactions, 747–750 Index practical uses of, 745–747, 745 tracers, 751 types of radiation in, 738, 738 units of, 740, 750–751 Radio telescopes, 667 Radio waves, 563, 568–569, 569, 570 Radios, tuning circuits of, 558 Radium, 738, 740–743, 742 Radon detection, 746 Rainbows atmospheric, 587, 587 on compact discs, 641, 641 Rainy roads, reflection on, 579, 579 Rarefaction, 354 Ray approximation, 578, 578 Ray diagrams for mirrors, 604–606, 605 for thin lenses, 615–616, 616 Rayleigh’s criterion, 665 Rays, 362, 362 RBE (relative biological effectiveness), 750–751, 750t RC circuits, 475–479, 476, 477 Reaction forces, 68 Real images, 599, 602 Recoil, 129–130, 129 Rectangular coordinate system, 10–11, 10, 44, 44 Red eyes in flash photography, 580 Reference circle, 334, 335 Reference frames See Frames of reference Reference levels, 99–100, 99 Reference lines, 11, 11, 148, 148 Reflecting telescopes, 662, 663 Reflection angle of, 580, 580 complete, 566 double reflections, 580–581, 580 fiber optics, 592, 592 Huygens’ principle and, 588–590, 589 interference patterns from, 631–632, 632 nonreflective coatings, 635, 635 overview of, 347–348, 347, 348, 578–581, 579, 580 phase changes on, 632–633, 632, 633 polarization by, 645–647, 646 red eyes in flash photographs, 580 seeing the road on a rainy night, 579, 579 specular vs diffuse, 579, 579 total internal reflection, 590–592, 590, 591, 592 in ultrasound imaging, 355 Refracting telescopes, 662, 663 Refraction, 581–585 at air-water boundary, 591–592, 591, 609, 611, 611 angle of, 581–585, 581, 582, 583 atmospheric, 612, 612 chromatic aberration, 621–622, 622 flat refracting surfaces, 610, 610, 611, 611 Huygens’ principle and, 588–590, 589 images formed at spherical surfaces, 608–611, 609, 610, 611 index of, 582–584, 582t magnification from, 609 mirages, 612, 612 sign conventions for, 609, 609 Snell’s law of, 583–585, 583 spherical aberrations, 602, 602, 621, 621 through glass, 583–584, 583 wave speed and, 582 Refractive index See Index of refraction Refractive myopia, 656 Refrigerators, 311–312, 311 Relative biological effectiveness (RBE), 750–751, 750t Relative velocity, 53–55, 53, 54 Relativistic energy, 683–687 Relativistic momentum, 682–683 Relativity, 672–689 constant speed of light in free space, 673–674, 674, 675 energy and, 683–687 Galilean, 672–673, 673 general, 687–689, 687, 689 length contraction, 681–682, 681 muons and, 678–679 principle of, 675, 678 relativistic momentum, 682–683 simultaneity and, 675–676, 676 tests of, 688–689, 689 time dilation, 676–680, 677, 678, 679 twin paradox, 680–681, 680 Rem (roentgen equivalent in man), 751 Reproduction constant, in nuclear fission, 760 Resistance, 450 equivalent, 467, 469–470, 472–473, 472 internal, 465–466, 465 load, 465–466 Ohm’s law and, 450–451, 450, 451, 554 resistivity and, 451–455, 452t in superconductors, 455–456, 455, 456 temperature variation of, 453–455, 454 thermometers, 454–455 Resistivity, 452 overview of, 451–453, 452t of superconductors, 455, 455t temperature coefficient of, 452t, 454–455 Resistors in alternating current circuits, 547–550, 547, 548 combined series and parallel connections, 472–473, 472 in energy transfer, 456–457 equivalent, 467, 469–470, 472–473, 472 in parallel, 468–473, 468, 469, 471, 472 problem-solving strategies for, 471–472 in RC circuits, 475–479, 476, 477 in RLC circuits, 557 in RL circuits, 538, 538 in series, 466–468, 466, 467, 470 symbols for, 427, 427, 451 voltage drop across, 557 Resolution in microscopes, 666–667 Rayleigh’s criterion, 665 of single-slit and circular apertures, 664–666, 664, 665, 666 in telescopes, 664, 667 Resonance, 373–374, 373, 374, 375–376, 376 Resonance frequency, 558–559, 558, 563 Resonant frequency, 373 Resonators, 694 Rest energy, 684, 685 Restoring forces, 105, 327, 337, 337 Resultant vectors, 41, 43, 43 Retina, 654, 654 Retroreflection, 580 Reversible processes, 313, 313 Reversible waves, 606 Revolutions per minute, 149 Revolving doors, 175–176, 175 Reynolds number, 234 Right-hand rule(s) for direction of wave propagation, 565 number (for direction of magnetic force), 495, 495 number (for direction of magnetic field), 505, 505 in screw threads, 156–157, 157 torque and, 176, 176 Right triangles, 