CONTENTS Preface ix Preface to the First Edition xi 1. Forces and Laws of Mechanics 1-29 1.1 Introduction 1 1.1.1Force and System of Forces 1 1.1.2Vector Representation 2 1.2 Equilibrium of Concurrent Forces 3 1.2.1Resultant of Two Forces: Law of Parallelogram of Forces 3 1.2.2The Law of Parallelogram of Forces 4 1.3 Resolution of a Force 5 1.3.1Components of a Force in a Plane 5 1.3.2Rectangular Components of a Force in Space 6 1.4 Resultant Force of a System of Coplanar Forces Acting at a Point 7 1.5 Triangle Law of Forces 8 1.6 Lami's Theorem 9 1.7 Polygon of Forces 10 1.8 k-ii Theorem 10 1.9 Basic Laws of Mechanics 10 1.9.1Mass 11 1.9.2Momentum 11 1.9.3Frame of Reference 11 1.9.4Newton's Laws of Motion 11 1.10 Solving Problems in Mechanics (Free-Body Diagram) 12 1.11 Some Illustrations for Drawing Free-Body Diagrams 13 1.12 Impulse-Momentum Theorem 16 Illustrative Examples 17 Exercises 28 2. Moments of Forces and Equilibrium 30-54 2.1 Introduction 30 2.1.1Moment of a Force or Torque 30 2.1.2Graphical Representation of a Moment 32 2.2 Varignon's Theorem 32 2.3 Couple 33 2.3.1 Torque in Vector Form 34 2.4 Equilibrium of a Particle and a Body 35 Illustrative Examples 36 Exercises 52 3.Frames and Plane Trusses 55-93 3.1 Introduction 55 3.2 Equilibrium of Structures 55 3.3 Origin of Reaction Forces and Couples 56 3.4 Reactions in Two-dimensional Structures 56 3.5 Reactions in Three-dimensional Structures 58 3.6 Pin-jointed Plane Frames 59 3.6.1Classification of Framed Structures 59 3.7 Stress Analysis by Analytical Method 61 3.8 Method of Sections 63 3.9 Beam with Distributed Load 63 Illustrative Examples 65 Exercises 89 4. Friction and Rolling 94-130 4.1 Introduction 94 4.1.1Coulomb's Laws of Friction 95 4.1.2Angle of Friction 96 4.1.3Cone of Friction 96 4.1.4Angle of Repose 96 4.2 Equilibrium of a Panicle on a Rough Inclined Plane 97 4.2.1Particle on Rough Horizontal Plane Acted on by an External Force 98 4.2.2Particle on a Rough Inclined Plane Acted on by an External Force 99 4.3 Types of Friction 100 4.4 Wedges 100 4.5 Belt Friction 100 4.6 Ratio of Tension in V-belt Drive (also True for Rope Drive) 102 4.7 Rolling Motion 104 4.7.1 Rolling without Slipping 104 4.7.2Rolling and Sliding 106 Illustrative Examples 107 Exercises 127 5.Principle of Virtual Work 131-151 5.1 Introduction 131 5.2 Principle of Virtual Work 131 5.3 Method of Virtual Work 134 Illustrative Examples 134 Exercises 146 6. Centroid, Centre of Gravity and Moment of Inertia 152-211 6.1 Introduction 752 6.2 Centre of Gravity 152 6.3 Centre of Gravity of a Flat Plate 153 6.4 Determination of Centroid of Some Simple Bodies 154 6.5 Moment of Inertia 160 6.5.1Physical Interpretation of Moment of Inertia 160 6.6 Radius of Gyration 161 6.7 Moment of Inertia about Co-ordinate Axes 767 6.8 Calculation of Moments of Inertia in Simple Cases (Centre of Mass) 164 Illustrative Examples 175 Exercises 206 7. Machines 212-235 7.1 Introduction 212 7.2 Definitions 212 7.3 Law of Machine 215 7.4 Variation of Mechanical Advantage 276 7.5 Variation of Efficiency 216 7.6 Reversibility of a Machine 217 7.7 Pulleys 217 7.8 Wheel and Axle 221 7.9 Wheel and Differential Axle 222 Illustrative Examples 224 Exercises 233 8.Power Transmission and Belt Friction 236-274 8.1Introduction 236 8.2 Open Belt Drive 236 8.3 Compound Belt System 239 8.4 Length of the Belt 239 8.4.1Open Belt Drive 240 8.4.2Cross Belt Drive 241 8.5 Belt-Friction 242 8.5.1Flat Belt System 242 8.5.2V-shaped Belt System 244 8.6 Maximum Power Transmitted 246 8.7 Effect of Centrifugal force on Power Transfer 246 8.8 