1. FOAM WOOD METAL Suppose you had three equally sized cubes of the following materials. Which one would be the heaviest?

2. The metal cube is heavier just as a brick is heavier than a sponge of the same size! They take up the same amount of space (volume) but the brick has more mass (heaviness of an object*)!

3. Volume of a Rectangular Solid =_____

4. Volume of a Rectangular Solid =L x W x H 4cm 2cm 3cm V=

5. Volume of a Rectangular Solid =L x W x H 4cm 2cm 3cm V= 16cm 3 V= 27cm 3 4cm x 2cm x 2cm 3cm x 3cm x 3cm Volume is a measure of the physical space an object take up,

6. Density (ρ) is a measure of how compact the atoms or molecules in a substance are. It is a ratio of an object’s mass (m) to its volume (v). SAMPLE PROBLEM If I have a wooden block that has a mass of 20g and a volume of 26cm 3, what is its density? 6 ρ = m/v density (g/cm 3 ) or (kg/m 3 ) mass (g) or (kg) Volume (cm 3 ) or (m 3 ) ρ = m/v density (g/cm 3 ) or (kg/m 3 ) mass (g) or (kg) Volume (cm 3 ) or (m 3 )

7. Density (ρ) is a measure of how compact the atoms or molecules in a substance are. It is a ratio of an object’s mass (m) to its volume (v). SAMPLE PROBLEM If I have a wooden block that has a mass of 20g and a volume of 26cm 3. What is its density? m=20g v=26cm 3 ρ = 20g/26cm 3 =0.77g/cm 3 ρ = m/v density (g/cm 3 ) or (kg/m 3 ) mass (g) or (kg) Volume (cm 3 ) or (m 3 ) ρ = m/v density (g/cm 3 ) or (kg/m 3 ) mass (g) or (kg) Volume (cm 3 ) or (m 3 )

8. Rank each object from the most dense to the least dense: [1] [2] [3] [4] 3kg 2kg 4kg 1kg (a) (b) (c) (d) 1kg (a) (b) (c) (d) [1] [2] [3] [4]

9. Rank each object from the most dense to the least dense: [1] [2] [3] [4] 3kg 2000g 3000g 10,000mg (a) (b) (c) (d) 2kg (a) (b) (c) (d) [1] [2] [3] [4]

10. Density Formula Manipulation Multiply both sides by v Divide both sides by p

11. Density Problems 1.If 10.0cm 3 of ice has a mass of 9.17g, what is the density of ice? 2.A piece of tin has a mass of 16.52g and a volume of 2.26 cm 3. What is the density of tin? 3.A piece of metal has a density of 11.3 g/cm 3 and a volume of 6.7 cm 3. What is the mass of this piece of metal? 4.A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density.

12. Density Problems 1.If 10.0cm 3 of ice has a mass of 9.17g, what is the density of ice? 2.A piece of tin has a mass of 16.52g and a volume of 2.26 cm 3. What is the density of tin? 3.A piece of metal has a density of 11.3 g/cm 3 and a volume of 6.7 cm 3. What is the mass of this piece of metal? 4.A cube 6cm by 5cm by 3cm has a mass of 450g. Calculate its density. 1.Density = 0.917g/cm 3 2.Density = 7.3g/cm 3 3.Mass = 75.7g 4.V= 90cm 3 thus p = 5g/cm 3 1.Density = 0.917g/cm 3 2.Density = 7.3g/cm 3 3.Mass = 75.7g 4.V= 90cm 3 thus p = 5g/cm 3 Density Worksheet!

13. Fill in the table and Create Scale Model Cubes ObjectDensity (g/cm3)Density (kg/m 3 )Mass (g)Volume (cm 3 )Length (cm) Aluminum2.7 g/cm 3 2700kg/m 3 21.6g Water1 g/cm 3 1000kg/m 3 27g Gold19.3 g/cm 3 19,300kg/m 3 1235.2g Wood0.85g/cm 3 850kg/m 3 6.8g Sugar1.6g/cm 3 1600kg/m 3 1.6g Color the Cubes an appropriate color, tape/glue them to a piece of computer paper and list each one’s mass, volume and density underneath it. First One: Aluminum mass = 21.6g Density = 2.7g/cm 3 Volume = mass / density V = 21.6g / 2.7g/cm 3 = 8cm 3 The cube must have side lengths of 2cm each because 2cm x 2cm x 2cm = 8cm 3

