Vector Mechanics for engineers : statics and dynamics

Cover Page Reactions at Supports and Connections for a Two-Dimensional Structure Reactions at Supports and Connections for a Three-Dimensional Structure Title Page Copyright Page About the Authors Brief Contents Table of Content Preface Guided Tour What Resources Support This Textbook? Acknowledgments Connect List of Symbols 1 Introduction 1.1 What Is Mechanics? 1.2 Fundamental Concepts and Principles 1.3 Systems of Units 1.4 Conversion from One System of Units to Another 1.5 Method of Problem Solution 1.6 Numerical Accuracy 2 Statics of Particles 2.1 Introduction Forces in a Plane 2.2 Force on a Particle. Resultant of Two Forces 2.3 Vectors 2.4 Addition of Vectors 2.5 Resultant of Several Concurrent Forces 2.6 Resolution of a Force into Components 2.7 Rectangular Components of a Force. Unit Vectors 2.8 Addition of Forces by Summing X and Y Components 2.9 Equilibrium of a Particle 2.10 Newton’s First Law of Motion 2.11 Problems Involving the Equilibrium of a Particle. Free-Body Diagrams Forces in Space 2.12 Rectangular Components of a Force in Space 2.13 Force Defined by Its Magnitude and Two Points on Its Line of Action 2.14 Addition of Concurrent Forces in Space 2.15 Equilibrium of a Particle in Space Review and Summary for Chapter 2 Review Problems Computer Problems 3 Rigid Bodies: Equivalent Systems of Forces 3.1 Introduction 3.2 External and Internal Forces 3.3 Principle of Transmissibility. Equivalent Forces 3.4 Vector Product of Two Vectors 3.5 Vector Products Expressed in Terms of Rectangular Components 3.6 Moment of a Force about a Point 3.7 Varignon’s Theorem 3.8 Rectangular Components of the Moment of a Force 3.9 Scalar Product of Two Vectors 3.10 Mixed Triple Product of Three Vectors 3.11 Moment of a Force about a Given Axis 3.12 Moment of a Couple 3.13 Equivalent Couples 3.14 Addition of Couples 3.15 Couples Can Be Represented by Vectors 3.16 Resolution of a Given Force into a Force at O and a Couple 3.17 Reduction of a System of Forces to One Force and One Couple 3.18 Equivalent Systems of Forces 3.19 Equipollent Systems of Vectors 3.20 Further Reduction of a System of Forces *3.21 Reduction of a System of Forces to a Wrench Review and Summary for Chapter 3 Review Problems Computer Problems 4 Equilibrium of Rigid Bodies 4.1 Introduction 4.2 Free-Body Diagram Equilibrium in Two Dimensions 4.3 Reactions at Supports and Connections for a Two-Dimensional Structure 4.4 Equilibrium of a Rigid Body in Two Dimensions 4.5 Statically Indeterminate Reactions. Partial Constraints 4.6 Equilibrium of a Two-Force Body 4.7 Equilibrium of a Three-Force Body Equilibrium in Three Dimensions 4.8 Equilibrium of a Rigid Body in Three Dimensions 4.9 Reactions at Supports and Connections for a Three-Dimensional Structure Review and Summary for Chapter 4 Review Problems Computer Problems 5 Distributed Forces: Centroids and Centers of Gravity 5.1 Introduction Areas and Lines 5.2 Center of Gravity of a Two-Dimensional Body 5.3 Centroids of Areas and Lines 5.4 First Moments of Areas and Lines 5.5 Composite Plates and Wires 5.6 Determination of Centroids by Integration 5.7 Theorems of Pappus-Guldinus 5.8 Distributed Loads on Beams *5.9 Forces on Submerged Surfaces Volumes 5.10 Center of Gravity of a Three-Dimensional Body. Centroid of a Volume 5.11 Composite Bodies 5.12 Determination of Centroids of Volumes by Integration Review and Summary for Chapter 5 Review Problems Computer Problems 6 Analysis of Structures 6.1 Introduction Trusses 6.2 Definition of a Truss 6.3 Simple Trusses 6.4 Analysis of Trusses by the Method of Joints 6.5 Joints Under Special Loading Conditions *6.6 Space Trusses 6.7 Analysis of Trusses by the Method of Sections *6.8 Trusses Made of Several Simple Trusses Frames and Machines 6.9 Structures Containing Multiforce Members 6.10 Analysis of a Frame 6.11 Frames Which Cease to Be Rigid When Detached from Their Supports 6.12 Machines Review and Summary for Chapter 6 Review Problems Computer Problems 7 Forces in Beams and Cables *7.1 Introduction *7.2 Internal Forces in Members Beams *7.3 Various Types of Loading and Support *7.4 Shear and Bending Moment in a Beam *7.5 Shear and