Question? Leave a message!




High School Physics Textbook

high school physics textbook principles and problems | download free pdf
JohnTheron Profile Pic
JohnTheron,Germany,Teacher
Published Date:09-07-2017
Website URL
Comment
The Free High School Science Texts: A Textbook for High School Students Studying Physics. 1 FHSST Authors December 9, 2005 1 See http://savannah.nongnu.org/projects/fhsstc Copyright° 2003 \Free High School Science Texts" Permission is 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". iContents 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 (Systµ eme 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 : Re°ection . . . . . . . . . . . . . . . . . . . . . . . 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 ii2.5 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 Re°ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Re°ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4.1 Di®use re°ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4.2 Regular re°ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4.3 Laws of re°ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Re°ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 iii4.8 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.5 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 125 7 Momentum 126 7.1 What is Momentum? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.2 The Momentum of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.3 Change in Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.4 What properties does momentum have? . . . . . . . . . . . . . . . . . . . . . . . 133 7.5 Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.6 Summary of Important Quantities, Equations and Concepts . . . . . . . . . . . . 139 8 Work and Energy 140 8.1 What are Work and Energy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 8.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 8.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8.3.1 Types of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8.4 Mechanical Energy and Energy Conservation . . . . . . . . . . . . . . . . . . . . 149 8.5 Summary of Important Quantities, Equations and Concepts . . . . . . . . . . . . 151 Essay 1: Energy 152 Essay 2: Tiny, Violent Collisions 158 iv9 Collisions and Explosions 159 9.1 Types of Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 9.1.1 Elastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 9.1.2 Inelastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 9.2 Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 9.3 Explosions: Energy and Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.4 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 175 10 Newtonian Gravitation 176 10.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 10.2 Mass and Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 10.2.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 10.3 Normal Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 10.4 Comparative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 10.4.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 10.5 Falling bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 10.6 Terminal velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 10.7 Drag force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 10.8 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 186 11 Pressure 187 11.1 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 187 Essay 3: Pressure and Forces 188 12 Heat and Properties of Matter 190 12.1 Phases of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 12.1.1 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 12.2 Phases of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 12.2.1 Solids, liquids, gasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.2.2 Pressure in °uids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.2.3 change of phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.3 Deformation of solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.3.1 strain, stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.3.2 Elastic and plastic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.4 Ideal gasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 12.4.1 Equation of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.4.2 Kinetic theory of gasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 12.4.3 Pressure of a gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 12.4.4 Kinetic energy of molecules . . . . . . . . . . . . . . . . . . . . . . . . . . 208 12.5 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 12.5.1 Thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 12.5.2 Temperature scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 12.5.3 Practical thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 12.5.4 Speci¯c heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 12.5.5 Speci¯c latent heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 12.5.6 Internal energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 12.5.7 First law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 215 12.6 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 215 v13 Electrostatics 216 13.1 What is Electrostatics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 13.2 Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 13.3 Electrostatic Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 13.3.1 Coulomb's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 13.4 Electric Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 13.4.1 Test Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 13.4.2 What do ¯eld maps look like? . . . . . . . . . . . . . . . . . . . . . . . . . 