Undergraduate Lecture Notes in Physics Series Editors Neil Ashby William Brantley Michael Fowler Elena Sassi Helmy S. Sherif For furthervolumes: http://www.springer.com/series/8917 Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts covering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. ULNP titles must provide at least one of the following: • An exceptionally clear and concise treatment of a standard undergraduate subject. • A solid undergraduate-level introduction to a graduate, advanced, or non- standard subject. • A novel perspective or an unusual approach to teaching a subject. ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching at the undergraduate level. ThepurposeofULNPistoprovideintriguing,absorbingbooksthatwillcontinue to be the reader’s preferred reference throughout their academic career. Hafez A. Radi • John O. Rasmussen Principles of Physics For Scientists and Engineers 123 Hafez A.Radi OctoberUniversity forModernSciences and Arts(MSA) 6thof OctoberCity Egypt JohnO.Rasmussen Universityof California atBerkeley andLawrence Berkeley Lab Berkeley,CA USA Solutionstotheexercisesareaccessibletoqualifiedinstructorsatspringer.comonthisbook’sproduct page. Instructors may click on the link additional information and register to obtain their restricted access. ISSN 2192-4791 ISSN 2192-4805 (electronic) ISBN 978-3-642-23025-7 ISBN 978-3-642-23026-4 (eBook) DOI 10.1007/978-3-642-23026-4 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2012947066 (cid:2)Springer-VerlagBerlinHeidelberg2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface This book on Principles of Physics is intended to serve fundamental college courses in scientific curricula. Physicsisoneofthemostimportanttoolstoaidundergraduates,graduates,and researchers in their technical fields of study. Without it many phenomena cannot be described, studied, or understood. The topics covered here will help students interpret such phenomena, ultimately allowing them to advance in the applied aspects of their fields. The goal of this text is to present many key concepts in a clear and concise, yet interestingway,makinguseofpracticalexamplesandattractivelycoloredillustrations wheneverappropriatetosatisfytheneedsoftoday’sscienceandengineeringstudents. Someoftheexamples,proofs,andsubsectionsinthistextbookhavebeenidentified asoptionalandareprecededwithanasterisk*.Forlessintensivecoursestheseoptional portionsmaybeomittedwithoutsignificantlyimpactingtheobjectivesofthechapter. Additionalmaterialmayalsobeomitteddependingonthecourse’srequirements. The first author taught the material of this book in many universities in the Middle East for almost four decades. Depending on the university, he leveraged different international textbooks, resources, and references. These used different approaches,butweremainlywritteninanexpansivemannerdeliveringaplethora of topics while targeting students who wanted to dive deeply into the subject matter. In this textbook, however, the authors introduce a large subset of these topics but in a more simplified manner, with the intent of delivering these topics andtheirkeyfactstostudentsallovertheworldandinparticulartostudentsinthe Middle East and neighboring regions where English may not be the native lan- guage. The second author went over the entire text with the background of study and/or teaching at Caltech, UC Berkeley, and Yale. Instructors teaching from this textbook will be able to gain online access from thepublishertothesolutionsmanual,which provides step-by-stepsolutions toall exercises contained in the book. The solutions manual also contains many tips, colored illustrations, and explanations on how the solutions were derived. v vi Preface Acknowledgments from Prof. Hafez A. Radi I owe special thanks to my wife and two sons Tarek and Rami for their ongoing supportand encouragement. I also owe special thanks tomy colleague and friend Prof. Rasmussen for his invaluable contributions to this book, and for everything that I learned from him over the years while carrying out scientific research at Lawrence Berkeley Lab. Additionally, I would like to express my gratitude to Prof. Ali Helmy Moussa, Prof. of Physics at Ain Shams University in Egypt, for his assistance, support, and guidance over the years. I also thank all my fellow professors and colleagues who provided me with valuable feedback pertaining to many aspects of this book, especially Dr. Sana’a Ismail, from Dar El Tarbiah School,IGCSE section andDr. Hesham Othmanfrom theFaculty ofEngineering atCairoUniversity.IwouldalsoliketothankProfessorMikeGuidry,Professorof PhysicsandAstronomyattheUniversityofTennesseeKnoxville,forhisvaluable recommendations. I am also grateful to the CD Odessa LLC for their Concept- Draw software suite which was used to create almost all the figures in this book. I finally extend my thanks and appreciation to Professor Nawal El-Degwi, ProfessorKhayriAbdel-Hamid,ProfessorSaidAshour,andthestaffmembersand teachingassistantsatthefacultyofEngineeringatMSAUniversity,Egypt,forall their support and input. Hafez A. Radi [email protected] Acknowledgments from Prof. John O. Rasmussen I would like to thank Prof. Radi for the opportunity to join him as coauthor. I am grateful to the many teachers, students, and colleagues from whom I learned various aspects of the fascinating world of the physical sciences, notably the late Drs. Linus Pauling, Isadore Perlman, Stanley Thompson, Glenn Seaborg, Earl Hyde, Hilding Slätis, Aage Bohr, Gaja Alaga, and Hans-Järg Mang. There are manyothers,stillliving,toonumeroustolisthere.Iwouldalsoliketoextendmy special thanks to my wife for her support and encouragement. John O. Rasmussen [email protected] Contents Part I Fundamental Basics 1 Dimensions and Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 The International System of Units . . . . . . . . . . . . . . . . . . . 3 1.2 Standards of Length, Time, and Mass. . . . . . . . . . . . . . . . . 5 1.3 Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1 Vectors and Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Properties of Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Vector Components and Unit Vectors. . . . . . . . . . . . . . . . . 