11, 11 RL circuits, 538–540, 538 RLC series circuits, 553–558 ELI the ICE man mnemonic, 553n impedance and, 554–555, 555t phase angles in, 555–556 phasor diagrams of, 553–554, 553, 554 problem-solving strategies for, 555 resonance in, 558–559, 558 rms (root-mean-square) current, 548–550, 549t, 551–552 rms (root-mean-square) speed, 264–265, 265t, 448 I.13 rms (root-mean-square) voltages, 549, 549t, 551 Roadway flashers, 477, 477 Rocket propulsion, 140–141, 140, 229 Rocket thrust, 141 Rods, 654 Roentgen, Wilhelm, 698 Roentgens, 750 Roller coasters, circular loops in, 159–160, 159 Root-mean-square (rms) speed, 264–265, 265t, 448 Rotational equilibrium, 178–179, 178, 182–183, 184 Rotational kinematics, 150–151, 150t See also Rotational motion Rotational kinetic energy, 189–190, 189, 190 Rotational motion, 147–169 angular acceleration, 147, 149–150, 183–189, 183, 184 angular frequency, 333 angular momentum, 190–193, 190, 191, 192 angular speed, 147–149, 148 basic equations of, 150–151, 150t center of gravity and, 179–181, 180, 181 centripetal acceleration, 154–160, 154, 155, 157, 158, 159 under constant angular acceleration, 150–151 Kepler’s laws, 165–168, 166, 167t kinetic energy in, 189–190, 189, 190 moment of inertia, 184–189, 184, 185, 186, 187t, 188 Newtonian gravitation and, 160–165, 161, 164t relation between angular and linear quantities, 151–154, 152 right-hand rule for, 156–157, 157 rotational equilibrium, 178–179, 178, 181–183, 182, 183 sign conventions in, 149–150 simple harmonic motion compared to, 331–334, 332 tangential acceleration, 152 tangential speed, 152, 152 torque, 174–178, 174, 175, 176, 177 under zero torque, 184 Rounding numbers, 6, 7–8 Russell, John Scott, 342 Rutherford, Ernest atomic model of, 713–714, 713 discovery of the nucleus by, 735 on nuclear reactions, 747–748 on radon, 746 R values, 286–287, 286t Rydberg constant, 715, 717 Rydberg equation, 715, 717 S Safety charged capacitors and, 433 circuit breakers, 470, 479, 479, 481 in electrical storms, 402 electric shock, 480 ground fault interrupters, 480, 526, 526, 527 around nuclear reactors, 761 third wire on consumer appliances, 480, 481 Satellites, telecommunications, 167–168 Scalar quantities, 19, 41, 42 Scattering, polarization by, 647, 647 Schrödinger, Erwin, 706 Schwarzschild radius, 688–689 Scientific notation, Sea breezes, 275, 275 Secondary coils, 521, 521 Secondary maxima, in diffraction, 637 Secondary winding, 559–560, 559 Second harmonic, 369, 370–372, 370 Second law of motion, Newton’s See Newton’s second law of motion Second law of planetary motion, Kepler’s, 166, 166 I.14 Index Second law of thermodynamics, 309–316 entropy and, 316–319, 318t, 319 heat engines and, 309–316, 309, 310, 311, 313, 314 human metabolism and, 319–321, 320t Kelvin–Planck formulation of, 312–313 Seconds, Sedimentation rate, 237, 237 Seiches, 375 Selective absorption, polarization by, 643–645, 644 Selectively permeable membranes, 235 Self-induced emf, 535 Self-inductance, 535–537, 535 Self-sustained chain reactions, 760 Semiconductors, 389, 451, 451 Semimajor axis, 166 Series connections capacitors in, 429–433, 430, 431, 432 resistors in, 466–468, 466, 467, 470 RLC circuits, 553–558, 553, 554, 555t series resonance circuits, 558–559, 558 Shear modulus, 206t, 207, 207 Shear stress, 207, 207 Shells and subshells, 720–721, 721t, 724, 724t Shock absorbers, 334, 340, 340 Shock waves, 365 Side-view mirrors, convex, 606, 606 SIDS (sudden infant death syndrome), 526–527 Sigma baryons, 766t, 769 Sign conventions for concave mirrors, 602 for coordinate systems, 11 for Doppler effect, 365, 367 for electric fields, 395, 395 for electric flux, 403 for electric potential energy, 416 first law of thermodynamics and, 300–301 for gravitational potential energy, 162–163 for heat engines, 309 in Kirchhoff’s rules, 479 for latent heat, 278 for mirrors, 604, 604t negative acceleration, 24 for potential energy, 106 for refracting surfaces, 609, 609t for rotational motion, 149–150 for spring forces, 327, 328 for thermal energy transfer, 275 for thin lenses, 615–616, 615, 615t, 621 for torque, 175, 188 for velocity vectors, 34 for work calculations, 91, 92, 114, 298 Significant figures, 5–8, Silicon, in nonreflective