223 13.4.3 Combined Charge Distributions . . . . . . . . . . . . . . . . . . . . . . . . 225 13.4.4 Parallel plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 13.4.5 What about the Strength of the Electric Field? . . . . . . . . . . . . . . . 229 13.5 Electrical Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 13.5.1 Work Done and Energy Transfer in a Field . . . . . . . . . . . . . . . . . 230 13.5.2 Electrical Potential Di®erence . . . . . . . . . . . . . . . . . . . . . . . . . 233 13.5.3 Millikan's Oil-drop Experiment . . . . . . . . . . . . . . . . . . . . . . . . 236 13.6 Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 239 14 Electricity 240 14.1 Flow of Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 14.2 Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 14.3 Voltage and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 14.4 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 14.5 Voltage and current in a practical circuit . . . . . . . . . . . . . . . . . . . . . . . 254 14.6 Direction of current °ow in a circuit . . . . . . . . . . . . . . . . . . . . . . . . . 256 14.7 How voltage, current, and resistance relate . . . . . . . . . . . . . . . . . . . . . . 258 14.8 Voltmeters, ammeters, and ohmmeters . . . . . . . . . . . . . . . . . . . . . . . . 262 14.9 An analogy for Ohm's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 14.10Power in electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 14.11Calculating electric power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 14.12Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 14.13Nonlinear conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 14.14Circuit wiring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 14.15Polarity of voltage drops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 14.16What are "series" and "parallel" circuits? . . . . . . . . . . . . . . . . . . . . . . 272 14.17Simple series circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 14.18Simple parallel circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 14.19Power calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 14.20Correct use of Ohm's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 14.21Conductor size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 14.22Fuses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 14.23Important Equations and Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 285 15 Magnets and Electromagnetism 288 15.1 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 15.2 Magnetic units of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 15.3 Electromagnetic induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 15.4 AC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 15.5 Measurements of AC magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 vi16 Electronics 315 16.1 capacitive and inductive circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 16.1.1 A capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 16.1.2 An inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 16.2 ¯lters and signal tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 16.3 active circuit elements, diode, LED and ¯eld e®ect transistor, operational ampli¯er316 16.3.1 Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 16.3.2 LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 16.3.3 Transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 16.3.4 The transistor as a switch . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 16.4 principles of digital electronics logical gates, counting circuits . . . . . . . . . . . 332 16.4.1 Electronic logic gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 16.5 Counting circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 16.5.1 Half Adder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 16.5.2 Full adder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 17 The Atom 335 17.1 Models of the Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 17.2 Structure of the Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 17.3 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 17.4 Energy quantization and electron con¯guration . . . . . . . . . . . . . . . . . . . 336 17.5 Periodicity of ionization energy to support atom arrangement in Periodic Table . 336 17.6 Successive ionisation energies to provide evidence for arrangement of electrons into core and valence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 17.7 Bohr orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 17.8 Heisenberg uncertainty Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 17.9 Pauli exclusion principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 17.10Ionization Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 17.11Electron con¯guration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 17.12Valency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 17.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 18 Modern Physics 342 18.1 Introduction to the idea of a quantum . . . . . . . . . . . . . . . . . . . . . . . . 342 18.2 The wave-particle duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 18.3 Practical Applications of Waves: Electromagnetic Waves . . . . . . . . . . . . . . 