Applied Mathematics (eBook)

Front Cover 1
Applied Mathematics: Made Simple 4
Copyright Page 5
Foreword 6
Table of Contents 7
CHAPTER ONE. MECHANICS 10
(1) Rigid Bodies 10
(2) Characteristics of a Force 11
(3) Measuring Force with a Spring 13
( 4 ) Mass and Weight 15
(5) The Unit of Force 17
(6) Newton's Third Law 18
(7) Simple Force Diagrams 19
CHAPTER TWO. PARALLEL FORCES AND RIGID BODIES 22
(1) Turning Effect of a Force 22
(2) The Beam Balance 27
( 3 ) Calculation of Moments 29
( 4 ) Resultant of Two Parallel Forces 31
(5) Centre of Gravity 37
(6) Composite Figures 40
( 7 ) Solid Figures 42
CHAPTER THREE. KINEMATICS 44
(1) Speed and Velocity 45
(2) Speed-Time Formulae 47
(3) Distance-Time Graphs 48
(4) Non-uniform Speeds 53
(5) Speed-Time Graphs 55
CHAPTER FOUR. MOTION WITH UNIFORM ACCELERATION IN ASTRAIGHT LINE 59
(1) Acceleration 59
(2) Equations of Motion 64
(3) Acceleration due to Gravity 68
CHAPTER FIVE. NEWTON'S LAWS OF MOTION 75
(1) Momentum 75
(2) The First Law 76
(3) The Second Law 77
(4) Impulse of a Force 81
(5) The Third Law 86
CHAPTER SIX. AN INTRODUCTION TO VECTORS 92
(1) Revision of Trigonometry 92
(2) Sine rule and Cosine rule 100
(3) Vector Quantities 105
(4) Vector Addition 110
(5) Resultant of Three Vectors 113
CHAPTER SEVEN. VECTOR ALGEBRA AND COPLANAR FORCES 116
(1) Addition and Subtraction 117
(2) Distributive Law and Associative Law 118
(3) Vectors in Elementary Geometry 122
(4) The Polygon of Forces 124
(5) Non-concurrent Vectors 127
(6) Resolution of Vectors 129
(7) Resolving Non-concurrent Vectors 135
(8) Locating the Line of Action 140
CHAPTER EIGHT. RELATIVE MOTION 144
(1) Latitude and Longitude 150
(2) Finding Latitude 152
(3) Finding Longitude 152
(4) Course Calculations 156
(5) Moving Reference Point 162
(6) Positions of Closest Approach 165
CHAPTER NINE. PROJECTILES 171
(1) Vector Components 172
(2) Acceleration 174
(3) Equations of Motion 175
(4) General Equations for Projectile Motion 178
(5) Motion Down an Inclined Plane 184
(6) Motion Down a Chord of a Circle 186
(7) Lines of Quickest Descent 187
CHAPTER TEN. FRICTION 188
(1) Force of Friction 189
(2) Experimental Investigation of Static Friction 192
(3) Motive Force at an Angle to the Slope 199
(4) Toppling before Sliding 202
(5) Stable and Unstable Equilibrium 204
(6) Freely Hanging Load 206
CHAPTER ELEVEN. RIGID BODIES IN EQUILIBRIUM UNDER THEACTION OF COPLANAR FORCES 210
(1) Point of Concurrency 210
(2) Force Normal to a Surface 215
(3) Frictional Force and Normal Reaction 218
(4) Equilibrium of a Body under the Action of More than Three Forces 221
CHAPTER TWELVE. WORK, ENERGY AND POWER 226
(1) Work 226
(2) Kinetic Energy 227
(3) Motion at an Angle to the Force Producing it 229
(4) Potential Energy 234
(5) Conservation of Energy 236
(6) Momentum 241
(7) Power 242
CHAPTER THIRTEEN. MACHINES 245
(1) Mechanical Advantage 245
(2) Levers 246
(3) Wheel and Axle 252
(4) Velocity Ratio 253
(5) Inclined Plane 258
(6) Pulleys 261
(7) The Law of the Machine 263
CHAPTER FOURTEEN. HYDROSTATICS I: DENSITY, RELATIVE DENSITY,AND BUOYANCY 266
(1) Density 267
(2) Mixtures 271
(3) The Relative-density Bottle 274
(4) Archimedes' Principle 276
(5) The Hydrometer 280
(6) Buoyancy and Equilibrium 282
CHAPTER FIFTEEN. HYDROSTATICS Ð: LIQUID PRESSURE 285
(1) Fundamental Principles 286
(2) Pascal's Law 287
(3) Pressure due to Weight of Liquid 288
(4) Hydraulic Machines 290
(5) Horizontal Thrust in a Liquid 293
CHAPTER SIXTEEN. HYDROSTATICS ÉÐ: BAROMETERS AND BOYLE'SLAW 296
(1) Atmospheric Pressure 296
(2) Pressure of a Gas 301
(3) Hare's Apparatus 301
( 4 ) Boyle's Law 303
(5) Pumps 306
(6) The Siphon 307
TABLES 310
Logarithms 311
Ântilogarithms 313
Natural Sines 315
Natural Cosines 317
Natural Tangents 319
Squares 321
Square Roots 323
Reciprocals 327
SI UNITS AND ABBREVIATIONS 329
ANSWERS 330
INDEX 352