Engineering Mechanics, Statics & Dynamics

Front Cover Unit Conversion Factors Half Title Page Title Page Copyright Page Contents Preface About the Authors Pearson’s Commitment to Diversity, Equity, and Inclusion Engineering Mechanics: Statics 1 Introduction 1.1 Engineering and Mechanics Problem Solving Numbers Space and Time Newton’s Laws International System of Units US Customary Units Angular Units Conversion of Units Results 1.2 Newtonian Gravitation Results 2 Vectors 2.1 Scalars and Vectors Vector Addition Product of a Scalar and a Vector Vector Subtraction Unit Vectors Results 2.2 Components in Two Dimensions Manipulating Vectors in Terms of Components Position Vectors in Terms of Components Results 2.3 Components in Three Dimensions Magnitude of a Vector in Terms of Components Direction Cosines Position Vectors in Terms of Components Components of a Vector Parallel to a Given Line Results 2.4 Dot Products Definition Dot Products in Terms of Components Vector Components Parallel and Normal to a Line Results 2.5 Cross Products Definition Cross Products in Terms of Components Evaluating a 3 x 3 Determinant Mixed Triple Products Results 3 Forces 3.1 Forces, Equilibrium, and Free-Body Diagrams Terminology Gravitational Forces Contact Forces Equilibrium Free-Body Diagrams Results 3.2 Two-Dimensional Force Systems 3.3 Three-Dimensional Force Systems 4 Systems of Forces and Moments 4.1 Two-Dimensional Description of the Moment Results 4.2 The Moment Vector Magnitude of the Moment Direction of the Moment Relation to the Two-Dimensional Description Varignon’s Theorem Results 4.3 Moment of a Force about a Line Definition Applications Results 4.4 Couples Results 4.5 Equivalent Systems Conditions for Equivalence Representing Systems by Equivalent Systems Representing a System by a Wrench Results 5 Objects in Equilibrium 5.1 Two-Dimensional Applications The Scalar Equilibrium Equations Supports Free-Body Diagrams Results 5.2 Statically Indeterminate Objects Redundant Supports Improper Supports Results 5.3 Three-Dimensional Applications The Scalar Equilibrium Equations Supports Results 5.4 Two-Force and Three-Force Members Two-Force Members Three-Force Members Results 6 Structures in Equilibrium 6.1 Trusses Results 6.2 The Method of Joints Results 6.3 The Method of Sections Results 6.4 Space Trusses Results 6.5 Frames and Machines Analyzing the Entire Structure Analyzing the Members Results 7 Centroids and Centers of Mass 7.1 Centroids of Areas Results 7.2 Composite Areas Results 7.3 Distributed Loads Describing a Distributed Load Determining Force and Moment The Area Analogy Results 7.4 Centroids of Volumes and Lines Results 7.5 Composite Volumes and Lines 7.6 The Pappus–Guldinus Theorems First Theorem Second Theorem Results 7.7 Centers of Mass of Objects Results 7.8 Centers of Mass of Composite Objects 8 Moments of Inertia Areas 8.1 Definitions 8.2 Parallel-Axis Theorems Results 8.3 Rotated and Principal Axes Rotated Axes Moment of Inertia about the X'-Axis Moment of Inertia about the Y'-Axis Principal Axes Results 8.4 Mohr’s Circle Determining Ix', Iy', and Ix'y' Determining Principal Axes and Principal Moments of Inertia Results Masses 8.5 Simple Objects Slender Bars Thin Plates Results 8.6 Parallel-Axis Theorem Results 9 Friction 9.1 Theory of Dry Friction Coefficients of Friction Angles of Friction Results 9.2 Wedges 9.3 Threads Motion Opposite to the Direction of the Axial Force Motion in the Direction of the Axial Force Results 9.4 Journal Bearings Results 9.5 Thrust Bearings and Clutches Results 9.6 Belt Friction Results 9.7 Current Research on Friction 10 Internal Forces and Moments Beams 10.1 Axial Force, Shear Force, and Bending Moment Results 10.2 Shear Force and Bending Moment Diagrams Results 10.3 Relations between Distributed Load, Shear Force, and Bending Moment Construction of the Shear Force Diagram Construction of the Bending Moment Diagram Results Cables 10.4 Loads Distributed Uniformly Along Straight Lines Shape of the Cable Tension of the Cable Length of the Cable Results 10.5 Loads Distributed Uniformly Along Cables Shape of the Cable Tension of the Cable Length of the Cable Results 10.6 Discrete Loads Determining the Configuration and Tensions Comments on Continuous and Discrete Models Results Liquids and Gases 10.7 Pressure and the Center of Pressure Center of Pressure Pressure in a Stationary Liquid Results 11 Virtual Work and Potential Energy 11.1 Virtual Work Work Principle of Virtual Work Application to Structures Results 11.2 Potential Energy Examples of Conservative Forces Principle of Virtual Work for Conservative