Table Of ContentF
OUNDATIONS
OF
P
HYSICS
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F
OUNDATIONS
OF
P
HYSICS
Steve Adams
MERCURY LEARNING AND INFORMATION
Dulles, Virginia
Boston, Massachusetts
New Delhi
Reprint and Revision Copyright ©2019 by MERCURY LEARNING AND INFORMATION LLC.
All rights reserved.
Original title and copyright: Principles of Physics. Copyright ©2017 by The Pantaneto Press. All rights
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Steve Adams. Foundations of Physics.
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For Alison
CONTENTS
Preface xxv
Chapter 1 The Language of Physics 1
1.0 Introduction 1
1.1 The S.I. System of Units 1
1.2 Dimensions 3
1.2.1 Method of Dimensions 4
1.3 Scientific Notation, Prefixes, and Significant Figures 5
1.4 Uncertainties 6
1.4.1 Types of Uncertainty 7
1.4.2 Combining Uncertainties 7
1.5 Dealing with Random and Systematic Experimental Errors 8
1.6 Differential Calculus 9
1.6.1 Derivatives and Rates of Change 9
1.6.2 Maximum and Minimum Values 11
1.7 Differential Equations 13
1.8 Integral Calculus 14
1.9 Vectors and Scalars 15
1.9.1 Adding Vectors 16
1.9.2 Resolving Vectors into Components 16
1.9.3 Multiplying Vectors 17
1.10 Symmetry Principles 19
1.11 Exercises 21
Chapter 2 Representing and Analyzing Data 23
2.0 Introduction 23
2.1 Experimental Variables 23
2.2 Recording Data 24
2.3 Straight Line Graphs 26
2.3.1 Interpreting Straight Line Graphs 26
2.3.2 Analyzing Straight Line Graphs 26
2.4 Plotting Graphs and Using Error Bars 27
2.4.1 Plotting Graphs by Hand 27
2.4.2 Finding a Gradient from a Straight Line Graph 28
2.4.3 Using a Spreadsheet Program 29
2.4.4 Using Error Bars 30
2.5 Logarithms 32
2.5.1 Logarithmic Scales and Logarithms 32
2.5.2 Using Logarithms 32
viii • FOUNDATIONS OF PHYSICS
2.6 Testing Mathematical Relationships Between Variables 33
2.6.1 Direct Proportion 33
2.6.2 Inverse Proportion 33
2.6.3 Inverse-Square Law 34
2.6.4 Power Law 34
2.6.5 Exponential Decay or Growth 34
2.7 Exercises 35
Chapter 3 Capturing, Displaying, and Analyzing Motion 37
3.0 Introduction 37
3.1 Motion Terminology 37
3.2 Graphs of Motion 38
3.3 Equations of Motion for Constant Acceleration:
The “Suvat” Equations 39
3.3.1 Derivation 1: From Graphs of Motion 40
3.3.2 Derivation 2: Using Calculus 41
3.4 Projectile Motion 41
3.4.1 Independence of Horizontal and Vertical
Components of Motion 41
3.4.2 Parabolic Paths 42
3.4.3 Range of a Projectile 43
3.5 Equation of Motion 43
3.6 Methods to Capture and Display Graphs of Motion 44
3.6.1 Motion Sensors and Dataloggers 44
3.6.2 Light Gates 45
3.6.3 Mobile Phones and Tablets 46
3.7 Exercises 48
Chapter 4 Forces and Equilibrium 51
4.1 Force as a Vector 51
4.1.1 Free Body Diagrams 51
4.1.2 Resolving Forces 52
4.1.3 Finding a Resultant Force 52
4.2 Mass, Weight, and Center of Gravity 54
4.2.1 Mass 54
4.2.2 Weight 55
4.2.3 Center of Gravity 55
4.3 Equilibrium of Coplanar Forces 57
4.3.1 Using the Triangle of Forces to Solve Equilibrium Problems 57
4.3.2 Resolving Forces to Solve Equilibrium Problems 58
4.4 Turning Effects of a Force: Moments, Torques, and Couples 59
4.4.1 Moments and Torques 59
4.4.2 Resultant Moment 60
CONTENTS • ix
4.4.3 Couples 60
4.4.4 Principle of Moments 61
4.5 Stability 63
4.5.1 Types of Mechanical Equilibrium 63
4.5.2 Degrees of Stability 65
4.6 Frictional Forces 66
4.6.1 Origin of Frictional ForcesBetween Surfaces in Contact 66
4.6.2 Static and Dynamic (Kinetic) Friction 67
4.6.3 Coefficients of Friction 67
4.6.4 Measuring the Coefficient of Static Friction 68
4.6.5 Measuring the Coefficient of Dynamic (Kinetic) Friction 69
4.7 Exercises 69
Chapter 5 Newtonian Mechanics 73
5.0 Introduction 73
5.1 Newton’s Laws of Motion 73
5.1.1 Newton’s First Law of Motion 73
5.1.2 Galilean Relativity 74
5.1.3 Newton’s Second Law of Motion 75
5.1.4 Free Fall 76
5.1.5 Newton’s Third Law of Motion 78
5.2 Linear Momentum 80
5.2.1 Newton’s Second Law in Terms of Linear Momentum 80
5.2.2 Impulse and Change of Momentum 80
5.2.3 Conservation of Linear Momentum 81
5.3 Work Energy and Power 84
5.3.1 Work 84
5.3.2 Gravitational Potential Energy Changes (Uniform Field) 86
5.3.3 Kinetic Energy 87
5.3.4 The Law of Conservation of Energy 87
5.3.5 Energy and Momentum in a 2D Collision 88
5.3.6 Energy Transfers 89
5.3.7 Power 90
5.4 Energy Resources 91
5.5 Propulsion Systems 92
5.5.1 Jet Propulsion 92
5.5.2 Rockets 93
5.5.3 Radiation Pressure 94
5.6 Frames of Reference 95
5.6.1 The Center of Mass Frame 96
5.6.2 Galilean Transformation 97
5.7 Theoretical Mechanics 98
5.7.1 Force and Energy 99