coatings, 635, 635 Simple harmonic motion See Harmonic motion, simple Simple magnifiers, 658–660, 658 Simultaneity, relativity of time and, 675–676, 676 Sine function, 11, 43, 44 Single-slit diffraction dark fringe calculations for, 638–639, 638, 639 resolution of, 664–666, 664 Singularity, 689 Sinoatrial node (SA), 458–459, 458 Sinusoidal curves, 335–336, 335, 342 SI (Système International) units, 1–2, 3t, 4t See also Units Slopes of graphs acceleration from, 25–26, 25, 26 average velocity from, 21–23, 22, 23 formula for, 22 instantaneous velocity from, 22–23, 23 from tangent lines, 22–23, 23 Small-angle approximation, 630 Smoke detectors, ionization-type, 745–746, 745 Snell’s law of refraction, 583–585, 583 Snowshoes, 211 Soap bubbles, interference in, 632–636, 633, 634, 635, 636 Soddy, Frederick, 746 Sodium, photoelectrons from, 697 Sodium chloride, structure of, 205, 698, 698, 699–700, 700 Soft magnetic materials, 492, 513 SOHCAHTOA mnemonic, 11n Solar cells, nonreflective coatings on, 635, 635 Solar days, 2t Solenoids, 510–512, 510, 512, 536–537 Solids crystalline vs amorphous, 204, 205 elasticity in, 204–209, 204, 206t, 207 speed of sound in, 357, 357t, 358 structure of, 204, 204 thermal expansion of, 251–256, 252, 252t, 253, 254 Solitons, 342 Somatic damage, from radiation, 750 Sonic booms, 365 Sound waves, 354–380 beats and, 376–378, 377 characteristics of, 354–356, 355 Doppler effect on, 363–367, 363, 364 elastic properties and, 356–357, 372–373 energy and intensity of, 358–363, 360t force vibrations and resonance, 373–374, 373, 374, 375–376, 376 harmonic series, 369, 370–373 interference in, 367–368, 367, 368 longitudinal, 342, 354 in musical instruments, 370–372, 371 OSHA noise-level regulations, 361 producing, 354, 354 speed of, 356–358, 357t standing waves in air columns, 374–376, 374, 376 standing waves in solids, 369–373, 369, 370, 371 thunder, 357 ultrasound applications, 355–356, 356 South pole, of magnets, 491, 493 Spacecraft, sails for, 567–568 Space heaters, 457–458 Spacetime, curvature of, 688 Sparks, 536 Speakers, 366, 368, 498, 498 Special relativity, 675–687 See also Relativity length contraction, 681–682, 681 relativistic energy, 683–687 relativistic momentum, 682–683 simultaneity and relativity of time, 675–676, 676 time dilation, 676–680, 677, 678, 679 twin paradox, 680–681, 680 Specific gravity, 210 Specific heat, 274–276, 274t, 302–304, 302t Spectra (plural, spectrum) absorption, 715 characteristic x-rays, 726–727, 726 of electromagnetic waves, 568–570, 569, 570, 586 emission, 714–715, 714 Spectral lines, 586–587, 587, 714–715, 714 Spectrometers, identifying gases with, 586–587, 587 Specular reflection, 579, 579 Speed angular, 147–151, 148, 156 average, 19–20, 22 deceleration and, 24 drift, 447–449, 447 escape, 164–165, 164t, 265 fluid, 224–225, 224, 225 instantaneous, 22 of light fixed value in free space, 673–674, 673, 675 luminiferous ether explanation, 673–674, 673 Michelson–Morley experiment, 674, 674 permeability and permittivity of free space and, 565 value of, 1, 565, 673 variation with medium, 582n, 584 in projectile motion, 49 root-mean-square, 264–265, 265t, 448 of sound, 356–358, 357t tangential, 152, 152, 156 terminal, 81, 236–237 velocity compared with, 20–21, 21 wave, 343–346, 345, 582, 582n work–energy theorem and, 95 Spheres electric fields of charged, 404–405, 405 moment of inertia for, 187t surface area of, 361 Spherical aberrations, 602, 602, 621, 621, 663 Spherical mirrors concave, 601–603, 602, 603, 606–607 convex mirrors, 603–606, 604, 605, 608 spherical aberration, 602, 602, 621, 621 Spherical waves, 361–363, 361, 362 Sphygmomanometers, 216, 216 Spinal tap, 244 Spin angular momentum, 512 Spin magnetic quantum number, 721–723, 721 Spontaneous decay, 742 Spontaneous emission, 728, 728 Springs elastic collisions and, 136–137, 136 harmonic motion of, 333–334, 336–337 Hooke’s law for, 105, 206, 327–331, 328, 330 spring constants, 105, 327–329, 328 spring potential energy, 104–109, 105, 107, 108 work and, 106, 114–115, 114 Squids, axons in, 483 Standard Model of particle physics, 773, 773 Standard temperature and pressure (STP), 259 Standing waves in air columns, 374–376, 374, 376 in electron orbits, 