OUR DYNAMIC UNIVERSE part 2 J A Hargreaves Lockerbie Academy August 20152016 CONTENTS CHAPTER 6: GRAVITATION CONTENTS TABLE OF CONTENTS GRAVITATION .................................................................................................................................................... 4 Suggested Activities ................................................................................................................................... 4 Astronomical Data ............................................................................................................................................. 4 Gravitational Field Strength on other planets ................................................................................................... 5 Projectiles .......................................................................................................................................................... 5 Projectiles fired Vertically .......................................................................................................................... 5 Projectiles fired horizontally...................................................................................................................... 5 Projectiles at an angle ............................................................................................................................... 7 Task: Launch Velocity ................................................................................................................................ 8 Notes on Projectile Motion ............................................................................................................................... 8 Projectiles: WORKED EXAMPLES ............................................................................................................. 11 Orbits and Newton’s Thought Experiment ...................................................................................................... 15 Gravity and Mass ............................................................................................................................................. 17 Newton’s Universal Law of Gravitation ........................................................................................................... 18 GRAVITATIONAL FIELDS ................................................................................................................................... 19 EQUATIONS OF MOTION / TUTORIAL 4 ....................................................................................................... 21 Gravity and mass/ Tutorial 5 ....................................................................................................................... 22 Gravitation exam questions ........................................................................................................................ 23 Section 4: Gravitation Answers ................................................................................................................... 25 Chapter 7: SPECIAL RELATIVITY ....................................................................................................................... 26 Suggested Activities ................................................................................................................................. 26 Special Relativity .............................................................................................................................................. 27 NOTATION ............................................................................................................................................... 28 Frames of Reference ............................................................................................................................... 28 Postulates of Special Relativity .................................................................................................................... 31 The Principles of Relativity .......................................................................................................................... 32 Time Dilation ............................................................................................................................................... 33 Another thought experiment .................................................................................................................. 35 Time Dilation and the Lorenz Transformation ............................................................................................ 36 Time Dilation Formula and the Lorentz Transformation ............................................................................. 40 Answering Lorenz Factor Questions ........................................................................................................ 40 Why we do not notice relativistic time differences in everyday life ....................................................... 42 Another example and some effects ........................................................................................................ 44 Length contraction ...................................................................................................................................... 45 Length paradox ........................................................................................................................................ 45 How do you measure a fish? ................................................................................................................... 45 Ladder paradox - solution........................................................................................................................ 46 THE MICHELSON-MORLEY EXPERIMENT ..................................................................................................... 47 Special Relativity .............................................................................................. 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Communicating Scientific Results ................................................................................................................ 49 Objective ................................................................................................................................................. 49 Learning outcome .................................................................................................................................... 49 Learning activity ...................................................................................................................................... 49 SPECIAL RELATIVITY / TUTORIALS 1 ............................................................................................................. 51 Time dilation / Tutorial 2 ............................................................................................................................. 52 Length Dilation / Tutorial 3.......................................................................................................................... 53 Relativity Miscellaneous/ Tutorial 4 ............................................................................................................ 54 EXAM QUESTIONS / Special Relativity ......................................................................................................... 56 Chapter 8: THE EXPANDING UNIVERSE ........................................................................................................... 59 6 The expanding Universe ........................................................................................................................... 59 J A Hargreaves Page 2 of 91 CONTENTS CHAPTER 6: GRAVITATION Suggested Activities ................................................................................................................................. 59 The Expanding Universe .................................................................................. 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The Doppler effect and redshift of galaxies ............................................................................................ 61 Analogy: Sweets on a conveyor belt........................................................................................................ 62 Equations ................................................................................................................................................. 62 Deriving the Doppler Equation Method 1 ............................................................................................... 63 Deriving the Doppler Equation Method 2 ............................................................................................... 64 Deriving the Doppler Equation Method 3 ............................................................................................... 65 Big Bang Theory ........................................................................................................................................... 67 Line spectra ............................................................................................................................................. 67 Redshift, z .................................................................................................................................................... 68 Blueshift................................................................................................................................................... 71 Anecdote ................................................................................................................................................