343 19 Inside atomic nucleus 345 19.1 What the atom is made of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 19.2 Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 19.2.1 Proton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 19.2.2 Neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 19.2.3 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 19.3 Nuclear force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 19.4 Binding energy and nuclear masses . . . . . . . . . . . . . . . . . . . . . . . . . . 349 19.4.1 Binding energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 19.4.2 Nuclear energy units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 19.4.3 Mass defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 19.4.4 Nuclear masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 vii19.5 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 19.5.1 Discovery of radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 19.5.2 Nuclear ®, ¯, and ° rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 19.5.3 Danger of the ionizing radiation . . . . . . . . . . . . . . . . . . . . . . . 354 19.5.4 Decay law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 19.5.5 Radioactive dating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 19.6 Nuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 19.7 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 19.7.1 Geiger counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 19.7.2 Fluorescent screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 19.7.3 Photo-emulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 19.7.4 Wilson's chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 19.7.5 Bubble chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 19.7.6 Spark chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 19.8 Nuclear energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 19.8.1 Nuclear reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 19.8.2 Fusion energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 19.9 Elementary particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 19.9.1 ¯ decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 19.9.2 Particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 19.9.3 Quarks and leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 19.9.4 Forces of nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 19.10Origin of the universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 A GNU Free Documentation License 382 viiiPart I Physics 1Physics is the study of the world around us. In a sense we are more quali¯ed to do physics than any other science. From the day we are born we study the things around us in an e®ort to understand how they work and relate to each other. Learning how to catch or throw a ball is a physics undertaking for example. In the ¯eld of study we refer to as physics we just try to make the things everyone has been studying more clear. We attempt to describe them through simple rules and mathematics. Mathematics is merely the language we use. The best approach to physics is to relate everything you learn to things you have already noticed in your everyday life. Sometimes when you look at things closely you discover things you had overlooked intially. It is the continued scrutiny of everything we know about the world around us that leads people to the lifelong study of physics. You can start with asking a simple question like "Why is the sky blue?" which could lead you to electromagnetic waves which in turn could lead you wave particle duality and to energy levels of atoms and before long you are studying quantum mechanics or the structure of the universe. In the sections that follow notice that we will try to describe how we will communicate the things we are dealing with. This is our langauge. Once this is done we can begin the adventure of looking more closely at the world we live in. 2Chapter 1 Units 1.1 PGCE Comments ² Explain what is meant by `physical quantity'. ² Chapter is too full of tables and words; need ¯gures to make it more interesting. ² Make researching history of SI units a small project. ² Multiply by one technique: not positive Suggest using exponents instead (i.e. use the ¡1 table of pre¯xes). This also works better for changing complicated units (km=h to ¡1 m:s etc....). Opinion that this technique is limited in its application. ² Edit NASA story. ² The Temperature section should be cut-down. SW: I have edited the original section but perhaps a more aggressive edit is justi¯ed with the details de®ered until the section on gases. 1.2 `TO DO' LIST ² Write section on scienti¯c notation, signi¯cant ¯gures and rounding. ² Add to sanity test table of sensible values for things. ² Graph Celsius/Kelvin ladder. ² Address PGCE comments above. 1.3 Introduction Imagine you had to make curtains and needed to buy material. The shop assistant would need to know how much material was required. Telling her you need material 2 wide and 6 long would be insu±cient you have to specify the unit (i.e. 2 metres wide and 6 metres long). Without the unit the information is incomplete and the shop assistant would have to guess. If you were making curtains for a doll's house the dimensions might be 2 centimetres wide and 6 centimetres long 3Base quantity Name Symbol length metre m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K amount of substance mole mol luminous intensity candela cd Table 1.1: SI Base Units It is not just lengths that have units, all physical quantities have units (e.g. time and tem- perature). 