CONVERSIONS BETWEEN U.S.CUSTOMARY UNITS AND SI UNITS (Continued) Times conversion factor U.S. Customary unit Equals SI unit Accurate Practical Moment of inertia (area) inch to fourth power in.4 416,231 416,000 millimeter to fourth power mm4 inch to fourth power in.4 0.4162313 1026 0.41631026 meter to fourth power m4 Moment of inertia (mass) slug foot squared slug-ft2 1.35582 1.36 kilogram meter squared kg·m2 Power foot-pound per second ft-lb/s 1.35582 1.36 watt (J/s or N·m/s) W foot-pound per minute ft-lb/min 0.0225970 0.0226 watt W horsepower (550 ft-lb/s) hp 745.701 746 watt W Pressure; stress pound per square foot psf 47.8803 47.9 pascal (N/m2) Pa pound per square inch psi 6894.76 6890 pascal Pa kip per square foot ksf 47.8803 47.9 kilopascal kPa kip per square inch ksi 6.89476 6.89 megapascal MPa Section modulus inch to third power in.3 16,387.1 16,400 millimeter to third power mm3 inch to third power in.3 16.387131026 16.431026 meter to third power m3 Velocity (linear) foot per second ft/s 0.3048* 0.305 meter per second m/s inch per second in./s 0.0254* 0.0254 meter per second m/s mile per hour mph 0.44704* 0.447 meter per second m/s mile per hour mph 1.609344* 1.61 kilometer per hour km/h Volume cubic foot ft3 0.0283168 0.0283 cubic meter m3 cubic inch in.3 16.387131026 16.431026 cubic meter m3 cubic inch in.3 16.3871 16.4 cubic centimeter (cc) cm3 gallon (231 in.3) gal. 3.78541 3.79 liter L gallon (231 in.3) gal. 0.00378541 0.00379 cubic meter m3 *An asterisk denotes an exactconversion factor Note:To convert from SI units to USCS units, divideby the conversion factor Temperature Conversion Formulas T(°C)5}5}[T(°F)232]5T(K)2273.15 9 5 T(K)5}}[T(°F)232]1273.155T(°C)1273.15 9 9 9 T(°F)5}}T(°C)1325}}T(K)2459.67 5 5 This page intentionally left blank Engineering Mechanics Dynamics Third Edition SI Edition Andrew Pytel The Pennsylvania State University Jaan Kiusalaas The Pennsylvania State University SI Edition prepared by Ishan Sharma Indian Institute of Technology, Kanpur Australia·Brazil·Japan·Korea·Mexico·Singapore·Spain·UnitedKingdom·UnitedStates EngineeringMechanics: ©1999,2010CengageLearning Dynamics,ThirdEdition ALLRIGHTSRESERVED.Nopartofthisworkcoveredbythecopyright AndrewPytelandJaanKiusalaas hereinmaybereproduced,transmitted,storedorusedinanyformorby SIEditionpreparedbyIshanSharma anymeansgraphic,electronic,ormechanical,includingbutnotlimitedto photocopying,recording,scanning,digitizing,taping,webdistribution, Publisher,GlobalEngineeringProgram: informationnetworks,orinformationstorageandretrievalsystems, ChristopherM.Shortt exceptaspermittedunderSection107or108ofthe1976UnitedStates SeniorDevelopmentalEditor: CopyrightAct,withoutthepriorwrittenpermissionofthepublisher. 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LaurenBetsos Director,ContentandMediaProduction: BarbaraFuller-Jacobson LibraryofCongressControlNumber:2009936717 ISBN-13:978-0-495-29563-1 ContentProjectManager:Jennifer ISBN-10:0-495-29563-9 Zeigler ProductionService:RPKEditorial CengageLearning Services 200FirstStamfordPlace,Suite400 Stamford,CT06902 Copyeditor:PatDaly USA Proofreader:MarthaMcMaster CengageLearningisaleadingproviderofcustomizedlearning Indexer:ShellyGerger-Knechtl solutionswithofficelocationsaroundtheglobe,includingSingapore, Compositor:IntegraSoftwareServices theUnitedKingdom,Australia,Mexico,Brazil,andJapan.Locateyour SeniorArtDirector: localofficeat:international.cengage.com/region. MichelleKunkler CengageLearningproductsarerepresentedinCanadaby InternalDesigner:CarmelaPeriera NelsonEducationLtd. CoverDesigner:AndrewAdams Foryourcourseandlearningsolutions,visit www.cengage.com/engineering. CoverImage:Copyright iStockphoto/OlgaPaslawska Purchaseanyofourproductsatyourlocalcollegestoreoratour preferredonlinestorewww.ichapters.com. PermissionsAccountManager,Text: KatieHuha PermissionsAccountManager,Images: DeannaEttinger TextandImagePermissionsResearcher: KristiinaPaul SeniorFirstPrintBuyer: DougWilke PrintedinCanada 12345671312111009 To Jean, Leslie, Lori, John, Nicholas and To Judy, Nicholas, Jennifer, Timothy This page intentionally left blank Contents PrefacetotheSIEdition xi Preface xiii Chapter11 IntroductiontoDynamics 1 11.1 Introduction 1 11.2 DerivativesofVectorFunctions 3 11.3 Position,Velocity,andAccelerationofaParticle 4 11.4 NewtonianMechanics 5 Chapter12 DynamicsofaParticle:Rectangular Coordinates 15 12.1 Introduction 15 12.2 Kinematics 16 12.3 Kinetics:Force-Mass-AccelerationMethod 27 12.4 DynamicsofRectilinearMotion 29 12.5 CurvilinearMotion 44 *12.6 AnalysisofMotionbytheAreaMethod 56 Chapter13 DynamicsofaParticle:Curvilinear Coordinates 69 13.1 Introduction 69 13.2 Kinematics—Path(Normal-Tangential)Coordinates 70 13.3 Kinematics—PolarandCylindricalCoordinates 82 13.4 Kinetics:Force-Mass-AccelerationMethod 95 Chapter14 Work-EnergyandImpulse-Momentum PrinciplesforaParticle 117 14.1 Introduction 117 14.2 WorkofaForce 118 14.3 PrincipleofWorkandKineticEnergy 122 14.4 ConservativeForcesandtheConservationofMechanical Energy 133 *Indicatesoptionalarticles vii