716, 716 in harbors, 375 in stretched strings, 369–373, 369, 370, 371 Stars, 688, 689, 694 States of matter, 204–205, 204, 205 Static friction, 77–78, 77, 78t, 158, 158 Stationary frames of reference, 53 Steam engines, 309, 315–316 Steam point, 248, 250, 250 Steering magnets, 510, 510 Stefan–Boltzmann constant, 289 Stefan’s law, 289, 291 Step-up/step-down transformers, 560 Stimulated absorption process, 727–728, 727 Stimulated emission process, 728, 728 Stoke’s law, 236 Stopping potential, 695 STP (standard temperature and pressure), 259 Strain, 205, 209 Strangeness, 769–770, 769, 771, 771t Streamline flow, 220–221, 221 Stress, 205–207, 209 Stress–strain curves, 207, 207 String theory, 775 Strong force, 62, 764, 765t, 772–773, 773 Subatomic particles, energy of, 685–686 See also Elementary particles Sublimation, 278 Submarine periscopes, 591 Substitution method, 71 Subtraction significant figures in, vector, 42, 42 Sudden infant death syndrome (SIDS), 526–527 Sun evolution of eyes and, 570 mass of, 167t nuclear fusion in, 761–762 polarization of light from, 647, 647 radiant energy from, 289 seeing, below the horizon, 612, 612 Sunglasses, polarized, 646–647 Index Superconducting magnets, 455–456, 456, 494 Superconductors, 455–456, 455t, 456 Supercritical reactors, 761 Superposition principle, 346, 420 electric forces and, 391–394, 392, 393, 395 in electric potential of point charges, 420 in wave interference, 346–347, 369, 376 Supplementary angles, 177 Surface-area-to-volume ratio, 235 Surface tension, 229–230, 229 Symbols See Notation Symmetry breaking, 773 Systems, 97–98, 109–110 Systems of equations, 71–72 T Tacoma Narrows bridge collapse (Washington), 373, 374 Tangent function, 11, 43, 44 Tangential acceleration, 152–154, 155–156, 237 Tangential speed, 152–154, 152, 156 Tangent lines, slopes from, 22–23, 23 Tau leptons, 766t, 767 Telecommunications, fiber optics in, 592, 592 Telescopes, 662–664, 662, 663, 664, 666–667 Televisions, 419–420, 510, 510, 630 Temperature absolute, 249, 250 average kinetic energy and, 264 blackbody radiation and, 693–694, 694 body, 289 in calorimetry problems, 277–278 Celsius scale, 248, 250–251, 250, 276 critical, 455, 455t Fahrenheit scale, 250–251, 250 Kelvin scale, 249–251, 249, 250, 276 molecular interpretation of, 264–266, 265, 265t resistance and, 453–455, 454 as scalar quantity, 41 speed of sound and, 357 standard temperature and pressure, 259 of stars, 694 thermal conduction and, 283–284, 284t zeroth law of thermodynamics, 246–247, 247 Temperature coefficient of resistivity, 452t, 454–455 Tensile strain, 206 Tensile strength, 208, 209t Tensile stress, 206 Tension, 70, 70 Terminal speed, 81, 236–237 Teslas, 494, 522 Thermal conduction, 283–285, 283, 284t Thermal conductivity, 284, 284t Thermal contact, 246 Thermal efficiency, 310, 313, 314–316 Thermal equilibrium, 246–247, 247 Thermal expansion, 251–257 bimetallic strips, 253–254, 254 coefficient of area expansion, 254–255, 255 coefficient of linear expansion, 252–254, 252t, 253 coefficient of volume expansion, 256 compressional stress from, 275–276 limited range of models, 256 thermal expansion joints, 252, 252 unusual behavior of water, 256–257, 257 Thermal physics, 246–266 See also Heat ideal gas law, 257–261, 259, 261 kinetic theory of gases, 262–266, 262, 265, 265t thermal expansion, 251–257, 252t, 253, 254, 257 thermometers, 247–251, 247, 248, 249, 250 Thermal radiation, 289–291, 289, 290, 693–694, 693, 694 Thermals, 275, 275 Thermocline, 288, 288 Thermodynamics, 297–322 first law of, 300–309, 302t, 305, 307, 308t second law of, 309–316, 309, 310, 311, 313, 314 work and, 297–300, 297 zeroth law of, 246–247, 247 Thermograms, 290, 290 Thermography, 290, 290 Thermometers, 246–247 calibration of, 247–248 constant-volume gas, 248–250, 248, 249, 250 mercury, 247–248, 247 platinum resistance, 454–455 radiation, 290, 290 temperature scales, 249–251, 250 Thermonuclear fusion reactions, 762 See also Nuclear fusion Thermostats, 253–254, 254 Thin films interference in, 632–636, 633, 634, 635, 636 Newton’s rings, 634–635, 634, 635 path length through, 633–634, 633 phase changes on reflection from, 633, 633 problem-solving strategies for, 635 wedge-shaped, 636, 636 