The Free High School Science Texts: A Textbook for High School Students Studying Physics. FHSST Authors1 August 5, 2005 1See http://savannah.nongnu.org/projects/fhsst Copyright c 2003 \Free High School Science Texts" Permissionis granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front- Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled \GNU Free Documentation License". i Contents I Physics 1 1 Units 3 1.1 PGCE Comments . 3 1.2 `TO DO' LIST . 3 1.3 Introduction . 3 1.4 Unit Systems . 4 1.4.1 SI Units (Systeme International d'Unit¶es) . 4 1.4.2 The Other Systems of Units . 5 1.5 The Importance of Units . 6 1.6 Choice of Units . 7 1.7 How to Change Units| the \Multiply by 1" Technique . 7 1.8 How Units Can Help You . 8 1.8.1 What is a `sanity test'? . 8 1.9 Temperature . 8 1.10 Scienti¯c Notation, Signi¯cant Figures and Rounding . 9 1.11 Conclusion . 10 2 Waves and Wavelike Motion 11 2.1 What are waves? . 11 2.1.1 Characteristics of Waves : Amplitude . 11 2.1.2 Characteristics of Waves : Wavelength . 12 2.1.3 Characteristics of Waves : Period . 12 2.1.4 Characteristics of Waves : Frequency . 13 2.1.5 Characteristics of Waves : Speed . 13 2.2 Two Types of Waves . 14 2.3 Properties of Waves . 15 2.3.1 Properties of Waves : Reection . 15 2.3.2 Properties of Waves : Refraction . 17 2.3.3 Properties of Waves : Interference . 19 2.3.4 Properties of Waves : Standing Waves . 20 2.3.5 Beats . 26 2.3.6 Properties of Waves : Di®raction . 28 2.3.7 Properties of Waves : Dispersion . 30 2.4 Practical Applications of Waves: Sound Waves . 30 2.4.1 Doppler Shift . 30 2.4.2 Mach Cone . 32 2.4.3 Ultra-Sound . 33 ii 2.5 Important Equations and Quantities . 35 3 Geometrical Optics 37 3.1 Refraction re-looked . 37 3.1.1 Apparent and Real Depth: . 38 3.1.2 Splitting of White Light . 39 3.1.3 Total Internal Reection . 40 3.2 Lenses . 40 3.2.1 Convex lenses . 41 3.2.2 Concave Lenses . 41 3.2.3 Magni¯cation . 42 3.2.4 Compound Microscope . 43 3.2.5 The Human Eye . 43 3.3 Introduction . 44 3.4 Reection . 44 3.4.1 Di®use reection . 44 3.4.2 Regular reection . 44 3.4.3 Laws of reection . 44 3.4.4 Lateral inversion . 45 3.5 Curved Mirrors . 45 3.5.1 Concave Mirrors (Converging Mirrors) . 45 3.5.2 Convex Mirrors . 46 3.5.3 Refraction . 46 3.5.4 Laws of Refraction . 47 3.5.5 Total Internal Reection . 48 3.5.6 Mirage . 49 3.6 The Electromagnetic Spectrum . 49 3.7 Important Equations and Quantities . 50 4 Vectors 51 4.1 PGCE Comments . 51 4.2 `TO DO' LIST . 51 4.3 Introduction . 52 4.3.1 Mathematical representation . 52 4.3.2 Graphical representation . 53 4.4 Some Examples of Vectors . 53 4.4.1 Displacement . 53 4.4.2 Velocity . 54 4.4.3 Acceleration . 57 4.5 Mathematical Properties of Vectors . 58 4.5.1 Addition of Vectors . 58 4.5.2 Subtraction of Vectors . 60 4.5.3 Scalar Multiplication . 61 4.6 Techniques of Vector Addition . 61 4.6.1 Graphical Techniques . 61 4.6.2 Algebraic Addition and Subtraction of Vectors . 71 4.7 Components of Vectors . 76 4.7.1 Block on an incline . 78 4.7.2 Vector addition using components . 79 iii 4.8 Do I really need to learn about vectors? Are they really useful? . 83 4.9 Summary of Important Quantities, Equations and Concepts . 83 5 Forces 85 5.1 `TO DO' LIST . 85 5.2 What is a force? . 85 5.3 Force diagrams . 85 5.4 Equilibrium of Forces . 87 5.5 Newton's Laws of Motion . 91 5.5.1 First Law . 92 5.5.2 Second Law . 93 5.5.3 Third Law . 97 5.6 Examples of Forces Studied Later . 101 5.6.1 Newtonian Gravity . 101 5.6.2 Electromagnetic Forces . 101 5.7 Summary of Important Quantities, Equations and Concepts . 102 6 Rectilinear Motion 104 6.1 What is rectilinear motion? . 104 6.2 Speed and Velocity . 104 6.3 Graphs . 106 6.3.1 Displacement-Time Graphs . 106 6.3.2 Velocity-Time Graphs . 108 6.3.3 Acceleration-Time Graphs . 109 6.3.4 Worked Examples . 111 6.4 Equations of Motion . ..