1.4 Unit Systems There are many unit systems in use today. Physicists, for example, use 4 main sets of units: SI units, c.g.s units, imperial units and natural units. Depending on where you are in the world or what area of physics you work in, the units will be di®erent. For example, in South Africa road distances are measured in kilometres (SI units), while in England they are measured in miles (imperial units). You could even make up your own system of units if you wished, but you would then have to teach people how to use it 1.4.1 SI Units (Systµ eme International d'Unit¶ es) These are the internationally agreed upon units and the ones we will use. Historically these units are based on the metric system which was developed in France at the time of the French Revolution. All physical quantities have units which can be built from the 7 base units listed in Table 1.1 (incidentally the choice of these seven was arbitrary). They are called base units because none of them can be expressed as combinations of the other six. This is similar to breaking a language down into a set of sounds from which all words are made. Another way of viewing the base units is like the three primary colours. All other colours can be made from the primary colours but no primary colour can be made by combining the other two primaries. Unit names are always written with lowercase initials (e.g. the metre). The symbols (or abbreviations) of units are also written with lowercase initials except if they are named after scientists (e.g. the kelvin (K) and the ampere (A)). To make life convenient, particular combinations of the base units are given special names. This makes working with them easier, but it is always correct to reduce everything to the base units. Table 1.2 lists some examples of combinations of SI base units assigned special names. Do not be concerned if the formulae look unfamiliar at this stage we will deal with each in detail in the chapters ahead (as well as many others) It is very important that you are able to say the units correctly. For instance, the newton is ¡2 another name for the kilogram metre per second squared (kg:m:s ), while the kilogram 2 ¡2 metre squared per second squared (kg:m :s ) is called the joule. Another important aspect of dealing with units is the pre¯xes that they sometimes have (pre¯xes are words or letters written in front that change the meaning). The kilogram (kg) is a 3 3 simple example. 1kg is 1000g or 1£ 10 g. Grouping the 10 and the g together we can replace 4Quantity Formula Unit Expressed in Name of Base Units Combination ¡2 Force ma kg:m:s N (newton) 1 ¡1 Frequency s Hz (hertz) T 2 ¡2 Work & Energy F:s kg:m :s J (joule) Table 1.2: Some Examples of Combinations of SI Base Units Assigned Special Names 3 3 the 10 with the pre¯x k (kilo). Therefore the k takes the place of the 10 . Incidentally the kilogram is unique in that it is the only SI base unit containing a pre¯x There are pre¯xes for many powers of 10 (Table 1.3 lists a large set of these pre¯xes). This is a larger set than you will need but it serves as a good reference. The case of the pre¯x symbol is very important. Where a letter features twice in the table, it is written in uppercase for exponents bigger than one and in lowercase for exponents less than one. Those pre¯xes listed in boldface should be learnt. Pre¯x Symbol Exponent Pre¯x Symbol Exponent 24 ¡24 yotta Y 10 yocto y 10 21 ¡21 zetta Z 10 zepto z 10 18 ¡18 exa E 10 atto a 10 15 ¡15 peta P 10 femto f 10 12 ¡12 tera T 10 pico p 10 9 ¡9 giga G 10 nano n 10 6 ¡6 mega M 10 micro ¹ 10 3 ¡3 kilo k 10 milli m 10 2 ¡2 hecto h 10 centi c 10 1 ¡1 deca da 10 deci d 10 Table 1.3: Unit Pre¯xes ¡3 As another example of the use of pre¯xes, 1£ 10 g can be written as 1mg (1 milligram). 1.4.2 The Other Systems of Units The remaining sets of units, although not used by us, are also internationally recognised and still in use by others. We will mention them brie°y for interest only. c.g.s Units In this system the metre is replaced by the centimetre and the kilogram is replaced by the gram. This is a simple change but it means that all units derived from these two are changed. For example, the units of force and work are di®erent. These units are used most often in astrophysics and atomic physics. Imperial Units These units (as their name suggests) stem from the days when monarchs decided measures. Here all the base units are di®erent, except the measure of time. This is the unit system you are most likely to encounter if SI units are not used. These units are used by the Americans and 5British. As you can imagine, having di®erent units in use from place to place makes scienti¯c communication very di±cult. This was the motivation for adopting a set of internationally agreed upon units. Natural Units This is the most sophisticated choice of units. Here the most fundamental discovered quantities (such as the speed of light) are set equal to 1. The argument for this choice is that all other quantities should be built from these fundamental units. This system of units is used in high energy physics and quantum mechanics. 