How things work! (PHYS 121) Daniel M. Sussman November 20, 2020 This is a set of lecture notes prepared for PHYS 121: How things work (Emory University, Fall 2020). There are undoubtedly typos and errors in this document: please feel free to email any corrections to: [email protected] 1 Contents Preface 6 Sources.........................................6 1 Quantitative thinking, estimation, and units!7 1.1 A brief introduction.................................7 1.1.1 Symmetry.................................7 1.1.2 Scale....................................9 1.2 Units { what's the fuss?............................. 10 1.2.1 Physical quantities have dimensions................... 10 1.3 Estimation and \Fermi problems"........................ 12 1.3.1 Scientific notation and orders of magnitude............... 12 1.3.2 Order of magnitude estimates...................... 12 1.3.3 Fermi estimation............................. 14 1.3.4 Case study: trees and paper....................... 15 1.3.5 Practice examples!............................ 17 1.4 Dimensional analysis............................... 17 1.4.1 Basics of dimensional analysis...................... 18 1.4.2 Case study 1: The Trinity detonation.................. 18 1.4.3 Case study 2: Can you estimate how fast your (car / train / plane) is going be watching raindrops rolling on the side windows?....... 21 2 The laws of motion, Part 1! 25 2.1 Inertia, friction, and why our intuition is often wrong............. 26 2.2 Skating....................................... 27 2.2.1 Acceleration and forces.......................... 28 2.2.2 Frames of reference............................ 29 2.3 Throwing stuff.................................. 30 2.3.1 Gravity.................................. 30 2.3.2 Free fall.................................. 31 2.3.3 Motion of a constantly accelerating object............... 31 2.3.4 Throwing stuff.............................. 32 2.4 Ramps....................................... 33 2.4.1 \Support" or \Normal" forces...................... 34 2.4.2 Energy and work............................. 36 2.4.3 Doing work................................ 37 2 2.4.4 Using a ramp!............................... 38 3 The laws of motion, Part 2! 39 3.1 Seesaws, levers, and mobiles........................... 39 3.1.1 Balancing a seesaw............................ 39 3.1.2 Newton's Laws of rotational motion................... 41 3.1.3 Torques.................................. 43 3.2 Wheels....................................... 45 3.2.1 Friction.................................. 45 3.2.2 Wheels................................... 46 3.2.3 Rotational motion, work, and energy.................. 47 3.3 Bumper cars.................................... 48 3.3.1 Linear momentum............................ 48 3.3.2 Angular momentum........................... 49 3.3.3 Impulses.................................. 50 4 Mechanical objects, Part 1! 52 4.1 Springs and scales................................. 52 4.1.1 Measuring weight............................. 52 4.1.2 Stretching and compressing a spring.................. 54 4.2 Bouncing balls................................... 57 4.3 Roller coasters................................... 59 4.3.1 The feeling of acceleration........................ 59 4.3.2 Riding a carousel in a playground.................... 60 4.3.3 Riding a rollercoaster........................... 62 5 Mechanical objects, Part 2! 64 5.1 Bicycles...................................... 64 5.1.1 Static stability { when do object fall over?............... 64 5.1.2 Dynamic stability { what keeps a bicycle upright while it's moving?. 66 5.1.3 Choosing the right gear.......................... 68 5.2 Satellites and planets............................... 69 5.2.1 Orbiting around.............................. 69 5.2.2 Kepler's Laws............................... 71 5.3 Rocket ships.................................... 73 5.3.1 Blasting off.................................. 73 5.3.2 ... into space!............................... 73 6 Fluids! 75 6.1 Gases....................................... 75 6.1.1 Air pressure and the ideal gas law.................... 76 6.2 Floating and buoyancy.............................. 78 6.3 Liquids and water pressure............................ 80 6.3.1 Pressure inside a liquid.......................... 80 6.3.2 Water seeks its own level......................... 82 3 7 Fluids and motion! 84 7.1 Flowing water................................... 84 7.1.1 Viscosity.................................. 84 7.2 Flow through a hose............................... 85 7.2.1 Flow through a straight hose....................... 85 7.2.2 Dynamic pressure variations: going around the bend.......... 87 7.3 Turbulent vs smooth flow............................ 87 7.4 Aerodynamics................................... 