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Solving problems at the (virtual) back of the envelope Andy Buffler UCT Physics [email protected] AIMS 2006 Estimation problems / order of magnitude calculations / ... aka “Fermi problems” ... after Enrico Fermi ... ... who (amongst many other things) fingered out the yield of the Trinity atomic bomb test from observing the distance traveled by small pieces of paper dropped from his hand during the detonation. ... and is associated with questions such as ... “How many piano tuners are there in the city of Chicago?” “How much faster or slower does a watch run when carried up a mountain?” How many golf balls would be needed to completely fill this room? How fast does your hair grow (in km/hour)? How many grains of sand are there on Muizenberg beach? Thinking about estimation problems: • • • • • What is really being asked? Do I need a physical model? If so, what idealizations or simplifications can I make? Which parameters really matter? How can I get reasonable values for these parameters? • Is my answer reasonable? If all the people of the world were crowded tightly together, how much area would we cover? How many R100 notes are in circulation in South Africa? How many pencils would it take to draw a straight line around the entire Earth, following the equator (if you could also draw on the surface of the ocean) How many elastic bands will a prisoner need to escape down a 10 metre high wall? How small does a human need to be in order to walk on water? Homework Answer all these questions before Friday 11:00. Bring your answers to class and be prepared to defend them publicly. Discuss things with your tutorial group and tutor, but have your own answers ready. Homework 1. What is the kinetic energy of a drifting continent? Homework 2. What is the heat output of a human? Homework 3. How many commercial aircraft are in the air right now? Homework 4. How high can an elephant jump? Homework 5. What is the photon flux at your eye from a faint visible star? Homework 6. How many atoms of Julius Caesar do you eat every day? Homework 7. Someone places 1 curie of uranium on your chest... ... what do you die of? Homework 8. A steel ball is dropped from a height of 3 metres onto a concrete floor. It bounces a large number of times but eventually comes to rest. Estimate the rise in temperature of the ball. Homework 9. Invent a problem of your own (you don’t have to know the answer). Email this problem (only) to [email protected] before 17:00 on Thursday. Solving problems at the (virtual) back of the envelope Part 2 Andy Buffler UCT Physics [email protected] AIMS 2006 How far does a car travel before one molecule layer of rubber is worn off the tires? What is the mass of air in this room? How many molecules are there in a sample of 1 litre of air in this room? What is the average spacing between these molecules? How many atoms are there in the human body? How much would the ocean surface rise if the ice caps melted? Physical theories Abstract, acontextual, external. Manifested in mathematical or linguistic form particularization, application Physical models Concrete, contextual, external Manifested in many forms idealization, simplification Real world (Phenomena) Concrete, experience, observation How fast does your hair grow (in km/hour)? How many golf balls would be needed to completely fill this room? How many hairs are there on your head? Could Bill Gates buy the whole of Muizenberg? A golf ball is dropped onto a concrete floor from a high flying airplane. How high will it bounce? How long does it take for a light bulb to turn off? Tutorial Answer the following 7 questions (suggested by yoursleves). Work within your groups and ask the tutors for help if needed. You have 1 hour to come up with reasonable answers. Use whatever resources you have available. You may leave the room. Write full answers, stating all approximations and assumptions you make. Hand in one set of solutions per group. Tutorial 1. How many people are born in the world every minute? Tutorial 2. How many bags of cement were used to construct the AIMS building? Tutorial 3. How many words are used in 2 hour lecture if the lecturer talks continuously? Tutorial 4. What volume of rain fell on the continent of Africa in 2006? Tutorial 5. What distance have you walked since the day you took your first steps? Tutorial 6. What is the total distance covered in a football game by all the players on the field? Tutorial 7. How much energy is required to boil the Earth’s oceans?