Bending-Moment Diagrams 7.6 Relations Among Load, Shear, and Bending Moment Cables *7.7 Cables with Concentrated Loads *7.8 Cables with Distributed Loads 7.9 Parabolic Cable *7.10 Catenary Review and Summary for Chapter 7 Review Problems Computer Problems 8 Friction 8.1 Introduction 8.2 The Laws of Dry Friction. Coefficients of Friction 8.3 Angles of Friction 8.4 Problems Involving Dry Friction 8.5 Wedges 8.6 Square-Threaded Screws 8.7 Journal Bearings. Axle Friction 8.8 Thrust Bearings. Disk Friction *8.9 Wheel Friction. Rolling Resistance 8.10 Belt Friction Review and Summary for Chapter 8 Review Problems Computer Problems 9 Distributed Forces: Moments of Inertia 9.1 Introduction Moments of Inertia of Areas 9.2 Second Moment, or Moment of Inertia, of an Area 9.3 Determination of the Moment of Inertia of an Area by Integration 9.4 Polar Moment of Inertia 9.5 Radius of Gyration of an Area 9.6 Parallel-Axis Theorem 9.7 Moments of Inertia of Composite Areas *9.8 Product of Inertia *9.9 Principal Axes and Principal Moments of Inertia *9.10 Mohr’s Circle for Moments and Products of Inertia Moments of Inertia of a Mass 9.11 Moment of Inertia of a Mass 9.12 Parallel-Axis Theorem 9.13 Moments of Inertia of Thin Plates 9.14 Determination of the Moment of Inertia of a Three-Dimensional Body by Integration 9.15 Moments of Inertia of Composite Bodies *9.16 Moment of Inertia of a Body with Respect to an Arbitrary Axis Through O. Mass Products of Inertia 9.17 Ellipsoid of Inertia. Principal Axes of Inertia *9.18 Determination of the Principal Axes and Principal Moments of Inertia of a Body of Arbitrary Shape Review and Summary for Chapter 9 Review Problems Computer Problems 10 Method of Virtual Work *10.1 Introduction *10.2 Work of a Force *10.3 Principle of Virtual Work *10.4 Applications of the Principle of Virtual Work *10.5 Real Machines. Mechanical Efficiency *10.6 Work of a Force During a Finite Displacement *10.7 Potential Energy *10.8 Potential Energy and Equilibrium *10.9 Stability of Equilibrium Review and Summary for Chapter 10 Review Problems Computer Problems 11 Kinematics of Particles 11.1 Introduction to Dynamics Rectilinear Motion of Particles 11.2 Position, Velocity, and Acceleration 11.3 Determination of the Motion of a Particle 11.4 Uniform Rectilinear Motion 11.5 Uniformly Accelerated Rectilinear Motion 11.6 Motion of Several Particles *11.7 Graphical Solution of Rectilinear-Motion Problems *11.8 Other Graphical Methods Curvilinear Motion of Particles 11.9 Position Vector, Velocity, and Acceleration 11.10 Derivatives of Vector Functions 11.11 Rectangular Components of Velocity and Acceleration 11.12 Motion Relative to a Frame in Translation 11.13 Tangential and Normal Components 11.14 Radial and Transverse Components Review and Summary for Chapter 11 Review Problems Computer Problems 12 Kinetics of Particles: Newton’s Second Law 12.1 Introduction 12.2 Newton’s Second Law of Motion 12.3 Linear Momentum of a Particle. Rate of Change of Linear Momentum 12.4 Systems of Units 12.5 Equations of Motion 12.6 Dynamic Equilibrium 12.7 Angular Momentum of a Particle. Rate of Change of Angular Momentum 12.8 Equations of Motion in Terms of Radial and Transverse Components 12.9 Motion Under a Central Force. Conservation of Angular Momentum 12.10 Newton’s Law of Gravitation *12.11 Trajectory of a Particle Under a Central Force *12.12 Application to Space Mechanics *12.13 Kepler’s Laws of Planetary Motion Review and Summary for Chapter 12 Review Problems Computer Problems 13 Kinetics of Particles: Energy and Momentum Methods 13.1 Introduction 13.2 Work of a Force 13.3 Kinetic Energy of a Particle. Principle of Work and Energy 13.4 Applications of the Principle of Work and Energy 13.5 Power and Efficiency 13.6 Potential Energy *13.7 Conservative Forces 13.8 Conservation of Energy 13.9 Motion Under a Conservative Central Force. Application to Space Mechanics 13.10 Principle of Impulse and Momentum 13.11 Impulsive Motion 13.12 Impact 13.13 Direct Central Impact 13.14 Oblique Central Impact 13.15 Problems Involving Energy and Momentum Review and Summary for Chapter 13 Review Problems Computer Problems 14 Systems of Particles 14.1 Introduction 14.2 Application