1. Archimedes Takes a Bath

2. Cast of Characters: The King The King The Queen The Queen The Goldsmith The Goldsmith Archimedes Archimedes Mrs. Archimedes Mrs. Archimedes

3. Syracuse – Second Century B.C.

5. Many weeks later…

6. Later that night…

7. Early the Next Day

8. Archimedes Laboratory … First test: Mass EQUAL! ? Which weighs more, a kilogram of feathers or a kilogram of lead? EQUAL! What is unequal between the feathers and lead?

9. Mass and Volume: A DENSITY RELATIONSHIP EQUALVOLUME MORE MASS MORE DENSE EQUAL MASS MORE VOLUME MORE DENSE How much matter in a given volume.

10. DENSITY: Intensive Property DENSITY If Archimedes could prove that both the masses and the volumes were the same for the crown and gold brick he could prove they had the same DENSITY. DENSITY Same DENSITY; Same material DENSITY No matter the amount of the same substance, the DENSITY is always the same. Mass? Volume? Density Au Au X X

11. DENSITY: THE EQUATION D m = V ?

12. Triangle of Knowledge! D m V

13. Volume: how much space you take Regular objects l w h r l x w x h(4/3)πr 3

14. Volume: Irregular Objects ?

15. The Breaking Point

16. WATER TEMPERATURE THE BATH HOUSE

17. Displaced water = EUREKA ! VOLUME OF OBJECT!

18. THE BATH HOUSE RUNNING HOME NAKED!

19. THE COMPARISON SAME MASS BUT WITH A LARGER VOLUME! LESS DENSE!= = THE CROWN IS NOT PURE!

20. THE KING GETS THE NEWS

21. MASS = grams (g) VOLUME = milliliters (mL) or cubic centimeters (cm 3 ) DENSITY = g/mL or g/cm 3 MASS = grams (g) VOLUME = milliliters (mL) or cubic centimeters (cm 3 ) DENSITY = g/mL or g/cm 3

22. D = m/V The Magic Triangle! m = DV V = m/D D m V

23. Metal 1 oran ge 2 yellow 3 magnet ic 4 silver 1 orange 2 yellow Mass (g) 4 sig figs Volum e (mL) Densit y (g / mL) Actual/ Name of metalCu 8.54 g/mL Brass 8.10 g/mL Iron 7.47 g/mL Al 2.56 g/mL Cu 8.54 g/mL Brass % Error DENSITY LAB TABLE CubesCylinders Use a RULER!

24. Used for measuring the inside of an object 34567812 Roll wheel to adjust width cm mm hundredths Calipers

25. hundredths cm mm cm & mm based on this mark 1 1 Find which hundredth line matches up Hundredth marks 5 cm

26. Calculate/measure Volume: Calculate/measure Volume: Cubes: Cubes: Cylinders: Cylinders: Measure Mass: Measure Mass: How do you?

27. ACTUAL VALUES Aluminum (Al)2.56 g/cm 3 Aluminum (Al)2.56 g/cm 3 Brass8.10 g/cm 3 Brass8.10 g/cm 3 Copper (Cu)8.54 g/cm 3 Copper (Cu)8.54 g/cm 3 Iron (Fe)7.47 g/cm 3 Iron (Fe)7.47 g/cm 3

28. Analyzing your results and the conclusion 1) What is the equation for density? 2) What are the units for mass, volume and density? 3) Did all of your “cubes” have the same volume? Should they have the same volume? Why or why not? 4) Did all of your cylinders have the same volume? Should they have the same volume? Why or why not? 5) Did all of your cubes have the same mass? Why or why not? 6) Did all of your cylinders have the same mass? Why or why not? 7) Did the same color cubes and cylinders have the same density? Why or why not? 8) Were the same color cubes and cylinders the same metal? What is your evidence? 9) Explain what was the most difficult part of this lab? 10) List three factors that contributed to your density values not being the same as the actual values? 11) If you could do the lab over again what would you have changed? Why?

29. Teacher notes: hand out calipers/explain how to use them discuss how to find the densities of the cubes and cylinders (these are going to be shared) After they finish calculating mass/volume they need to calculate density Walk around and make sure they are measuring correctly After they finish calculating density, they need to write their procedure (step by step) hand out questions, these need to be glued in the page after their procedure. everything is due monday (including density practice)

30. Actu al/ Nam e of met alCu 8.5 4 g/ mL Bras s 8.10 g/m L Iron 7.47 g/mL Al 2.56 g/m L Cu 8.54 g/mL Bras s 8.10 g/mL Met al 1 ora ng e 2 yello w 3 mag netic 4 silve r 1 orang e 2 yello w

32. Used for measuring the inside of an object 34567812

33. 5678341256783412

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35. DensityBook value Cu8.58.9 Cu8.58.9 Brass9.1-9.38.0 Brass9.1-9.38.0 Al2.9-3.12.7 Al2.9-3.12.7 Fe9.4-9.67.6 Fe9.4-9.67.6 Pb 11.311.3 Pb 11.311.3 Zn7.1 Zn7.1

36. Cu8.40 g/cm 3 Brass8.08 g/cm 3 Al2.64 g/cm 3 Fe7.39 g/cm 3 Pb 10.2 g/cm 3