1.5 The Importance of Units Without units much of our work as scientists would be meaningless. We need to express our thoughts clearly and units give meaning to the numbers we calculate. Depending on which units we use, the numbers are di®erent (e.g. 3.8 m and 3800 mm actually represent the same length). Units are an essential part of the language we use. Units must be speci¯ed when expressing physical quantities. In the case of the curtain example at the beginning of the chapter, the result of a misunderstanding would simply have been an incorrect amount of material cut. However, sometimes such misunderstandings have catastrophic results. Here is an extract from a story on CNN's website: (NOTE TO SELF: This quote may need to be removed as the licence we are using allows for all parts of the document to be copied and I am not sure if this being copied is legit in all ways?) NASA: Human error caused loss of Mars orbiter November 10, 1999 WASHINGTON (AP) Failure to convert English measures to metric values caused the loss of the Mars Climate Orbiter, a spacecraft that smashed into the planet instead of reaching a safe orbit, a NASA investigation concluded Wednesday. The Mars Climate Orbiter, a key craft in the space agency's exploration of the red planet, vanished after a rocket ¯ring September 23 that was supposed to put the spacecraft on orbit around Mars. An investigation board concluded that NASA engineers failed to convert English measures of rocket thrusts to newton, a metric system measuring rocket force. One English pound of force equals 4.45 newtons. A small di®erence between the two values caused the spacecraft to approach Mars at too low an altitude and the craft is thought to have smashed into the planet's atmosphere and was destroyed. The spacecraft was to be a key part of the exploration of the planet. From its station about the red planet, the Mars Climate Orbiter was to relay signals from the Mars Polar Lander, which is scheduled to touch down on Mars next month. \The root cause of the loss of the spacecraft was a failed translation of English units into metric units and a segment of ground-based, navigation-related mission software," said Arthus Stephenson, chairman of the investigation board. This story illustrates the importance of being aware that di®erent systems of units exist. Furthermore, we must be able to convert between systems of units 61.6 Choice of Units There are no wrong units to use, but a clever choice of units can make a problem look simpler. The vast range of problems makes it impossible to use a single set of units for everything without making some problems look much more complicated than they should. We can't easily compare the mass of the sun and the mass of an electron, for instance. This is why astrophysicists and atomic physicists use di®erent systems of units. We won't ask you to choose between di®erent unit systems. For your present purposes the SI system is perfectly su±cient. In some cases you may come across quantities expressed in units other than the standard SI units. You will then need to convert these quantities into the correct SI units. This is explained in the next section. 1.7 How to Change Units the \Multiply by 1" Technique Firstly you obviously need some relationship between the two units that you wish to convert between. Let us demonstrate with a simple example. We will consider the case of converting millimetres (mm) to metres (m) the SI unit of length. We know that there are 1000mm in 1m which we can write as 1000mm = 1m: 1 Now multiplying both sides by we get 1000mm 1 1 1000mm = 1m; 1000mm 1000mm which simply gives us 1m 1 = : 1000mm This is the conversion ratio from millimetres to metres. You can derive any conversion ratio in this way from a known relationship between two units. Let's use the conversion ratio we have just derived in an example: Question: Express 3800mm in metres. Answer: 3800mm = 3800mm£ 1 1m = 3800mm£ 1000mm = 3:8m Note that we wrote every unit in each step of the calculation. By writing them in and cancelling them properly, we can check that we have the right units when we are ¯nished. We m started with `mm' and multiplied by ` '. This cancelled the `mm' leaving us with just `m' mm the SI unit we wanted to end up with If we wished to do the reverse and convert metres to millimetres, then we would need a conversion ratio with millimetres on the top and metres on the bottom. 71.8 How Units Can Help You We conclude each section of this book with a discussion of the units most relevant to that particular section. It is important to try to understand what the units mean. That is why thinking about the examples and explanations of the units is essential. If we are careful with our units then the numbers we get in our calculations can be checked in a `sanity test'. 1.8.1 What is a `sanity test'? This isn't a special or secret test. All we do is stop, take a deep breath, and look at our answer. Sure we always look at our answers or do we? This time we mean stop and really look does our answer make sense? Imagine you were calculating the number of people in a classroom. If the answer you got was 1 000 000 people you would know it was wrong that's just an insane number of people to have in a classroom. That's all a sanity check is is your answer insane or not? But what units were we using? We were using people as our unit. This helped us to make sense of the answer. If we had used some other unit (or no unit) the number would have lacked meaning and a sanity test would have been much harder (or even impossible). It is useful to have an idea of some numbers before we start. For example, let's consider masses. An average person has mass 70kg, while the heaviest person in medical history had a mass of 635kg. If you ever have to calculate a person's mass and you get 7000kg, this should fail your sanity check your answer is insane and you must have made a mistake somewhere. In the same way an answer of 0:00001kg should fail your sanity test. The only problem with a sanity check is that you must know what typical values for things are. In the example of people in a classroom you need to know that there are usually 2050 people in a classroom. Only then do you know that your answer of 1 000 000 must be wrong. Here is a table of typical values of various things (big and small, fast and slow, light and heavy you get the idea): Category Quantity Minimum Maximum Mass People Height Table 1.4: Everyday examples to help with sanity checks (NOTE TO SELF: Add to this table as we go along with examples from each section.) Now you don't have to memorise this table but you should read it. The best thing to do is to refer to it every time you do a calculation. 