Forces Stability of Equilibrium Results Appendices Appendix A Results from Mathematics A.1 Algebra Quadratic Equations Natural Logarithms A.2 Trigonometry A.3 Derivatives A.4 Integrals A.5 Taylor Series A.6 Vector Analysis Cartesian Coordinates Cylindrical Coordinates A.7 Matrices Appendix B Properties of Areas and Lines B.1 Areas B.2 Lines Appendix C Properties of Volumes and Homogeneous Objects Solutions to Practice Problems Answers to Even-Numbered Problems Index Engineering Mechanics: Dynamics 12 Introduction 12.1 Engineering and Mechanics Problem Solving Numbers Space and Time Newton’s Laws International System of Units US Customary Units Angular Units Conversion of Units Results 12.2 Newtonian Gravitation Results 13 Motion of a Point 13.1 Position, Velocity, and Acceleration Results 13.2 Straight-Line Motion Description of the Motion Analysis of the Motion Results 13.3 Straight-Line Motion When the Acceleration Depends on Velocity or Position Results 13.4 Curvilinear Motion—Cartesian Coordinates Results 13.5 Angular Motion Angular Motion of a Line Rotating Unit Vector Results 13.6 Curvilinear Motion—Normal and Tangential Components Planar Motion Circular Motion Three-Dimensional Motion Results 13.7 Curvilinear Motion—Polar and Cylindrical Coordinates Results 13.8 Relative Motion Results 14 Force, Mass, and Acceleration 14.1 Newton’s Second Law Equation of Motion for the Center of Mass Inertial Reference Frames Results 14.2 Applications—Cartesian Coordinates and Straight-Line Motion 14.3 Applications—Normal and Tangential Components 14.4 Applications—Polar and Cylindrical Coordinates 14.5 Orbital Mechanics Determination of the Orbit Types of Orbits Results 15 Energy Methods 15.1 Work and Kinetic Energy Principle of Work and Energy Evaluating the Work Power Results 15.2 Work Done by Particular Forces Weight Springs Results 15.3 Potential Energy and Conservative Forces Potential Energy Conservative Forces Results 15.4 Relationships between Force and Potential Energy Results 16 Momentum Methods 16.1 Principle of Impulse and Momentum Results 16.2 Conservation of Linear Momentum and Impacts Conservation of Linear Momentum Impacts Results 16.3 Angular Momentum Principle of Angular Impulse and Momentum Central-Force Motion Results 16.4 Mass Flows Results 17 Planar Kinematics of Rigid Bodies 17.1 Rigid Bodies and Types of Motion Translation Rotation about a Fixed Axis Planar Motion Results 17.2 Rotation about a Fixed Axis Results 17.3 General Motions: Velocities Relative Velocities The Angular Velocity Vector Results 17.4 Instantaneous Centers Results 17.5 General Motions: Accelerations Results 17.6 Sliding Contacts Results 17.7 Moving Reference Frames Motion of a Point Relative to a Moving Reference Frame Inertial Reference Frames Results 18 Planar Dynamics of Rigid Bodies 18.1 Momentum Principles for a System of Particles Force–Linear Momentum Principle Moment–Angular Momentum Principles Results 18.2 The Planar Equations of Motion Rotation about a Fixed Axis General Planar Motion Results Appendix: Moments of Inertia Simple Objects Parallel-Axis Theorem 19 Energy and Momentum in Rigid-Body Dynamics 19.1 Work and Energy Kinetic Energy Work and Potential Energy Power Results 19.2 Impulse and Momentum Linear Momentum Angular Momentum Results 19.3 Impacts Conservation of Momentum Coefficient of Restitution Results 20 Three-Dimensional Kinematics and Dynamics of Rigid Bodies 20.1 Kinematics Velocities and Accelerations Moving Reference Frames Results 20.2 Euler’s Equations Rotation about a Fixed Point General Three-Dimensional Motion Equations of Planar Motion Results 20.3 The Euler Angles Objects with an Axis of Symmetry Arbitrary Objects Results Appendix: Moments and Products of Inertia Simple Objects Thin Plates Parallel-Axis Theorems Moment of Inertia about an Arbitrary Axis Principal Axes 21 Vibrations 21.1 Conservative Systems Examples Solutions Results 21.2 Damped Vibrations Subcritical Damping Critical and Supercritical Damping Results 21.3 Forced Vibrations Oscillatory Forcing Function Polynomial Forcing Function Results Appendix A Results from Mathematics A.1 Algebra Quadratic Equations Natural Logarithms A.2 Trigonometry A.3 Derivatives A.4 Integrals A.5 Taylor Series A.6 Vector Analysis Cartesian Coordinates Cylindrical Coordinates A.7 Matrices Appendix B Properties of Areas and Lines B.1 Areas B.2 Lines Appendix C Properties of Volumes and Homogeneous Objects Appendix D Spherical Coordinates Appendixe E D'Alembert’s Principle Solutions to Practice Problems Answers to Even-Numbered Problems Index Properties of Areas and Lines