General Physics I: Classical Mechanics David G. Simpson Dept. of Natural Sciences, Prince George’s Community College, Largo, Maryland Larry L. Simpson Union Carbide Corporation (ret.), South Charleston, West Virginia Fall 2020 Last updated: October 8, 2020 Contents Acknowledgments 11 1 What is Physics? 12 2 Units 14 2.1 Systems of Units. 14 2.2 SI Units . 15 2.3 CGS Systems of Units . 19 2.4 British Engineering Units . 19 2.5 Units as an Error-Checking Technique . 19 2.6 Unit Conversions . 20 2.7 Currency Units. 22 2.8 Odds and Ends. 22 3 Problem-Solving Strategies 24 4 Density 26 4.1 Specific Gravity . 27 4.2 Density Trivia . 27 5 Kinematics in One Dimension 29 5.1 Position . 29 5.2 Velocity . 29 5.3 Acceleration . 30 5.4 Higher Derivatives . 31 5.5 Dot Notation. 31 5.6 Inverse Relations. 31 5.7 Constant Acceleration . 32 5.8 Summary . 34 5.9 Geometric Interpretations . 35 6 Vectors 37 6.1 Introduction . 37 6.2 Vector Arithmetic: Graphical Methods. 38 6.3 Vector Arithmetic: Algebraic Methods. 38 6.4 The Zero Vector . 43 6.5 Derivatives.......................................... 43 1 Prince George’s Community College General Physics I Simpson & Simpson 6.6 Integrals . 44 6.7 Other Vector Operations . 44 7 The Dot Product 45 7.1 Definition . 45 7.2 Component Form . 45 7.3 Properties . 46 7.4 Matrix Formulation . 48 8 Kinematics in Two or Three Dimensions 49 8.1 Position . 49 8.2 Velocity . 49 8.3 Acceleration . 49 8.4 Inverse Relations. 50 8.5 Constant Acceleration . 50 8.6 Vertical vs. Horizontal Motion . 51 8.7 Summary . 52 9 Projectile Motion 54 9.1 Range . 55 9.2 Maximum Altitude. 56 9.3 Shape of the Projectile Path . 57 9.4 Hitting a Target on the Ground. 57 9.5 Hitting a Target on a Hill. 59 9.6 Exploding Projectiles . 60 9.7 Other Considerations . 60 9.8 The Monkey and the Hunter Problem . 60 9.9 Summary . 62 10 Newton’s Method 63 10.1 Introduction . 63 10.2 The Method . 63 10.3 Example: Square Roots . 63 10.4 Projectile Problem . 65 11 Mass 66 12 Force 67 12.1 The Four Forces of Nature . 67 12.2 Hooke’s Law. 68 12.3 Weight . 68 12.4 Normal Force . 68 12.5 Tension . 69 13 Newton’s Laws of Motion 70 13.1 First Law of Motion . 70 13.2 Second Law of Motion. 70 13.3 Third Law of Motion . 72 2 Prince George’s Community College General Physics I Simpson & Simpson 14 The Inclined Plane 73 15 Atwood’s Machine 75 16 Statics 79 16.1 Mass Suspended by Two Ropes . 79 16.2 The Elevator . 82 16.3 The Catenary . 82 17 Friction 84 17.1 Introduction . 84 17.2 Static Friction . 84 17.3 Kinetic Friction . 85 17.4 Rolling Friction . 85 17.5 The Coefficient of Friction. 85 18 Blocks and Pulleys 87 18.1 Horizontal Block and Vertical Block. 87 18.2 Inclined Block and Vertical Block . 88 19 Resistive Forces in Fluids 91 19.1 Introduction . 91 19.2 Model I: FR / v....................................... 91 2 19.3 Model II: FR / v ...................................... 93 20 Circular Motion 96 20.1 Introduction . 96 20.2 Centripetal Force . 97 20.3 Centrifugal Force . 98 20.4 Relations between Circular and Linear Motion. 99 20.5 Examples . 99 21 Work 100 21.1 Introduction . 100 21.2 Case I: Constant F k r ....................................100 21.3 Case II: Constant F ¬ r ...................................101 21.4 Case III: Variable F k r ...................................101 21.5 Case IV (General Case): Variable F ¬ r ...........................102 21.6 Summary . 102 22 Simple Machines 103 22.1 Inclined Plane . 104 22.2 Wheel and Axle . 104 22.3 Pulley . 105 22.4 Lever . 106 22.5 Wedge . 108 22.6.