Thin-lens equation, 614–615 Thin lenses See Lenses Third harmonic, 369, 370–372, 370 Third law of motion, Newton’s, 68–69, 68, 69 Third law of planetary motion, Kepler’s, 166, 166 Thomson, J J., 713, 713 Thorium, decay series starting with, 747, 747, 747t Threshold energy, 749 Threshold of hearing, 359–360, 379, 379 Threshold of pain, 359–360, 379, 379 Threshold voltage, 698–699 Thrust, rocket, 141 Thunder, 357 Time approximate values of measured, 2–3, 2t gravity and, 688 moving vs stationary clocks, 678 proper, 678 in relativistic mechanics, 675–676, 676 time dilation, 676–680, 677, 678, 679 units of, Time constant(s) of an RC circuit, 476, 476, 478 of an RL circuit, 538–539, 538 Time dilation, 678 muons and, 678–679, 679 overview of, 676–678, 677 pendulum periods and, 679–680 proper time and, 678 twin paradox and, 680–681, 680 Tokamaks, 763, 763 Tonometers, 130 Top quarks, Torque, 174–189, 175 angular acceleration and, 183–189, 183, 184 angular momentum and, 190–193, 191, 192 axis of rotation, 176 batons and, 185–186, 185, 186 bicycle gears and, 185, 185 center of gravity and, 179–181, 180, 181 conditions for equilibrium, 178–179, 178 on a current loop in a magnetic field, 499–502, 499, 501 equilibrium examples, 181–183, 182, 183 on falling buckets, 188–189, 188 magnitude of, 176 moment of inertia, 184–189, 184, 185, 186, 187t, 188 Newton’s first law and, 175 Newton’s second law and, 183–184, 183 of revolving doors, 175–176, 175 on a rotating object, 184–185, 184 of seesaws, 178–179, 178 supplementary angles and, 177 of swinging doors, 177–178, 177 of weighted forearms, 182, 182 Torricelli, Evangelista, 215 I.15 Torricelli’s law, 225 Total acceleration, 155–156 Total energy, in relativistic mechanics, 684 Total internal reflection, 590–592, 590, 591, 592 Totally destructive interference, 367 Tracers, radioactive, 751 Trajectories See Projectile motion Transformers, AC, 559–561, 559, 561 Translational equilibrium, torque and, 178 Transmission axis, 643 Transmission electron microscopes, 705–706, 705 Transmutation, 742 Transport phenomena, 234–237, 235, 236, 237 Transverse waves, 341–342, 342, 564–565 Traveling waves, 341–344, 341, 342, 343, 344 Trebuchets, 202, 202 Triangle method of addition, 41, 42 Trigonometry in simple harmonic motion, 335, 335 trigonometric functions, 11–12 in two-dimensional collisions, 138–139 Triple point of water, 249 Tritium, 3, 687, 762–763 Tubes, sound waves in, 374–376, 374, 376 Tubular capacitors, 436, 436 Tuning forks, 354, 354, 375–376, 376 Turbulent flow, 221, 221, 227, 234 TV (television), 419–420, 510, 510, 630 Twin paradox, 680–681, 680 Two-body problems, 76, 80–81 Two-dimensional (glancing) collisions, 137–140, 137, 139 U Uhlenbeck, George, 721 Ultimate strength, 207 Ultrasonic waves, 355 Ultrasound, 355–356, 356 Ultraviolet (UV) light, 569, 570 Uncertainty, 5–6 Uncertainty principle, 707–708, 707, 765 Underdamped oscillation, 340, 340 Underwater vision, 609 Unified mass unit, 735 Uniform acceleration, 25 Units of acceleration, 4t, 24, 64t, 149 of angular acceleration, 149 of angular displacement, 148 of angular speed, 148 of area, 4t of capacitance, 425 conversion of, of decay activity, 740 of density, 209 of displacement, 18 of electric charge, 388, 508 of electric current, 445, 508 of electric fields, 394 of electric potential difference, 418 of energy, 98, 111, 121, 162, 423 of entropy, 316 of force, 63–64, 64t Gaussian system, 3, 4t of heat, 273 of inductance, 536 of inductive reactance, 551 of intensity of sound waves, 358 of ionizing radiation, 750 of kinetic energy, 95, 423 of length, 1, 735 of magnetic fields, 494 of magnetic flux, 522 of mass, 1–2, 63, 64t, 735 of momentum, 124 of power, 111 prefixes for, 3t of pressure, 211, 215 of radiation, 750–751 I.16 Index Units (Continued ) of resistance, 450 SI (Système International), 1–3, 3t, 4t of specific heat, 274 of speed, 19 stress, 206 of temperature, 249–251, 250 of torque, 175 unified mass, 735 U.S customary, 3, 4t of velocity, 4t of viscosity, 232 of wavelengths, 568 of weight, 66 of work, 90, 91 Universal gas constant, 259 Universal gravitation constant, 66, 339, 687 Universe, increase of entropy in, 316–317, 319 Unpolarized light, 643, 643 Up quarks, Upwelling, 