14. Fill in the table and Create Scale Model Cubes ObjectDensity (g/cm3)Density (kg/m 3 )Mass (g)Volume (cm 3 )Length (cm) Aluminum2.7 g/cm 3 2700kg/m 3 21.6.2g8cm 3 2cm Water1 g/cm 3 1000kg/m 3 27g27cm 3 3cm Gold19.3 g/cm 3 19,300kg/m 3 1235.2g64cm 3 4cm Wood0.85g/cm 3 850kg/m 3 6.8g8cm 3 2cm Sugar1.6g/cm 3 1600kg/m 3 1.6g1cm 3 1cm Color the Cubes an appropriate color, tape/glue them to a piece of computer paper and list each one’s mass, volume and density underneath it. First One: Aluminum mass = 21.6g Density = 2.7g/cm 3 Volume = mass / density V = 21.6g / 2.7g/cm 3 = 8cm 3 The cube must have side lengths of 2cm each because 2cm x 2cm x 2cm = 8cm 3

15. Aluminum Water Gold Wood Understanding the Meaning of Density ObjectDensity (g/cm 3 )Density (kg/m 3 ) Aluminum2.7 g/cm 3 2700kg/m 3 Water1 g/cm 3 1000kg/m 3 Gold19.3 g/cm 3 19,300kg/m 3 Wood0.85g/cm 3 850kg/m 3 Sugar1.6g/cm 3 1600kg/m 3 Sugar Suppose we have 5 different cubes all with an equal volume of 1cm 3. How much will each one weigh? QUESTION

16. Aluminum Water Gold Wood Understanding the Meaning of Density ObjectDensity (g/cm3)Density (kg/m 3 ) Aluminum2.7 g/cm 3 2700kg/m 3 Water1 g/cm 3 1000kg/m 3 Gold19.3 g/cm 3 19,300kg/m 3 Wood0.85g/cm 3 850kg/m 3 Sugar1.6g/cm 3 1600kg/m 3 Sugar Suppose we have 5 different cubes all with an equal volume of 1cm 3. How much will each one weigh? QUESTION 2.7g 1g 1.6g19.3g 0.85g

17. Density of Water: 1g/cm 3 or 1000kg/m 3 Water 1m 3 Water 1m 3 Assuming 1kg = 2.2lbs, how much would 1m 3 of water weigh? Could you lift it? Show me how big that is using meter sticks.

18. Which has a higher density? Aluminum

19. The Density is the same: 2.7g/cm 3 If we had two cubes of aluminum that each have a volume of 1cm 3, each one should have a mass of 2.7g m = 2.7g v= 1cm 3 m = 2.7g v= 1cm 3 m = 2.7g v= 1cm 3 m = 2.7g v= 1cm 3 What happens to density if we put the two blocks together? m = 5.4g v = 2cm 3 p = 2.7g/cm 3

20. WOOD BLOCK WOOD BLOCK Mass = 20g Volume 26cm 3 Density ≈ 0.77g/cm 3 WOOD BLOCK TWO WOOD BLOCKS WOOD BLOCK Mass = 10g Volume 13cm 3 Mass = 10g Volume 13cm 3 Cut in half Density ≈ 0.77g/cm 3 What Happens if I cut one of the small wooden blocks in half again? WOOD BLOCK WOOD BLOCK Mass = ??? Volume = ??? Density = ??? 20

21. DENSITY KEY CONCEPT Density does NOT depend on the amount of the substance you have. Regardless of whether you have a small piece of gold or a giant truck full of it, the density of that gold will be 19.3g/cm 3. Likewise, a drop of water has the same density as a swimming pool full of water (1g/cm 3 ). DENSITY KEY CONCEPT Density does NOT depend on the amount of the substance you have. Regardless of whether you have a small piece of gold or a giant truck full of it, the density of that gold will be 19.3g/cm 3. Likewise, a drop of water has the same density as a swimming pool full of water (1g/cm 3 ).

22. Volume: the amount of space something takes up! BATHTUB

23. What happens to the level of the water when you step in a bathtub?

24. BATHTUB

25. Volume or Water Displacement Water is generally incompressible. An object will displace a volume of water equal to the volume of the object itself when submerged. Both cm 3 and ml measure volume or the amount of space an object takes up. 1ml is = 1cm 3 Water displacement is useful for determining the volume of irregularly shaped objects. TOILET WATER DETENTION!

26. ---60ml If you place a large screw into a graduated cylinder with 60ml of water in it and the water level rises to 80ml, what is the volume of the screw? 1ml = 1cm 3

27. ---60ml ---80ml If you place a large screw into a graduated cylinder with 60ml of water in it and the water level rises to 80ml, what is the volume of the screw?

