ENERGY METHODS IN APPLIED MECHANICS
CONTENTS PART ONE REVISION OF MATHEMATICS REVISIONARY MATHEMATICS INTRODUCTION RADIANS AND DEGREES MEASUREMENT OF ANGLES TRIANGLE CALCULATIONS BRACKETS FRACTIONS PERCENTAGES LAWS OF INDICES SIMULTANEOUS EQUATIONS REVISION TEST 1 REVISIONARY MATHEMATICS PART TWO STATICS AND STRENGTH OF MATERIALS THE EFFECTS OF FORCES ON MATERIALS TENSILE FORCE COMPRESSIVE FORCE SHEAR FORCE STRESS STRAIN ELASTICITY, LIMIT OF PROPORTIONALITY AND ELASTIC LIMIT HOOKE’S LAW DUCTILITY, BRITTLENESS AND MALLEABILITY 2 10 MODULUS OF RIGIDITY THERMAL STRAIN 2 12 COMPOUND BARS TENSILE TESTING THE TENSILE TEST WORKED PROBLEMS ON TENSILE TESTING FURTHER WORKED PROBLEMS ON TENSILE TESTING PROOF STRESS FORCES ACTING AT A POINT SCALAR AND VECTOR QUANTITIES CENTRE OF GRAVITY AND EQUILIBRIUM FORCES THE RESULTANT OF TWO COPLANAR FORCES TRIANGLE OF FORCES METHOD THE PARALLELOGRAM OF FORCES METHOD RESULTANT OF COPLANAR FORCES BY CALCULATION RESULTANT OF MORE THAN TWO COPLANAR FORCES COPLANAR FORCES IN EQUILIBRIUM 4 10 RESOLUTION OF FORCES SUMMARY SIMPLY SUPPORTED BEAMS THE MOMENT OF A FORCE EQUILIBRIUM AND THE PRINCIPLE OF MOMENTS SIMPLY SUPPORTED BEAMS HAVING POINT LOADS SIMPLY SUPPORTED BEAMS WITH COUPLES REVISION TEST 2 FORCES, TENSILE TESTING AND BEAMS FORCES IN STRUCTURES WORKED PROBLEMS ON MECHANISMS AND PIN-JOINTED TRUSSES GRAPHICAL METHOD METHOD OF JOINTS (A MATHEMATICAL METHOD) THE METHOD OF SECTIONS (A MATHEMATICAL METHOD) BENDING MOMENT AND SHEAR FORCE DIAGRAMS BENDING MOMENT (M) SHEARING FORCE (F) WORKED PROBLEMS ON BENDING MOMENT AND SHEARING FORCE DIAGRAMS UNIFORMLY DISTRIBUTED LOADS FIRST AND SECOND MOMENTS OF AREAS CENTROIDS THE FIRST MOMENT OF AREA CENTROID OF AREA BETWEEN A CURVE AND THE X-AXIS CENTROID OF AREA BETWEEN A CURVE AND THE Y-AXIS WORKED PROBLEMS ON CENTROIDS OF SIMPLE SHAPES FURTHER WORKED PROBLEMS ON CENTROIDS OF SIMPLE SHAPES SECOND MOMENTS OF AREA OF REGULAR SECTIONS SECOND MOMENT OF AREA FOR ‘BUILT-UP’ SECTIONS REVISION TEST 3 FORCES IN STRUCTURES, BENDING MOMENT AND SHEAR FORCE DIAGRAMS, AND SECOND MOMENTS OF AREA BENDING OF BEAMS TO PROVE THAT S = = M E Y I R WORKED PROBLEMS ON THE BENDING OF BEAMS 10 TORQUE 10 1 COUPLE AND TORQUE 10 2 WORK DONE AND POWER TRANSMITTED BY A CONSTANT TORQUE 10 3 KINETIC ENERGY AND MOMENT OF INERTIA 10 4 POWER TRANSMISSION AND EFFICIENCY 11 TWISTING OF SHAFTS TO PROVE THAT T ? = = T G R J L WORKED PROBLEMS ON THE TWISTING OF SHAFTS REVISION TEST 4 BENDING OF BEAMS, TORQUE AND TWISTING OF SHAFTS PART THREE DYNAMICS 12 LINEAR AND ANGULAR MOTION 12 1 THE RADIAN 12 2 LINEAR AND ANGULAR VELOCITY 12 3 LINEAR AND ANGULAR ACCELERATION 12 4 FURTHER EQUATIONS OF MOTION 12 5 RELATIVE VELOCITY 13 LINEAR MOMENTUM AND IMPULSE 13 1 LINEAR MOMENTUM 13 2 IMPULSE AND IMPULSIVE FORCES 14 FORCE, MASS AND ACCELERATION 14 1 INTRODUCTION 14 2 NEWTON’S LAWS OF MOTION 14 3 CENTRIPETAL ACCELERATION 14 4 ROTATION OF A RIGID BODY ABOUT A FIXED AXIS 14 5 MOMENT OF INERTIA (I) 15 WORK, ENERGY AND POWER 15 1 WORK 15 2 ENERGY 15 3 POWER 15 4 POTENTIAL AND KINETIC ENERGY 15 5 KINETIC ENERGY OF ROTATION REVISION TEST 5 LINEAR AND ANGULAR MOTION, MOMENTUM AND IMPULSE, FORCE, MASS AND ACCELERATION, WORK, ENERGY