1.9 Temperature We need to make a special mention of the units used to describe temperature. The unit of temperature listed in Table 1.1 is not the everyday unit we see and use. Normally the Celsius scale is used to describe temperature. As we all know, Celsius temper- atures can be negative. This might suggest that any number is a valid temperature. In fact, the temperature of a gas is a measure of the average kinetic energy of the particles that make up the gas. As we lower the temperature so the motion of the particles is reduced until a point is reached 8where all motion ceases. The temperature at which this occurs is called absolute zero. There is o no physically possible temperature colder than this. In Celsius, absolute zero is at¡273 C. Physicists have de¯ned a new temperature scale called the Kelvin scale. According to this scale absolute zero is at 0K and negative temperatures are not allowed. The size of one unit kelvin is exactly the same as that of one unit Celsius. This means that a change in temperature of 1 degree kelvin is equal to a change in temperature of 1 degree Celsius the scales just start in di®erent places. Think of two ladders with steps that are the same size but the bottom most step on the Celsius ladder is labelled -273, while the ¯rst step on the Kelvin ladder is labelled 0. There are still 100 steps between the points where water freezes and boils. 102 Celsius 375 Kelvin 101 Celsius 374 Kelvin water boils - 100 Celsius 373 Kelvin 99 Celsius 372 Kelvin 98 Celsius 371 Kelvin . . . 2 Celsius 275 Kelvin 1 Celsius 274 Kelvin ice melts - 0 Celsius 273 Kelvin -1 Celsius 272 Kelvin -2 Celsius 271 Kelvin . . . -269 Celsius 4 Kelvin -270 Celsius 3 Kelvin -271 Celsius 2 Kelvin -272 Celsius 1 Kelvin absolute zero - -273 Celsius 0 Kelvin (NOTE TO SELF: Come up with a decent picture of two ladders with the labels water boiling and freezingin the same place but with di®erent labelling on the steps) This makes the conversion from kelvin to Celsius and back very easy. To convert from Cel- sius to kelvin add 273. To convert from kelvin to Celsius subtract 273. Representing the Kelvin o temperature by T and the Celsius temperature by T , K C T = To + 273: (1.1) K C It is because this conversion is additive that a di®erence in temperature of 1 degree Celsius is equal to a di®erence of 1 kelvin. The majority of conversions between units are multiplicative. For example, to convert from metres to millimetres we multiply by 1000. Therefore a change of 1m is equal to a change of 1000mm. 1.10 Scienti¯c Notation, Signi¯cant Figures and Rounding (NOTE TO SELF: still to be written) 91.11 Conclusion In this chapter we have discussed the importance of units. We have discovered that there are many di®erent units to describe the same thing, although you should stick to SI units in your calculations. We have also discussed how to convert between di®erent units. This is a skill you must acquire. 10Chapter 2 Waves and Wavelike Motion Waves occur frequently in nature. The most obvious examples are waves in water, on a dam, in the ocean, or in a bucket. We are most interested in the properties that waves have. All waves have the same properties so if we study waves in water then we can transfer our knowledge to predict how other examples of waves will behave. 2.1 What are waves? 1 Waves are disturbances which propagate (move) through a medium . Waves can be viewed as a transfer energy rather than the movement of a particle. Particles form the medium through which waves propagate but they are not the wave. This will become clearer later. Lets consider one case of waves: water waves. Waves in water consist of moving peaks and troughs. A peak is a place where the water rises higher than when the water is still and a trough is a place where the water sinks lower than when the water is still. A single peak or trough we call a pulse. A wave consists of a train of pulses. So waves have peaks and troughs. This could be our ¯rst property for waves. The following diagram shows the peaks and troughs on a wave. Peaks Troughs In physics we try to be as quantitative as possible. If we look very carefully we notice that the height of the peaks above the level of the still water is the same as the depth of the troughs below the level of the still water. The size of the peaks and troughs is the same. 2.1.1 Characteristics of Waves : Amplitude The characteristic height of a peak and depth of a trough is called the amplitude of the wave. The vertical distance between the bottom of the trough and the top of the peak is twice the amplitude. We use symbols agreed upon by convention to label the characteristic quantities of 1 Light is a special case, it exhibits wave-like properties but does not require a medium through which to propagate. 11