28. ---60ml ---80ml If you place a large screw into a graduated cylinder with 60ml of water in it and the water level rises to 80ml, what is the volume of the screw? The difference is 20ml

29. ---60ml ---80ml If you place a large screw into a graduated cylinder with 60ml of water in it and the water level rises to 80ml, what is the volume of the screw? 20cm 3 1ml = 1cm 3 The difference is 20ml

30. ---57.4ml ---81.6ml If you place a large screw into a graduated cylinder with 57.4ml of water in it and the water level rises to 81.6ml, what is the volume of the screw?

31. ---57.4ml ---81.6ml If you place a large screw into a graduated cylinder with 57.4ml of water in it and the water level rises to 81.6ml, what is the volume of the screw? Get the difference! Final – initial position 81.6ml – 57.4ml = 24.2ml

32. ---57.4ml ---81.6ml If you place a large screw into a graduated cylinder with 57.4ml of water in it and the water level rises to 81.6ml, what is the volume of the screw? Get the difference! Final – initial position 81.6ml – 57.4ml = 24.2ml 24.2cm 3 1ml = 1cm 3

33. A 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10 mL mark, from this information, calculate the density of iron. An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 12 ml. The height of the water rose to 17 ml. If the mass of the stone was 25 g, what was its density?

34. A 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10 mL mark, from this information, calculate the density of iron. An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 12 ml. The height of the water rose to 17 ml. If the mass of the stone was 25 g, what was its density? -------- 45.50ml -------- 49.10ml 49..1-ml – 45.5ml = 3.6ml ml and cm 3 are interchangeable. So mass = 28.5g and volume = 3.6cm 3 p =m/v 28.5g / 3.6cm 3 = 7.9g/cm 3

35. YOUR TASK Measure the volume of a large screw ________ Measure the volume of a 10g mass________ What is the screw’s density?________ A paper clip is too small to accurately measure its volume. Come up with a method that can be used to determine the volume of one paper clip. Write it down in your notebook. What is the volume of a single paper clip______ YOUR TASK Measure the volume of a large screw ________ Measure the volume of a 10g mass________ What is the screw’s density?________ A paper clip is too small to accurately measure its volume. Come up with a method that can be used to determine the volume of one paper clip. Write it down in your notebook. What is the volume of a single paper clip______ Read at the base of the meniscus! Keep it flat, read at eye level!

36. What if an object is too big to fit in a graduated cylinder? 1)You might consider using a beaker instead but in general a graduated cylinder is far more accurate at measuring volume than a beaker. 2)So we can use something called an overflow can.

37. Overflow Can. 1)Fill the can above the drain line with water. 2)Let the excess drip out until the water is level with the drain. 3)Now any object placed in it will cause the water to overflow through the drain.

38. Overflow Can. 1)Fill the can above the drain line with water. 2)Let the excess drip out until the water is level with the drain. 3)Now any object placed in it will cause the water to overflow through the drain. 4)Catch the water in a graduated cylinder or other device and measure its volume in ml. 5)This is the volume of the object in cm 3

39. CLASS ACTIVITY Determine the density a rock: a 200g mass a 500g mass What metal is the mass made of? (use the internet to look up your density value). DENSITY

40. CLASS ACTIVITY Determine the mass in grams of the following volumes of water: VOLUME (ml)MASS (g) 5 20 32 40 46 50 Pattern?

41. Key Points Water displacement is used to determine the volume of irregularly shaped objects. Milliliters (ml) and centimeters cubed (cm 3 ) are interchangeable. 1ml = 1cm 3 For H 2 O 1g = 1ml = 1cm 3

42. Density and Flotation Task: Given 3 eggs, salt, water, and 3 beakers, make it so that one egg sinks, one egg floats and one egg stays suspended in the middle of the water. Objects sink or float based upon density. If an object is less dense that water (p < 1g/cm 3 ) it will float. If an object is more dense than water (p < 1g/cm 3 ) it will sink.

43. ObjectDensity (g/cm 3 )Sink or Float Aluminum2.7 g/cm 3 Penny7.2 g/cm 3 Gold19.3 g/cm 3 Wood0.85g/cm 3 Sugar1.6g/cm 3 Ice0.917g/cm 3 Baby Oil0.83g/cm 3 Mercury13.94g/cm 3 Will a penny sink or float in liquid mercury?