89 7.4.1 Slow-moving stuff and laminar airflow.................. 89 7.4.2 Faster-moving stuff and turbulent airflow................ 90 7.4.3 Curveball!................................. 92 8 Heat and and insulation! 95 8.1 Stoves....................................... 95 8.1.1 Thermal energy in solids (aka, \stuff on fire”)............. 96 8.1.2 Warming an object up.......................... 97 8.2 How heat flows.................................. 98 8.2.1 Conduction of heat............................ 98 8.2.2 Convection of heat............................ 98 8.2.3 Radiation................................. 99 8.3 Insulation..................................... 100 8.3.1 Limiting thermal conduction....................... 101 8.3.2 Limiting convective heat loss....................... 101 8.3.3 Limiting radiative heat loss....................... 102 9 Thermodynamics! 104 9.1 The laws of thermodynamics!.......................... 104 9.1.1 The \zeroth" law of thermodynamics.................. 105 9.1.2 The first law of thermodynamics.................... 106 9.1.3 The second law of thermodynamics................... 106 9.1.4 The third law of thermodynamics.................... 108 9.2 Engines and automobiles!............................ 108 9.2.1 Work, heat, and temperature in a piston................ 108 9.2.2 Abstract engines............................. 110 9.2.3 An ideal gas engine............................ 110 9.2.4 More realistic engines........................... 112 9.3 Air conditioners!................................. 113 9.3.1 Phase changes from solids, liquids, and gases.............. 113 9.3.2 Vapor-compression refrigerator..................... 115 10 Mechanical Waves! 117 10.1 Clocks....................................... 117 10.1.1 Harmonic oscillators again........................ 117 10.1.2 Resonance and natural frequencies................... 119 10.1.3 Clocks................................... 119 4 10.2 Musical instruments............................... 121 10.2.1 Vibrations, oscillations, harmonics.................... 121 10.2.2 Other musical instruments........................ 122 10.2.3 Sound waves................................ 124 10.3 Water waves.................................... 126 10.3.1 Capillary waves.............................. 126 10.3.2 Gravity waves............................... 127 10.3.3 The tides................................. 128 11 Light! 130 11.1 What is light?................................... 130 11.1.1 Historical interlude............................ 130 11.1.2 Electromagnetic radiation........................ 131 11.2 Mirrors!...................................... 133 11.3 Rainbows!..................................... 135 11.3.1 Refraction of light............................ 135 11.3.2 Chromatic aberration........................... 137 11.3.3 Sun and rain............................... 138 11.4 The sky is blue!.................................. 140 11.4.1 Tyndall and Rayleigh........................... 140 11.4.2 Einstein.................................. 141 11.4.3 What the sky looks like......................... 141 12 Random walks! 143 12.1 Random walks................................... 144 12.2 Fermi estimation revisited............................ 146 12.3 Masks and COVID-19.............................. 147 12.3.1 Particles, big and small.......................... 147 12.3.2 A mask is not a sieve........................... 149 12.3.3 Random walks and impact capture................... 150 5 Preface So, what is this course about? I like to think that physics, at its heart, is the idea that the world around us is understandable, and so in PHYS 121 we'll be spending time trying to understand a little bit about how things work. We'll discuss the science behind everyday things { motion, music, materials, and much more { and see how amazing complex behavior can follow from just a few simple, general ideas. The material is structure around investigating everyday objects and phenomena in the world { bumper cars, basketballs, balloons, bicycles... { and we'll spend time thinking about the physical principles the help us understand how things work. But that's not the goal of this course. I want you to come away from this class knowing what it means to think like a physicist. No matter what your background or your major is, a central value of a liberal arts education is being able to think from many different perspectives. An artist (for example) and a physicist might approach the same question in very different ways, and even if ultimately a physicist's approach doesn't resonate with you, I hope you'll walk away with an enriched perspective for understanding another way of seeing the world. So, in a nutshell, what does