Archimedes: Infinite Secrets
1. Archimedes was the first to discover the value for what number which is the
mathematical equivalent of inventing the wheel?
2. Archimedes was from what city state?
3. Archimedes was so preoccupied with mathematics who had to carry him to take a
bath?
4. What was the king’s problem?
5. Where did Archimedes make his discovery about the solution to finding the volume
of the crown?
6. What did he shout as he ran naked through the streets?
7. Was the goldsmith honest?
8. For what inventions was Archimedes best known and feared for?
9. What did Archimedes design for the city of Syracuse?
10. What war machine did Archimedes greatly improve?
11. What feat did Archimedes do for the King to demonstrate his abilities with levers
and pulleys?
12. What is Archimedes famous boast?
13. What is pi (π)?
14. What shape did he first use to approximate the circumference of a circle?
15. What is the numerical value of pi (π)?
16. How many grains of sand did Archimedes estimate would fill the Universe?
17. What did Archimedes do to fool competing mathematicians?
18. What did the Romans want to do with Archimedes?
19. How did Archimedes die in 212 B.C.?
20. What happened to Greek mathematics after Archimedes?
Now let's review what we've learned about fluids. Try to find these answers without looking in your binder or the textbook. If you still can't remember then use your binder or Chapter 11 to find the answers. Be sure to show your work!!
1. What is a fluid? What two states of matter are fluids? Give an example of each.
matter that flows; gasses and liquids; air, water
2. What is the formula for pressure? What are the SI units of pressure? What is the pressure on an object with force 2 N and area 4 m2?
force/area; Pa = N/m2; 0.5 Pa
3. What is Pascal's Principle? What is the force at one end of a hydraulic pump that has a surface area of 4 m2 with Force 10 N and surface area 5 m2 at the other end.
fluids push equally in all directions; 10/4 = X/5 so... X = 12.5
4. What is Bernoulli's Principle? Explain how an airplane wing (airfoil) works in terms of Bernoulli's Principle. Draw a picture of the wing showing the splitting of the air stream and where lift occurs due to a push from higher air pressure.
fast fluids = low pressure; see Chapter 11;
5. How high is the atmosphere? What is the pressure of air at sea level in atm and Pa? (You'll probably need to look these figures up!)
100 km; 1 atm, 101,300 Pa
6. What is the buoyancy force? How is buoyancy force related to Pascal's Principle? What is Archimedes Principle? What is the buoyancy force on an object that displace 10 N of water by weight? Explain whether an object that has a weight of 40 N and experiences a buoyancy force of 50 N is water will sink or float.
upward (against gravity) push of fluids; Buoyancy is directly related to Pascal's Principle which says fluids push equally in all directions; 10N; float
7. Write the formula for density in SI units. What is the density of an object with mass 3 g and volume 6 cm3? What is the density of an object with mass 50 kg and 100 m2?
g/cm3; 0.5 g/cm3; 0.5 kg/m3
8. Explain a method for finding the mass of a liquid like water. What is the weight in Newtons of 400 grams of water?
find mass of liquid in a cup then find mass of cup and subtract; if acceleration due to gravity is rounded to 10 m/s2 then 400 g water = 4N