INTRODUCTORY PHYSICS PROBLEMS
Chapter 1 ? Units and Significant Figures 1 11 INTRODUCTION: UNITS HELP TELL US HOW MUCH 1 12 UNIT CONVERSIONS 1 13 POWER OF 10 CONVERSIONS 5 14 SIGNIFICANT FIGURES 7 15 CHAPTER 1 SUMMARY 8 Practice Problems 9 Section 12 9 Section 13 10 Section 14 12 Chapter 2 ? Motion in a Straight Line 15 21 INTRODUCTION: DESCRIBING MOTION IN THE WORLD 15 22 MOTION QUANTITIES 15 23 DISPLACEMENT, POSITION, AND COORDINATE SYSTEMS 16 24 AVERAGE AND INSTANTANEOUS VELOCITY 17 25 AVERAGE AND INSTANTANEOUS ACCELERATION 18 26 MOTION ON A LINE WITH CONSTANT ACCELERATION 19 27 FREE FALL 23 28 WHAT IF ACCELERATION IS NOT CONSTANT? 28 ? 29 CHAPTER 2 SUMMARY 28 Practice Problems 29 Section 24 29 Section 25 30 Section 26 32 Section 27 40 Chapter 3 ? Motion in Two and Three Dimensions 47 31 INTRODUCTION: THREE DIMENSIONS ARE MORE REALISTIC THAN ONE 47 32 DIMENSIONS BEHAVE SEPARATELY 47 33 VECTOR MATH: COMPONENTS AND MAGNITUDE AND DIRECTION 49 34 DOING BASIC MATH WITH VECTORS: ADDING VECTORS, MULTIPLICATION BY A SCALAR 53 35 TWO-DIMENSIONAL CONSTANT ACCELERATION PROBLEMS 54 36 PROJECTILE MOTION 57 37 MOTION IN THREE DIMENSIONS 64 38 CHAPTER 3 SUMMARY 64 Practice Problems 66 Section 33 66 Section 34 69 Section 35 72 Section 36 77 Chapter 4 ? Introduction to Forces 95 41 INTRODUCTION: FORCES CAUSE MOTION 95 42 NEWTON’S SECOND LAW 95 43 NEWTON’S FIRST AND THIRD LAWS 99 44 CHAPTER 4 SUMMARY 100 Practice Problems 101 Section 42 101 ? Chapter 5 ? Specific Types of Forces, and Force Problems 107 51 INTRODUCTION: THERE ARE DIFFERENT TYPES OF FORCES 107 52 FREE BODY DIAGRAMS 107 53 WHAT FORCES ARE ON MY OBJECT? 109 54 GRAVITY (NEAR EARTH) 109 55 KINETIC FRICTION 112 56 STATIC FRICTION 115 57 SPRING FORCES 118 58 COMMON FORCE PROBLEMS, TYPE 1: RAMP PROBLEMS 120 59 COMMON FORCE PROBLEMS, TYPE 2: PROBLEMS WITH ELEVATORS 125 510 COMMON FORCE PROBLEMS, TYPE 3: PROBLEMS WITH A ROPE AND PULLEY 126 511 COMMON FORCE PROBLEMS, TYPE 4: COMBINING FORCE AND KINEMATICS PROBLEMS 130 512 CHAPTER 5 SUMMARY 133 Practice Problems: 135 Section 54 (Gravity near Earth) 135 Section 55 (Kinetic friction) 139 Section 56 (Static Friction) 144 Section 57 (Spring Forces) 148 Section 58 (Ramp Problems) 150 Section 59 (Problems with Elevators) 154 Section 510 (Problems with a Rope and a Pulley) 156 Section 511 (Combining Force and Kinematics Problems) 162 Chapter 6 ? Energy, and Work 169 61 INTRODUCTION: MOTION HAS ENERGY 169 62 WORK BY A CONSTANT FORCE 169 63 WORK DONE BY SPRINGS, WHERE FORCE CHANGES WITH POSITION 171 64 NET WORK 172 65 KINETIC ENERGY 174 66 THE WORK-KINETIC ENERGY THEOREM 175 67 POTENTIAL ENERGY 176 68 MECHANICAL ENERGY 178 69 CONSERVATION OF MECHANICAL ENERGY 180 610 POWER 185 611 CHAPTER 6 SUMMARY 186 