09_109_Final_Questions

09_109_Final_Questions - P HYSICS 109: FINAL EXAM PROBLEMS...

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PHYSICS 109: FINAL EXAM PROBLEMS 2009 The final will be twelve of these: four from each part . It will be pledged : you must not use any source of information during the exam. You will not need calculators, as you can see. When asked for approximate times, the right century is enough. PART I 1. Explain briefly what features of the Babylonian numbering and measuring systems were superior to ours: sketch the way they represented 1, 2, 10, 25, 60, 5400. 2. Approximately when and where was Thales? What did he contribute to the development of science? How did he measure the height of a pyramid? How did he measure the distance away of a ship? 3. According to the historical record, who first did geometry? And why? And approximately when? Who first approached geometry as a purely intellectual exercise? 4. Approximately when and where was Pythagoras? Briefly, what did his followers believe? Why did they think the stars moved across the sky daily? Why did they think numbers related to music? 5. Draw a couple of diagrams to prove Pythagoras’ Theorem, that is, reproduce two equal squares containing four identical triangles, as in the flashlet, and explain your proof. 6. Reproduce the Pythagoreans proof that the square root of two is irrational, that is, it isn’t a fraction: but do it for 3. Explain why the argument doesn’t hold for 9. 7. Approximately when and where was Plato? What institution did he found? What was its purpose? What did it say above the doorway? 8. Describe with sketches Plato’s Five Regular Solids. Prove with diagrams that there can only be five. Plato made a specific suggestion to the astronomers as to how they should try to account for the motion of the planets. What was it? 9. Approximately when and where was Aristotle? What was his school called? What were the four elements? Why did things move? What’s the difference between what he called “natural motion” and “violent motion”? What were his quantitative rules of falling motion? 10. Approximately when and where was Strato? What two arguments did he give against Aristotle’s description of natural falling motion? 11. Approximately when and where was Eratosthenes? Describe how he figured out the size of the earth.
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2 12. Approximately when and where was Aristarchus? Explain how he figured out the distance to the Moon. 13. (a) How did Aristarchus try to find the distance to the sun? How accurate was he? What important conclusion could he reach anyway? (b) How (according to Archimedes) did Aristarchus account for the fact that the stars don’t seem to change over the course of a year in the way you’d expect if the Earth is really circling around the sun? 14. How did Archimedes prove the crown wasn’t pure gold? 15.
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09_109_Final_Questions - P HYSICS 109: FINAL EXAM PROBLEMS...

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