of Newton’s Laws to the Motion of a System of Particles. Effective Forces 14.3 Linear and Angular Momentum of a System of Particles 14.4 Motion of the Mass Center of a System of Particles 14.5 Angular Momentum of a System of Particles About Its Mass Center 14.6 Conservation of Momentum for a System of Particles 14.7 Kinetic Energy of a System of Particles 14.8 Work-Energy Principle. Conservation of Energy for a System of Particles 14.9 Principle of Impulse and Momentum for a System of Particles *14.10 Variable Systems of Particles *14.11 Steady Stream of Particles *14.12 Systems Gaining or Losing Mass Review and Summary for Chapter 14 Review Problems Computer Problems 15 Kinematics of Rigid Bodies 15.1 Introduction 15.2 Translation 15.3 Rotation About a Fixed Axis 15.4 Equations Defining the Rotation of a Rigid Body About a Fixed Axis 15.5 General Plane Motion 15.6 Absolute and Relative Velocity in Plane Motion 15.7 Instantaneous Center of Rotation in Plane Motion 15.8 Absolute and Relative Acceleration in Plane Motion *15.9 Analysis of Plane Motion in Terms of a Parameter 15.10 Rate of Change of a Vector with Respect to a Rotating Frame 15.11 Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration *15.12 Motion About a Fixed Point *15.13 General Motion *15.14 Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration *15.15 Frame of Reference in General Motion Review and Summary for Chapter Review Problems Computer Problems 16 Plane Motion of Rigid Bodies: Forces and Accelerations 16.1 Introduction 16.2 Equations of Motion for a Rigid Body 16.3 Angular Momentum of a Rigid Body in Plane Motion 16.4 Plane Motion of a Rigid Body. D’Alembert’s Principle *16.5 A Remark on the Axioms of the Mechanics of Rigid Bodies 16.6 Solution of Problems Involving the Motion of a Rigid Body 16.7 Systems of Rigid Bodies 16.8 Constrained Plane Motion Review and Summary for Chapter 16 Review Problems Computer Problems 17 Plane Motion of Rigid Bodies: Energy and Momentum Methods 17.1 Introduction 17.2 Principle of Work and Energy for a Rigid Body 17.3 Work of Forces Acting on a Rigid Body 17.4 Kinetic Energy of a Rigid Body in Plane Motion 17.5 Systems of Rigid Bodies 17.6 Conservation of Energy 17.7 Power 17.8 Principle of Impulse and Momentum for the Plane Motion of a Rigid Body 17.9 Systems of Rigid Bodies 17.10 Conservation of Angular Momentum 17.11 Impulsive Motion 17.12 Eccentric Impact Review and Summary for Chapter 17 Review Problems Computer Problems 18 Kinetics of Rigid Bodies in Three Dimensions *18.1 Introduction *18.2 Angular Momentum of a Rigid Body in Three Dimensions *18.3 Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body *18.4 Kinetic Energy of a Rigid Body in Three Dimensions *18.5 Motion of a Rigid Body in Three Dimensions *18.6 Euler’s Equations of Motion. Extension of D’Alembert’s Principle to the Motion of a Rigid Body in Three Dimensions *18.7 Motion of a Rigid Body About a Fixed Point *18.8 Rotation of a Rigid Body About a Fixed Axis *18.9 Motion of a Gyroscope. Eulerian Angles *18.10 Steady Precession of a Gyroscope *18.11 Motion of an Axisymmetrical Body Under No Force Review and Summary for Chapter 18 Review Problems Computer Problems 19 Mechanical Vibrations 19.1 Introduction Vibrations Without Damping 19.2 Free Vibrations of Particles. Simple Harmonic Motion 19.3 Simple Pendulum (Approximate Solution) *19.4 Simple Pendulum (Exact Solution) 19.5 Free Vibrations of Rigid Bodies 19.6 Application of the Principle of Conservation of Energy 19.7 Forced Vibrations Damped Vibrations *19.8 Damped Free Vibrations *19.9 Damped Forced Vibrations *19.10 Electrical Analogues Review and Summary for Chapter 19 Review Problems Computer Problems Appendix Photo Credits Index Answers to Problems Centroids of Common Shapes of Areas and Lines Moments of Inertia of Common Geometric Shapes Back Cover Gives your students the best opportunity to learn statics and dynamics. This book provides extensive practice through sample problems, exercise sets, and online delivery of homework problems to your students. The text focuses on the correct understanding of the principles of mechanics and on their application to the solution of engineering problems