256, 288, 288 Uranium alpha decay in, 741 decay series starting with, 747, 747t nuclear fission of, 686, 758–760, 759 in nuclear reactors, 760–761, 760 radon in mines of, 746 separating isotopes of, 504 U.S customary system of units, 3, 4t UV (ultraviolet) light, 569, 570 V Valence electrons, 643 Vascular flutter, 227, 227 Vector quantities characteristics of, 18–19 notation of, 10, 19, 41, 65 Vectors, 41–56 addition of, 41–43, 42, 43, 45–47, 46 algebraic addition of, 45–47, 46 components of, 43–47, 43, 44, 45, 46 equality of, 41, 41 on motion diagrams, 26–27, 27 negative, 42 in Newton’s second law, 63, 65 notation of, 10, 19, 41, 65 polar coordinates of, 12 in projectile motion, 48–53, 48, 49, 51, 52 subtraction of, 42, 42 in two dimensions, 47–48, 47 Velocity, 19–23 after perfectly inelastic collisions, 131–132, 131 average, 20–23, 21, 22, 23, 28, 47 in constant acceleration, 28–29, 29t escape, 164–165, 164t, 265 as a function of displacement, 29, 29t as a function of time, 29, 29t graphical interpretation of, 21–22, 22 in harmonic motion, 335–337, 335 instantaneous, 22–23, 23, 47 kinematics velocity equation, 64 relative, 53–55, 53, 54 in simple harmonic motion, 330–331, 330 speed compared with, 19–21, 21 in two dimensions, 47–50, 49 units of, 4t Velocity vs time graphs, 25–26, 25, 26, 28, 29 Venturi tubes, 224, 224 Verne, Jules, 164–165 Vibrational motion harmonic vs circular motion, 331–334, 332 Hooke’s law, 105, 327–331, 328, 330 pendulum motion and, 337–339, 337 resonance and, 373–374, 373, 374, 375–376, 376 standing waves and, 369–373, 369, 370, 371 Virtual images, 599, 604, 604, 605 Virtual photons, 764, 765 Viscosity coefficient of, 232, 232t fluid flow and, 221, 231–232, 232 motion through a viscous medium, 236–237, 236, 237 units of, 232 of various fluids, 232t Visible light, 569, 570 Volta, Alessandro, 445 Voltage See also Electric potential AC transformers and, 559–560, 559 in an AC circuit, 547–548, 548, 550–552, 550, 552 open-circuit, 465 phasor diagrams, 553–554, 553, 554 in RLC series circuits, 553–556, 553, 554 rms, 549, 549t, 550 terminology, 428 threshold, 698–699 Voltmeters, 450 Volts, 418, 465 Volume, units of, 4t W Water boiling point of, 248 cohesive forces in, 230, 230 compressibility of, 209 contact angles, 231, 231 density of, 210t, 257, 257 freezing point of, 248 latent heat of evaporation in, 278 latent heat of fusion in, 278 molecular geometry of, 438, 438 osmosis of, 235 phase changes of, 278–281, 279, 279t polarization of, 438, 438 refraction at water-air boundary, 591–592, 591, 609, 611, 611 specific heat of, 275, 275 surface tension of, 229–230, 229 thermal expansion of, 256–257, 257 triple point of, 249 Waterproofing agents, 231, 231 Watson, J D., 700 Watts, 111 Wave(s), 340–348 See also Wavelength; Wave optics avalanches from, 341 density, 342, 342 diffraction of, 636–642 discovery of, 577 of electrons, 704–706, 705 Fraunhofer, 637–639, 637, 639 Fresnel bright spots, 637, 637 gratings, 640–642, 640, 641, 698 order number in, 640–642 resolution in patterns, 664–666, 664, 665, 666 single-slit, 638–639, 638, 639 x-ray, 698, 698 Doppler effect on, 363–367, 363, 364 energy and intensity of, 358–363, 360t Huygens’ principle, 588–590, 588, 589 intensity of, 566–568 interference in conditions for, 627–628 constructive, 346, 346, 367, 629, 629, 633 destructive, 346, 347, 367, 629, 633, 638 imperfections in lenses and, 634–635, 634 from Lloyd’s mirror, 631–632, 632 nature of light and, 577 Newton’s rings, 634–635, 634, 635 nonreflective coatings, 635, 635 overview of, 346–347, 346, 347 positions of bright and dark fringes, 630–631 of sound waves, 367–368, 367, 368, 376–378, 377 in television signals, 630 in thin films, 632–636, 633, 634, 635, 636 wavelength measurement by, 631 in a wedge-shaped film, 636, 636 Young’s double-slit experiment, 628–631, 628, 629, 630 longitudinal vs transverse, 341–342, 341, 342 matter, 704 mirages, 612, 612 plane, 362–363, 362, 564–565, 565 polarization of, 642–647, 643, 644, 646, 647 reflection of angle of, 580, 580 double images, 580 double reflections, 580–581, 580 fiber optics, 592, 592 Huygens’ principle and, 588–590, 589 interference patterns from, 631–632, 632 nonreflective