Practice Problems 188 Section 62 (Work Done by Constant Forces), Section 63 (Work Done by Springs) and Section 64 (Net Work) 188 Section 65 (Kinetic Energy) 192 Section 66 (Work-Kinetic Energy Theorem) 192 Section 67 (Potential Energy) 195 Section 68 (Mechanical Energy) 196 Section 69 (Conservation of Mechanical Energy) 198 Section 610 (Power) 204 Chapter 7 ? Linear Momentum and Collisions 207 71 INTRODUCTION: COLLISIONS AND MOMENTUM 207 72 LINEAR MOMENTUM 207 73 LINEAR MOMENTUM PROBLEMS WITHOUT COLLISIONS 208 74 COLLISIONS AND LINEAR MOMENTUM 209 75 COLLISIONS, PROBLEM TYPE 1: PERFECTLY INELASTIC COLLISIONS WITH ONE DIMENSION 210 76 COLLISIONS, PROBLEM TYPE 2: ELASTIC COLLISIONS WITH ONE DIMENSION 211 77 PERFECTLY INELASTIC COLLISIONS WITH TWO DIMENSIONS 215 78 HOW MUCH FORCE HAPPENED? 219 79 EXTRA TOPIC: CENTER OF MASS AND LINEAR MOMENTUM CONSERVATION 220 710 CHAPTER 7 SUMMARY 222 Practice Problems 224 Section 73 (Linear Momentum Problems without Collisions) 224 Section 75 (Perfectly Inelastic Collisions with One Dimension) 225 Section 76 (Elastic Collisions with One Dimension) 229 Section 77 (Perfectly Inelastic Collisions with Two Dimensions) 233 Section 78 (How Much Force Happened) 239 Section 79 (Center of Mass) 240 Chapter 8 ? Uniform Circular Motion (Moving in a Circle at Constant Speed) 243 81 INTRODUCTION: SOMETIMES THINGS MOVE IN A CIRCLE 243 82 CENTRIPETAL AND TANGENTIAL DIRECTIONS 243 83 CENTRIPETAL ACCELERATION 244 84 NET FORCE IN THE CENTRIPETAL DIRECTION (ALSO CALLED CENTRIPETAL FORCE) 245 85 CHAPTER 8 SUMMARY 248 Practice Problems 248 Section 83 (Centripetal Acceleration) 248 Section 84 (Net Force in the Centripetal Direction; Also Called Centripetal Force) 250 Chapter 9 ? Rotation Motion and Forces 255 91 INTRODUCTION: ROTATIONAL MOTION IS LIKE LINEAR MOTION 255 92 UNITS FOR ANGLE: RADIANS AND REVOLUTIONS 255 93 ROTATION EQUIVALENTS OF POSITION, VELOCITY, AND ACCELERATION 256 94 MOTION WITH CONSTANT ANGULAR ACCELERATION 257 95 MOMENT OF INERTIA (ROTATION EQUIVALENT OF MASS) 260 96 TORQUE (ROTATION EQUIVALENT OF FORCE) 262 97 NEWTON’S SECOND LAW (ROTATION EQUIVALENT) 264 98 RELATING ANGULAR DISPLACEMENT, ANGULAR VELOCITY, AND ANGULAR ACCELERATION TO LINEAR DISPLACEMENT, LINEAR VELOCITY, AND LINEAR ACCELERATION 267 99 EXTRA TOPIC: TORQUE IS A VECTOR; CALCULATING ITS COMPONENTS 269 910 CHAPTER 9 SUMMARY 271 Practice Problems 273 Section 92 (Units for Angle) 273 Section 94 (Motion with Constant Angular Acceleration) 276 Section 95 (Moment of Inertia) 278 Section 96 (Torque) 280 Section 97 (Newton’s Second Law) 282 Section 98 (Relating Angular Displacement, Angular Velocity, and Angular Acceleration to Linear Displacement, Linear Velocity, and Linear Acceleration) 284 Section 