44. Mercury Video

45. QUIZ: make an 8 item density column. 7 Layer Density Column ObjectDensity g/cm 3 Honey1.42 Light Corn Syrup1.33 Dawn Dish Soap1.06 Water1.00 Vegetable Oil.92 Baby Oil.83 Rubbing Alcohol0.79 You must use 3 solids! Hand in a labeled picture in COLOR! Bring it in for extra credit! Objects generally sink or float based upon density. More dense = sinks Less dense - floats Objects generally sink or float based upon density. More dense = sinks Less dense - floats

46. How much of an Object will Float above Water? Zinc 0.92g/cm 3 7.13g/cm 3 The zinc will sink as its denser than water The zinc will sink as its denser than water The ice floats as its less dense than water The ice floats as its less dense than water But how much is underneath the water? But how much is underneath the water? If 92% is under water then the other 8% is visible! ICE CUBE About 8% visible

47. Just the Tip of the Iceberg!!! Photo via: Adventure-Journal 90% of this ice berg is below water (salt water )

48. Most of an Iceberg is below water! Think about this and ships traveling in the ocean. The TITANIC Most of an Iceberg is below water! Think about this and ships traveling in the ocean. The TITANIC Artistic Rendition of an iceberg. Wiki commons

50. Flotation Problems (Handout) Knock on Wood A branch snaps and falls into a river. It has a density of 0.7g/cm 3, will it sink or float and if it floats how much of it will be visible? Floating Basketball A basketball has a mass of 624g and a volume of 7512cm 3. What percentage of a basketball will be visible above water?

51. Rank each object from the most dense to the least dense: A B C D D E F Most Dense [1] [2] [3] [4] [5] [6] Least Dense

52. Buoyancy: How can a ship made of iron that weighs about 200 million pounds float? FOIL SHAPEPREDICTIONOBSERVATIONEXPLANATION Boat Sink or Float Ball Sink or Float Block Sink or Float

53. Aluminum Foil Boats Objective: To design/build two different aluminum foil boats that will hold as many pennies as possible without sinking. Procedure 1.Obtain two 20cmx20cm pieces of aluminum foil. 2.Build your boats. 3.Test them by adding pennies until they sink. 4.Dry the pennies off and return them. 5.Which boat in the class won? Why? Objective: To design/build two different aluminum foil boats that will hold as many pennies as possible without sinking. Procedure 1.Obtain two 20cmx20cm pieces of aluminum foil. 2.Build your boats. 3.Test them by adding pennies until they sink. 4.Dry the pennies off and return them. 5.Which boat in the class won? Why?

54. Shape and density determine if something will float.

55. 55 Buoyant Force: When an object displaces water the water pushes back on it. What happens to the weight of an object when placed in water?

56. Intro to Forces: PHET Sim Force: a push or a pull (unit: Newtons) If Forces are balanced an object will not move or change its motion! Unbalanced forces lead to changes in motion. https://phet.colorado.edu/en/simulation/forces-and-motion-basics

57. Buoyant Force (upward push of water) Weight Force (heaviness of object) 1.If Weight is greater than Buoyant Force an object sinks. 2.If Buoyant Force is greater than weight the object rises and then floats. 3.When Buoyant Force equals weight the object floats or suspends.

58. Which is greater: the Weight or Buoyant Force? 58

59. Floating: Buoyant Force = Weight F = 100N If a 100N boat is floating the water must be pushing on it with a force of 100N If we add weight (50N) to the boat it will sink down deeper and the buoyant force will increase. F = 150N

60. Buoyant Force (upward push of water) Weight Force (heaviness of object) Archimedes Principle: Buoyant force is equal to the weight of the fluid displaced. The more water an object displaces the more buoyant force pushing on it. This is why a block of aluminum sinks but an aluminum foil boat floats. Shape is important!

61. If you were to hold a basketball under water it will push back very hard and would fly upwards if your were to release it. Buoyant Force > Weight

62. If you were to hold a basketball under water it will push back very hard and would fly upwards if your were to release it. Buoyant Force > Weight When floating the buoyant force on ball equals its weight.

63. Why is it easier to lift a person in water? 50N Weight (force) Lift (force)

64. Why is it easier to lift a person in water? 50N Weight (force) Lift (force) Weight (force) Lift (force) Buoyant (force) The water helps you!

65. Concrete Boats Heavy iron ships can float because they are shaped to displace a large amount of water and being hollow and filled with air reduces their overall density. Its easier to pick someone up in water because the water helps you (buoyant force).