coatings, 635, 635 overview of, 347–348, 347, 348, 578–581, 579, 580 phase changes on, 632–633, 632, 633 polarization by, 645–647, 646 red eyes in flash photographs, 580 seeing the road on a rainy night, 579, 579 specular vs diffuse, 579, 579 total internal reflection, 590–592, 590, 591, 592 refraction of, 581–585 at air-water boundary, 591–592, 591, 611, 611 angle of, 581–585, 581, 582, 583 atmospheric, 612, 612 chromatic aberration in, 621–622, 622 flat refracting surfaces, 610, 610, 611, 611 Huygens’ principle and, 588–590, 589 images formed at spherical surfaces, 608–611, 609, 610, 611 magnification from, 609 mirages, 612, 612 sign conventions for, 609, 609 Snell’s law of, 583–585, 583 spherical aberrations, 602, 602, 621, 621 through glass, 583–584, 583 wave speed and, 582 resonance in, 373–374, 373, 374, 375–376, 376 seiches, 375 sign conventions for, 609, 609 solitons, 342 spherical, 361–363, 361, 362 standing, 369–376, 369, 370, 371, 374, 376, 716, 716 transverse, 564–565 ultrasonic, 355 wave fronts Doppler effect and, 364 Huygens’ principle and, 588–590, 588, 589 in ray approximation, 578, 578 of sound, 362, 362 wave speed, 343–344 index of refraction and, 582, 582n on strings, 344–346, 345 Young’s double-slit experiment, 628–631, 628, 629, 630 Wave function, 706, 723, 723 Wavelength, 343 of characteristic x-rays, 726–727 Compton, 702 cutoff, 697 de Broglie, 703–705, 715–716 dispersion and, 585–587, 586, 587 Doppler effect on, 364–365 in electron microscopes, 705 of electrons, 703–705 evolution of the eye and, 570 frequency and, 568 measured by interference, 631 overview of, 343–344, 344 of photons, 703, 717–718 refraction and, 583–585, 583 units of, 568 Wavelets, 588, 588 Wave mechanics See Quantum physics Wave optics, 627–647 Index change of phase from reflection, 631–632, 632 conditions for interference, 627–628 diffraction, 636–642, 637, 638, 639, 640 diffraction gratings, 640–642, 640, 641 polarization of light waves, 642–647, 643, 644, 646, 647 thin film interference, 632–636, 633, 634, 635, 636 Young’s double-slit experiment, 628–631, 628, 629, 630 Weak force, 62, 764, 765t, 772–773, 773 Webers, 494, 522 Weight, 66–68, 73–74 Weight loss, 321 Wetting agents, 231, 231 Wheels, rotating, 151 White clothing, 290 Wien’s displacement law, 694 Wilson, Robert W., 774, 774 Wire harmonics of, 372–373 levitating a, 508–509 magnetic fields of loops, 509–512, 509, 510, 512 magnetic fields of straight, 505–507, 505, 506 magnetic force between two, 507–509, 507 magnetic force on current-carrying, 496–499, 496, 497, 498 twisted, 510 Work, 90–97 See also Work–energy theorem in charging capacitors, 433–434, 433 by constant forces, 90–94, 90, 91, 92 electric potential energy and, 413–417, 413, 414, 422–423 entropy and, 319 in first law of thermodynamics, 300–301, 303–308 in fluid dynamics, 223–224 frictional, 93–94 gravitational, 98–99, 98, 163–164 from heat engines, 309–310, 309 in isobaric processes, 298–300, 298, 303–304, 308t, 399 kinetic energy and, 94–95, 94, 95 nonconservative forces and, 93–94, 97 spring forces and, 106, 114–115, 114 in thermodynamic processes, 297–300, 297 by a varying force, 113–115, 113, 114 Work–energy theorem, 95–96 converting caloric to mechanical energy, 273–274, 273 gravitational potential energy and, 99 nonconservative forces and, 97 rotational kinetic energy in, 189–190, 189, 190 spring forces and, 106 statement of, 95–96 for systems, 109 Work functions, 696, 696t I.17 X Xi baryons, 766t X-ray(s), 570, 570 characteristic, 699, 726–727, 726 Compton effect, 701–703, 701 diffraction of, 698, 698, 699–701, 699, 700 in electromagnetic spectrum, 569 microscopes, 706 quantum theory and, 699, 699 to study masterpiece paintings, 699 X-ray tubes, 698, 698 Y Yerkes Observatory (Wisconsin), 663 Young, Thomas, 577, 628–630, 628, 629, 630 Young’s double-slit experiment, 628–631, 628, 629, 630 Young’s modulus, 206–207, 206, 206t Z Zeeman effect, 720 Zeiss, Carl, 635 Zero-point energy, 250 Zeros, significant figures and, 6–7 Zeroth law of thermodynamics, 246–247, 247 Zonules, 655 This page intentionally left blank PHYSICAL CONSTANTS Quantity Symbol Value Speed of light in vacuum c 3.00 ϫ 108 Permittivity of free space Coulomb constant, 1/4pe0 