99 (Extra Topic: Torque Vector Components) 288 Chapter 10 ? Rotation: Energy, Momentum, and Rolling 291 101 INTRODUCTION: ENERGY AND MOMENTUM FOR ROTATION 291 102 ROTATION AND KINETIC ENERGY 291 103 ROLLING (WITHOUT SLIPPING) 293 104 ROTATION EQUIVALENT OF WORK 296 105 ROTATION EQUIVALENT OF POWER 297 106 ANGULAR MOMENTUM 298 107 CONSERVATION OF ANGULAR MOMENTUM 300 108 CHAPTER 10 SUMMARY 304 Practice Problems 305 Section 102 (Rotation and Kinetic Energy) 305 Section 103 (Rolling, without Slipping) 307 Section 104 (Rotation and Work) 310 Section 105 (Rotation and Power) 311 Section 106 (Angular Momentum) 313 Section 107 (Conservation of Angular Momentum and Rotation Collisions) 314 Chapter 11 ? Newton’s More General Law of Gravity 319 111 INTRODUCTION: GRAVITY IS DIFFERENT AWAY FROM THE GROUND 319 112 NEWTON’S LAW OF GRAVITY 319 113 CONNECTING M?G WITH NEWTON’S LAW OF GRAVITY 321 114 POTENTIAL ENERGY FROM GRAVITY USING NEWTON’S LAW OF GRAVITY 322 115 NEWTON’S LAW OF GRAVITY WITH CONSERVATION OF MECHANICAL ENERGY 324 116 NEWTON’S LAW OF GRAVITY WITH CIRCULAR MOTION 328 117 CHAPTER 11 SUMMARY 330 Practice Problems 331 Section 112 (Newton’s Law of Gravity) 331 Section 114 (Potential Energy from Gravity Using Newton’s Law of Gravity) 332 Section 115 (Newton’s Law of Gravity with Conservation of Mechanical Energy) 334 Section 116 (Newton’s Law of Gravity with Circular Motion) 338 Chapter 12 ? Simple Harmonic Motion 341 121 INTRODUCTION: MOTION REPEATS 341 122 REPETITIVE MOTION QUANTITIES, AND SIMPLE HARMONIC MOTION 341 123 POSITION, VELOCITY AND ACCELERATION 342 124 SIMPLE HARMONIC MOTION AND OBJECTS ON SPRINGS 344 125 SIMPLE HARMONIC MOTION: SIMPLE PENDULUM 347 126 OBJECT CONNECTED TO A SPRING AND MECHANICAL ENERGY 348 127 CHAPTER 12 SUMMARY 351 Practice Problems 352 Sections 122, 123, and 124 (Repetitive Motion Quantities; Position, Velocity, and Acceleration; Simple Harmonic Motion and Objects on Springs) 352 Section 125 (Simple Pendulum) 356 Section 126 (Object Connected to a Spring and Mechanical Energy) 357 Chapter 13 ? Math Review 361 131 INTRODUCTION: PHYSICS USES MATH 361 132 ALGEBRA PROBLEMS – SOLVING FOR A VARIABLE 361 133 EXPONENTIAL NUMBERS 362 134 SOLVING WHEN SOMETHING IS SQUARED, PART 1 363 135 SOLVING WHEN SOMETHING IS SQUARED, PART 2 365 136 TWO EQUATIONS AT ONCE 366 137 TRIGONOMETRY 369 138 CIRCLE GEOMETRY REVIEW 371 139 CHAPTER 13 SUMMARY 371 Practice Problems 372 Section 132 (Algebra Problems – Solving for a Variable) 372 Section 133 (Exponential Numbers) 374 Section 134 (Solving When Something is Squared, Part 1) 375 Section 135 (Solving When Something Is Squared, Part 2 – Quadratic Formula) 377 Section 136 (Two Equations at Once) 379 Section 137 (Trigonometry) 382