Design Considerations 241 8.9 Advantages and Disadvantages of Flat Belt Drive 249 8.10 Advantages and Disadvantages of V-belt Drive 249 Illustrative Examples 249 Exercises 270 9.Particle Kinematics, Rectilinear and Plane-Curvilinear Motion, Projectile and Constrained Motion 275-350 9.1Introduction 275 9.2 Rectilinear and Plane-Curvilinear Motion 276 9.2.1Average and Instantaneous Speed, Velocity and Acceleration 276 9.2.2Components of Velocity 278 9.2.3Relative Velocity and Relative Acceleration 282 9.2.4Angular Velocity 284 9.3 Projectile 288 9.3.1Motion of a Projectile and Its Trajectory 288 9.3.2Velocity and Direction of Motion after a Given Time 289 9.3.3Velocity and Direction of Motion at a Given Height h 290 9.3.4Range (R) on the Horizontal Plane Through O 292 9.3.5Parabolic Path 292 9.3.6Angles of Projection 294 9.4 Particle Projected from a Height 294 9.5 Range and Time of Flight up an Inclined Plane 296 9.5.1Maximum Range up an Inclined Plane 299 9.5.2Directions of Projections for a Given Range up an Inclined Plane 301 9.6 Range and Time of Right Down an Tnclined Plane 301 9.7Constrained Motion 302 9.7.1Motion of a Lift 302 9.7.2 Motion of Two Bodies Connected by a String Passing over a Smooth Pulley 304 9.7.3Motion of two masses when one mass is placed upon a rough horizontal plane and the odier is hanging vertically connected by a string passing over a smooth pulley at the edge of horizontal surface 304 9.7.4Motion of the two masses when one mass is placed upon a rough inclined plane and the other is hanging vertically connected by a string passing over a smooth pulley at the top of the plane 305 9.7.5 Motion of two masses connected by a string passing over a smooth pulley placed over the vertex of the two rough inclined planes 306 Illustrative Examples 307 Exercises 344 10. Particle and Rigid Body Dynamics 351-403 10.1 Introduction 351 10.2 Newton's Laws of Motion 353 10.2.1 The First Law of Motion 353 10.2.2 The Second Law of Motion 354 10.2.3 The Third Law of Motion 356 10.3 Friction 358 10.4 Rectilinear Motion 359 10.4.1 Motion in a Straight Line 359 10.4.2 Rectilinear Motion under Variable Acceleration 360 10.5 D'alembert's Principle 361 10.5.1 Rigid Body 361 10.5.2 D'Alembert's Principle (Analysis) 362 10.6 General Equations of Motion 364 10.7 Motion of Centre of Intertia Translational Motion 366 10.8 Motion about Centre of Mass 367 10.9 Rolling without Slipping Down an Inclined Plane 369 Illustrative Examples 371 Exercises 395 11. Work and Energy 404-458 11.1 Introduction 404 11.2 Displacement and Work 404 11.3 Work done by Constant Force in Rectilinear Motion 406 11.4 Work Done by Force of Gravity 406 11.5 Work Done by Spring Force (Elastic Force) 407 11.6 Work Done by Gravitational Force 408 11.7 Energy 408 11.8 Kinetic Energy 409 11.9 Potential Energy 409 11.10 Principle of Work and Energy 411 11.11 Law of Conservation of Energy 412 11.12 Power and Efficiency 414 11.13 Impulse and Momentum 414 11.14 Impulsive Force and Impulsive Motion 416 11.15 Impact and Conservation of Momentum 417 11.16 Coefficient of Restitution 417 11.17 Conservation of Linear Momentum 419 Illustrative Examples 420 Exercises 451 12. Vibrations 459-489 12.1 Introduction 459 12.2 Characteristics of a Vibrating System 460 12.3 Simple Harmonic Motion (SHM) 462 12.4 Longitudinal, Transverse and Torsional Vibrations 464 12.5 Effective Stiffness of Combinations of Spring 467 12.6 Solution of Differential Equation for SHM 469 12.7 Energy in Simple Harmonic Motion 470 Illustrative Examples 472 Exercises 486 Bibliography 491 Index 493-496