22 2.4 Multiplying Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Part II Mechanics 3 Motion in One Dimension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1 Position and Displacement. . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Average Velocity and Average Speed. . . . . . . . . . . . . . . . . 42 3.3 Instantaneous Velocity and Speed. . . . . . . . . . . . . . . . . . . . 44 3.4 Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.5 Constant Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.6 Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.7 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4 Motion in Two Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.1 Position, Displacement, Velocity, and Acceleration Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 vii viii Contents 4.3 Uniform Circular Motion. . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 Tangential and Radial Acceleration. . . . . . . . . . . . . . . . . . . 90 4.5 Non-uniform Circular Motion. . . . . . . . . . . . . . . . . . . . . . . 91 4.6 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5 Force and Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.1 The Cause of Acceleration and Newton’s Laws . . . . . . . . . . 103 5.2 Some Particular Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3 Applications to Newton’s Laws . . . . . . . . . . . . . . . . . . . . . 113 5.4 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6 Work, Energy, and Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.1 Work Done by a Constant Force . . . . . . . . . . . . . . . . . . . . 137 6.2 Work Done by a Variable Force. . . . . . . . . . . . . . . . . . . . . 142 6.3 Work-Energy Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.4 Conservative Forces and Potential Energy. . . . . . . . . . . . . . 151 6.5 Conservation of Mechanical Energy . . . . . . . . . . . . . . . . . . 157 6.6 Work Done by Non-conservative Forces . . . . . . . . . . . . . . . 159 6.7 Conservation of Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.8 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 6.9 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 7 Linear Momentum, Collisions, and Center of Mass . . . . . . . . . . . 181 7.1 Linear Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . 181 7.2 Conservation of Linear Momentum. . . . . . . . . . . . . . . . . . . 184 7.3 Conservation of Momentum and Energy in Collisions. . . . . . 187 7.3.1 Elastic Collisions in One and Two Dimensions . . . . 187 7.3.2 Inelastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . 194 7.4 Center of Mass (CM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 7.5 Dynamics of the Center of Mass . . . . . . . . . . . . . . . . . . . . 199 7.6 Systems of Variable Mass . . . . . . . . . . . . . . . . . . . . . . . . . 203 7.6.1 Systems of Increasing Mass. . . . . . . . . . . . . . . . . . 204 7.6.2 Systems of Decreasing Mass; Rocket Propulsion . . . 205 7.7 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 8 Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 8.1 Radian Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 8.2 Rotational Kinematics; Angular Quantities. . . . . . . . . . . . . . 228 8.3 Constant Angular Acceleration. . . . . . . . . . . . . . . . . . . . . . 232 8.4 Angular Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 8.5 Relating Angular and Linear Quantities. . . . . . . . . . . . . . . . 233 8.6 Rotational Dynamics; Torque. . . . . . . . . . . . . . . . . . . . . . . 238 8.7 Newton’s Second Law for Rotation . . . . . . . . . . . . . . . . . . 240 8.8 Kinetic Energy, Work, and Power in Rotation . . . . . . . . . . . 248 Contents ix 8.9 Rolling Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 8.10 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 9 Angular Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 9.1 Angular Momentum of Rotating Systems . . . . . . . . . . . . . . 269 9.1.1 Angular Momentum of a Particle . . . . . . . . . . . . . . 269 9.1.2 Angular Momentum of a System of Particles. . . . . . 271 9.1.3 Angular Momentum of a Rotating Rigid Body. . . . . 271 9.2 Conservation of Angular Momentum. . . . . . . . . . . . . . . . . . 277 9.3 The Spinning Top and Gyroscope. . . . . . . . . . . . . . . . . . . . 285 9.4 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 10 Mechanical Properties of Matter. . . . . . . . . . . . . . . . . . . . . . . . . 303 10.1 Density and Relative Density. . . . . . . . . . . . . . . . . . . . . . . 304 10.2 Elastic Properties of Solids . . . . . . . . . . . . . . . . . . . . . . . . 306 10.2.1 Young’s Modulus: Elasticity in Length. . . . . . . . . . 307 10.2.2 Shear Modulus: Elasticity of Shape . . . . . . . . . . . . 310 10.2.3 Bulk Modulus: Volume Elasticity. . . . . . . . . . . . . . 312 10.3 Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 10.4 Fluid Statics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 10.5 Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 10.6 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Part III Introductory Thermodynamics 11 Thermal Properties of Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . 357 11.1 Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 11.2 Thermal Expansion of Solids and Liquids . . . . . . . . . . . . . . 360 11.2.1 Linear Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 361 11.2.2 Volume Expansion . . . . . . . . . . . . . . . . . . . . . . . . 362 11.3 The Ideal Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 11.4 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 12 Heat and the First Law of Thermodynamics . . . . . . . . . . . . . . . . 379 12.1 Heat and Thermal Energy . . . . . . . . . . . . . . . . . . . . . . . . . 379 12.1.1 Units of Heat, The Mechanical Equivalent of Heat . . . . . . . . . . . . . . . . . . . . . . . . 379 12.1.2 Heat Capacity and Specific Heat . . . . . . . . . . . . . . 380 12.1.3 Latent Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 12.2 Heat and Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 12.3 The First Law of Thermodynamics. . . . . . . . . . . . . . . . . . . 395 12.4 Applications of the First Law of Thermodynamics . . . . . . . . 396 12.5 Heat Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 12.6 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416