AND POWER 16 FRICTION 16 1 INTRODUCTION TO FRICTION 16 2 COEFFICIENT OF FRICTION 16 3 APPLICATIONS OF FRICTION 16 4 FRICTION ON AN INCLINED PLANE 16 5 MOTION UP A PLANE WITH THE PULLING FORCE P PARALLEL TO THE PLANE 16 6 MOTION DOWN A PLANE WITH THE PULLING FORCE P PARALLEL TO THE PLANE 16 7 MOTION UP A PLANE DUE TO A HORIZONTAL FORCE P 16 8 THE EFFICIENCY OF A SCREW JACK 17 MOTION IN A CIRCLE 17 1 INTRODUCTION 17 2 MOTION ON A CURVED BANKED TRACK 17 3 CONICAL PENDULUM 17 4 MOTION IN A VERTICAL CIRCLE 17 5 CENTRIFUGAL CLUTCH 18 SIMPLE HARMONIC MOTION 18 1 INTRODUCTION TO SIMPLE HARMONIC MOTION (SHM) 18 2 THE SPRING-MASS SYSTEM 18 3 THE SIMPLE PENDULUM 18 4 THE COMPOUND PENDULUM 18 5 TORSIONAL VIBRATIONS 19 SIMPLE MACHINES 19 1 MACHINES 19 2 FORCE RATIO, MOVEMENT RATIO AND EFFICIENCY 19 3 PULLEYS 19 4 THE SCREW-JACK 19 5 GEAR TRAINS 19 6 LEVERS REVISION TEST 6 FRICTION, MOTION IN A CIRCLE, SIMPLE HARMONIC MOTION AND SIMPLE MACHINES PART FOUR HEAT TRANSFER AND FLUID MECHANICS 20 HEAT ENERGY AND TRANSFER 20 1 INTRODUCTION 20 2 THE MEASUREMENT OF TEMPERATURE 20 3 SPECIFIC HEAT CAPACITY 20 4 CHANGE OF STATE 20 5 LATENT HEATS OF FUSION AND VAPORISATION 20 6 A SIMPLE REFRIGERATOR 20 7 CONDUCTION, CONVECTION AND RADIATION 20 8 VACUUM FLASK 20 9 USE OF INSULATION IN CONSERVING FUEL 21 THERMAL EXPANSION 21 1 INTRODUCTION 21 2 PRACTICAL APPLICATIONS OF THERMAL EXPANSION 21 3 EXPANSION AND CONTRACTION OF WATER 21 4 COEFFICIENT OF LINEAR EXPANSION 21 5 COEFFICIENT OF SUPERFICIAL EXPANSION 21 6 COEFFICIENT OF CUBIC EXPANSION REVISION TEST 7 HEAT ENERGY AND TRANSFER, AND THERMAL EXPANSION 22 HYDROSTATICS 22 1 PRESSURE 22 2 FLUID PRESSURE 22 3 ATMOSPHERIC PRESSURE 22 4 ARCHIMEDES’ PRINCIPLE 22 5 MEASUREMENT OF PRESSURE 22 6 BAROMETERS 22 7 ABSOLUTE AND GAUGE PRESSURE 22 8 THE MANOMETER 22 9 THE BOURDON PRESSURE GAUGE 22 10 VACUUM GAUGES 22 11 HYDROSTATIC PRESSURE ON SUBMERGED SURFACES 22 12 HYDROSTATIC THRUST ON CURVED SURFACES 22 13 BUOYANCY 22 14 THE STABILITY OF FLOATING BODIES 23 FLUID FLOW 23 1 DIFFERENTIAL PRESSURE FLOWMETERS 23 2 ORIFICE PLATE 23 3 VENTURI TUBE 23 4 FLOW NOZZLE 23 5 PITOT-STATIC TUBE 23 6 MECHANICAL FLOWMETERS 23 7 DEFLECTING VANE FLOWMETER 23 8 TURBINE TYPE METERS 23 9 FLOAT AND TAPERED-TUBE METER 23 10 ELECTROMAGNETIC FLOWMETER 23 11 HOT-WIRE ANEMOMETER 23 12 CHOICE OF FLOWMETER 23 13 EQUATION OF CONTINUITY 23 14 BERNOULLI’S EQUATION 23 15 IMPACT OF A JET ON A STATIONARY PLATE 24 IDEAL GAS LAWS 24 1 BOYLE’S LAW 24 2 CHARLES’ LAW 24 3 THE PRESSURE LAW 24 4 DALTON’S LAW OF PARTIAL PRESSURE 24 5 CHARACTERISTIC GAS EQUATION 24 6 WORKED PROBLEMS ON THE CHARACTERISTIC GAS EQUATION 24 7 FURTHER WORKED PROBLEMS ON THE CHARACTERISTIC GAS EQUATION 25 THE MEASUREMENT OF TEMPERATURE 25 1 LIQUID-IN-GLASS THERMOMETER 25 2 THERMOCOUPLES 25 3 RESISTANCE THERMOMETERS 25 4 THERMISTORS 25 5 PYROMETERS 25 6 TEMPERATURE INDICATING PAINTS AND CRAYONS 25 7 BIMETALLIC THERMOMETERS 25 8 MERCURY-IN-STEEL THERMOMETER 25 9 GAS THERMOMETERS 25 10 CHOICE OF MEASURING DEVICES REVISION TEST 8 HYDROSTATICS, FLUID FLOW, GAS LAWS AND TEMPERATURE MEASUREMENT A LIST OF FORMULAE FOR MECHANICAL ENGINEERING PRINCIPLES GREEK ALPHABET ANSWERS TO MULTIPLE-CHOICE QUESTIONS