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# Density

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1. Density

2. Introduction

3. Introduction • We can see the difference in density of different materials when we look at ... • wood floating on water • helium balloons floating in the air

4. Introduction • We can see the difference in density of different materials when we look at ... • iron sinking in water • lava lamps

5. Introduction

6. Properties

7. Properties • Density is an intensive property of matter. • The density of matter does not depend on the amount of matter. • Density does depend on the composition of the matter

8. m V D = Properties • Density is the mass of the matter divided by the volume of the matter. • The density of matter generally decreases as the temperature of the matter increases.

9. Properties • The density of some materials is given in this chart:

10. Properties

11. Doing the Math

12. m D m V D = V = Doing the Math • Density is the mass of the matter divided by the volume of the matter. • The volume of matter is the mass divided by the density. • The mass of matter is the density times the volume. m = D•V

13. Doing the Math

14. Examples

15. Examples • Example 1:

16. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block?

17. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm)

18. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm) = 750 cm3

19. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm) = 750 cm3 m D = V

20. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm) = 750 cm3 m 340 g D = = V 750 cm3

21. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm) = 750 cm3 m 340 g D = = = 0.453333333 g/cm3 V 750 cm3

22. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm) = 750 cm3 m 340 g D = = = 0.453333333 g/cm3 = 0.45 g/cm3 V 750 cm3

23. Examples • Example 1: • A block of wood has a length of 15 cm, a width of 10. cm, and a height of 5.0 cm. The block also has a mass of 340 g. What is the density of the block? V = l•w•h = (15 cm)(10. cm)(5.0 cm) = 750 cm3 m 340 g D = = = 0.453333333 g/cm3 = 0.45 g/cm3 V 750 cm3

24. Examples

25. Examples • Example 2:

26. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block?

27. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block? m D = V

28. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block? m m D = ➔ V = V D

29. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block? m m 37.4 g D = ➔ V = = V D 11.4 g/cm3

30. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block? m m 37.4 g D = ➔ V = = = 3.280701754 cm3 V D 11.4 g/cm3

31. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block? m m 37.4 g D = ➔ V = = = 3.280701754 cm3 V D 11.4 g/cm3 V = 3.28 cm3

32. Examples Example 2: A block of lead has a mass of 37.4 g. Lead has a density of 11.4 g/cm3. What is the volume of the block? m m 37.4 g D = ➔ V = = = 3.280701754 cm3 V D 11.4 g/cm3 V = 3.28 cm3

33. Examples

34. Examples • Example 3:

35. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l

36. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l

37. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm)

38. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm) = 0.157 cm3

39. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm) = 0.157 cm3 m D = V

40. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm) = 0.157 cm3 m D = ➔ V

41. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm) = 0.157 cm3 m D = ➔ m = D•V V

42. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm) = 0.157 cm3 m D = ➔ m = D•V = (8.86 g/cm3)(0.157 cm3) V

43. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.05000 cm)2(20.0 cm) = 0.157 cm3 m D = ➔ m = D•V = (8.86 g/cm3)(0.157 cm3) V m = 1.39 g

44. Examples • Example 3: • What is the mass of a 20.0 cm length of copper wire with a density of 8.86 g/cm3 and a radius of 0.0500 cm? The volume of a cylinder is V = π•r2•l V = π•r2•l = π(0.0500 cm)2(20.0 cm) = 0.157 cm3 m D = ➔ m = D•V = (8.86 g/cm3)(0.157 cm3) V m = 1.39 g