Permeability of free space e0 ke 0 Elementary charge Planck’s constant Electron mass e h ប ϭ h/2 me Proton mass mp Neutron mass mn Avogadro’s number Universal gas constant Boltzmann’s constant Stefan-Boltzmann constant Molar volume of ideal gas at STP NA R kB s V Rydberg constant Bohr radius Electron Compton wavelength Gravitational constant Standard free-fall acceleration Radius of Earth (at equator) Mass of Earth Radius of Moon Mass of Moon RH a0 h/mec G g RE ME RM MM SI unit 10Ϫ12 8.85 ϫ 8.99 ϫ 109 1.26 ϫ 10Ϫ6 (4p ϫ 10Ϫ7 exactly) 1.60 ϫ 10Ϫ19 6.63 ϫ 10Ϫ34 1.05 ϫ 10Ϫ34 9.11 ϫ 10Ϫ31 5.49 ϫ 10Ϫ4 1.672 65 ϫ 10Ϫ27 1.007 276 1.674 95 ϫ 10Ϫ27 1.008 665 6.02 ϫ 1023 8.31 1.38 ϫ 10Ϫ23 5.67 ϫ 10Ϫ8 22.4 2.24 ϫ 10Ϫ2 1.10 ϫ 107 5.29 ϫ 10Ϫ11 2.43 ϫ 10Ϫ12 6.67 ϫ 10Ϫ11 9.80 6.38 ϫ 106 5.98 ϫ 1024 1.74 ϫ 106 7.36 ϫ 1022 m/s C2/N и m2 N и m2/C2 T и m/A C Jиs Jиs kg u kg u kg u molϪ1 J/mol и K J/K W/m2 и K4 L/mol m3/mol mϪ1 m m N и m2/kg2 m/s2 m kg m kg The values presented in this table are those used in computations in the text Generally, the physical constants are known to much better precision PERIODIC TABLE OF THE ELEMENTS Group Group I II H Group Group Group Group Group Group III IV V VI VII Transition elements H Be 6.94 9.012 2s1 2s Na 11 3s1 12 Ca 20 Atomic number 10.81 Electron configuration Al 4s Ca Sr 21 44.96 4s 37 Sc Y 22 47.90 3d 14s 38 Ti 23 50.94 3d 24s 39 V Zr 24 51.996 d 34 s 40 Cr Nb 25 54.94 3d 54s1 41 Mn Mo 26 55.85 3d 54s 42 Fe Tc 27 Ru Rh 87.62 88.906 91.22 92.91 95.94 (99) 101.1 102.91 5s1 5s 4d 15s 4d 25s 4d 45s1 4d 55s1 4d 55s 4d 75s1 4d 85s1 Cs 55 6s1 Fr Ba 56 57-71* 6s 87 Ra Hf 72 178.49 137.34 88 89-103** Ta 73 180.95 Re 75 186.2 Os 76 190.2 46 106.4 Ir e 4d 10 77 Pt 192.2 78 Ds (261) (262) 6d 27s d 37 s La 57 138.91 58 140.12 d 16s Ac Ce (263) Pr (262) 59 140.91 Th 90 Pa 60 144.24 5d 14f 16s 4f 36s 89 Nd (265) U 61 (147) 4f 46s 91 Pm (266) 4f 56s 92 Np Sm 62 150.4 Pu 63 Am 35 52 4p I 53 126.90 131.30 4d 105s1 4d 105s 5p 5p 5p 5p 5p 5p Hg Tl Au 79 80 81 Pb 111 †† Gd 112 (285) 64 Tb Cm Bk Bi 83 Po 84 At 85 (210) (218) (222) 6p 6p 6p 6p 65 Dy 66 162.50 97 Cf Ho 67 164.93 Es 68 167.26 4f 116s 98 Er 99 Tm 69 168.93 Yb 70 173.04 (249) Note: Atomic mass values given are averaged over isotopes in the percentages in which they exist in nature † For an unstable element, mass number of the most stable known isotope is given in parentheses †† Elements 111–114 have not yet been named (254) Lu 71 174.97 4f 126s 4f 136s 4f 146s 5d 14f 146s Fm Md No Lr 100 101 102 5f 26d 17s 5f 36d 17s 5f 46d 17s 5f 66d 07s 5f 76d 07s 5f 76d 17s 5f 86d 17s 5f 106d 07s 5s116d 07s 5f 126d 07s 5f 136d 07s 6d 07s (247) 86 114 6d 27s (245) Rn 208.98 (289) 158.92 96 82 6d 17s (243) 54 127.60 (231) (239) Xe 121.75 (232) (239) 36 83.80 (227) (238) Kr 118.69 5d 14f 76s 5d 14f 86s 4f 106s 95 3p Br 4p T 18 114.82 157.25 4f 76s 94 51 Ar 39.948 79.91 4p Sb 17 112.40 (272) 152.0 4f 66s 93 Eu 50 34 10 2p Cl 3p Se Ne 20.18 35.453 78.96 4p Sn 16 3p 33 18.998 32.06 As 1s F 2p S 107.87 110 †† (271) 15 74.92 4p 49 6p †† 5d 96s1 Mt 7s 4p In 48 6p 5d 76s Hs (226) 3d 104s Cd 47 5d 106s 5d 66s Bh 109 3d 104s 72.59 2p P 3p 32 O 15.999 30.97 Ge 5d 106s1 5d 56s 108 69.72 Ag 14 3p 31 207.2 Sg 107 65.37 Ga 204.37 5d 46s 106 30 200.59 Db 105 Zn 14.007 28.09 196.97 d 36 s 104 29 N 2p Si 195.09 Rf 7s1 **Actinide series 74 Pd 5d 26s (223) *Lanthanide series W 183.85 Cu 63.54 3d 84s 45 85.47 132.91 28 58.71 3d 74s 44 Ni 2p 13 26.98 58.93 3d 64s 43 Co C 12.011 3p 20 40.08 4s1 2p 40.08 3s 19 39.102 Rb Symbol Atomic mass † 24.31 22.99 K Mg B He 4.0026 1s 1s1 Li 1.0080 1.0080 (253) (255) (255) 103 (257) d 17 s ... addition to Essentials of College Physics, Dr Serway is the co-author of College Physics, Seventh Edition; Physics for Scientists and Engineers, Sixth Edition; Principles of Physics, Fourth Edition; ... strength of Essentials of College Physics starts with the foundation Essentials of College Physics provides students with a clear and logical presentation of the basic concepts and principles of physics. .. for success Briefer than the average college physics text, Essentials of College Physics comprehensively covers all the standard topics in classical and modern physics Instructors will notice a