1. Unit 8, Chapter 27 CPO Science Foundations of Physics

2. Unit 8: Matter and Energy  27.1 Properties of Solids  27.2 Properties of Liquids and Fluids  27.3 Properties of Gases Chapter 27 The Physical Properties of Matter

3. Chapter 27 Objectives  Perform calculations involving the density of solids, gases, and liquids.  Apply the concepts of force, stress, strain, and tensile strength to simple structures.  Describe the cause and some consequences of thermal expansion in solids, liquids, and gases.  Explain the concept of pressure and calculate pressure caused by the weight of fluids.  Explain how pressure is created on a molecular level.  Understand and apply Bernoulli’s equation to flow along a streamline.  Apply the gas laws to simple problems involving pressure, temperature, mass, and volume.

4. Chapter 27 Vocabulary Terms  stress  density  strain  tensile strength  cross section area  pressure  volume  tension  compression  elastic, elasticity  fluid  brittle  ductile  safety factor  modulus of elasticity  alloy  airfoil  buoyancy  fluid mechanics  ideal gas law  Boyle’s law  streamline  laminar flow  turbulent flow  Bernoulli’s equation  pascal (Pa)  Charles’ law  gas constant (R)  composite material  thermal expansion

5. 27.1 Properties of Solids Key Question: How do you measure the strength of a solid material? *Students read Section 27.1 AFTER Investigation 27.1

6. 27.1 Properties of Solids  The density of a material is the ratio of mass to volume.  Density is a physical property of the material and stays the same no matter how much material you have.

7. 27.1 Density  = m V Mass (kg) Volume (m 3 or L) Density (kg/m 3 )  Most engineers and scientists use the greek letter rho (ρ) to represent density.

8. 27.1 Densities of Common Materials  Which materials are less dense than water?

9. 27.1 Properties of Solids  The concept of physical “strength” means the ability of an object to hold its form even when force is applied.  To evaluate the properties of materials, it is sometimes necessary to separate out the effects of design, such as shape and size.

10. 27.1 Stress  The stress in a material is the ratio of the force acting through the material divided by the cross section area through which the force is carried.  The metric unit of stress is the pascal (Pa).  One pascal is equal to one newton of force per square meter of area (1 N/m 2 ).  = F A Force (N) Area (m 2 ) Stress (N/m 2 )

11. 27.1 Properties of Solids

12. 26.1 Properties of Solids  A thicker wire can support more force at the same stress as a thinner wire because the cross section area is increased.

13. 26.1 Tensile strength  The tensile strength is the stress at which a material breaks under a tension force.  The tensile strength also describes how materials break in bending.

14. 27.1 Tensile strength

15. 27.1 Properties of solids  The safety factor is the ratio of how strong something is compared with how strong it has to be.  The safety factor allows for things that might weaken the wire (like rust) or things you did not consider in the design (like heavier loads).  A safety factor of 10 means you choose the wire to have a breaking strength of 10,000 newtons, 10 times stronger than it has to be.

16. 27.1 Evaluate 3 Designs  Three designs have been proposed for supporting a section of road.  Each design uses three supports spaced at intervals along the road.  A total of 4.5 million N of force is required to hold up the road.  Evaluate the strength of each design.  The factor of safety must be 5 or higher even when the road is bumper-to-bumper on all 4 lanes with the heaviest possible trucks.

17. 27.1 Evaluate Design #1  High strength steel tubes  Cross section = 0.015 m 2  Tensile strength = 600 Mpa

18. 27.1 Evaluate Design #2  Aluminum alloy tubes  Cross section = 0.015 m 2  Tensile strength = 290 Mpa

19. 27.1 Evaluate Design #3  Steel cables  Cross section = 0.03 m 2  Tensile strength = 400 Mpa

20. 27.1 Properties of solids  Elasticity measures the ability of a material to stretch.  The strain is the amount a material has been deformed, divided by its original size.

21. 27.1 Strain  The Greek letter epsilon (ε) is usually used to represent strain.  =  l l Change in length (m) Original length (m) Strain

22. 27.1 Properties of solids  The modulus of elasticity plays the role of the spring constant for solids.  A material is elastic when it can take a large amount of strain before breaking.  A brittle material breaks at a very low value of strain.

23. 27.1 Modulus of Elasticity

24. 27.1 Stress for solids  Calculating stress for solids is similar to using Hooke's law for springs.  Stress and strain take the place of force and distance in the formula:  = -E  Modulus of elasticity (pa) Strain Stress (Mpa)

25. 27.1 Properties of solids  The coefficient of thermal expansion describes how much a material expands for each change in temperature.  Concrete bridges always have expansion joints.  The amount of contraction or expansion is equal to the temperature change times the coefficient of thermal expansion.

26. 27.1 Thermal Expansion  l =  (T 2 -T 1 ) l Change in temperature ( o C) Original length (m) Coefficient of thermal expansion Change in length (m)

27. 27.1 Thermal Expansion  Which substances will expand or contract the most with temperature changes?

28. 27.1 Plastic  Plastics are solids formed from long chain molecules.  Different plastics can have a wide range of physical properties including strength, elasticity, thermal expansion, and density.

29. 27.1 Metal  Metals that bend and stretch easily without cracking are ductile.  The properties of metals can be changed by mixing elements.  An alloy is a metal that is a mixture of more than one element.  Steel is an alloy.

30. 27.1 Wood  Many materials have different properties in different directions.  Wood has a grain that is created by the way trees grow.  Wood is very difficult to break against the grain, but easy to break along the grain.  A karate chop easily breaks wood along its grain.

31. 27.1 Composite materials  Composite materials are made from strong fibers supported by much weaker plastic.  Like wood, composite materials tend to be strongest in a preferred direction.  Fiberglass and carbon fiber are two examples of useful composite materials.

32. 27.2 Properties of Liquids and Fluids Key Question: What are some implications of Bernoulli’s equation? *Students read Section 27.2 AFTER Investigation 27.2

33. 27.2 Properties of Liquids and Fluids  Fluids can change shape and flow when forces are applied to them.  Gas is also a fluid because gases can change shape and flow.  Density, buoyancy and pressure are three properties exhibited by liquids and gases.

34. 27.2 Density vs. Buoyancy  The density of a liquid is the ratio of mass to volume, just like the density of a solid.  An object submerged in liquid feels an upward force called buoyancy.  The buoyancy force is exactly equal to the weight of liquid displaced by the object.  Objects sink if the buoyancy force is less than their own weight.

36. 27.2 Pressure  Forces applied to fluids create pressure instead of stress.  Pressure is force per unit area, like stress.  A pressure of 1 N/m 2 means a force of one newton acts on each square meter.

37. 27.2 Pressure  Like stress, pressure is a ratio of force per unit area.  Unlike stress however, pressure acts in all directions, not just the direction of the applied force.

38. 27.2 Pressure  The concept of pressure is central to understanding how fluids behave within themselves and also how fluids interact with surfaces, such as containers.  If you put a box with holes underwater, pressure makes water flow in from all sides.  Pressure exerts equal force in all directions in liquids that are not moving.

39. 27.2 Properties of liquids and gases  Gravity is one cause of pressure because fluids have weight.  Air is a fluid and the atmosphere of the Earth has a pressure.  The pressure of the atmosphere decreases with altitude.

40. 27.2 Properties of liquids and gases  The pressure at any point in a liquid is created by the weight of liquid above that point.

41. 27.2 Pressure in liquids  The pressure at the same depth is the same everywhere in any liquid that is not moving. P =  g d Density (kg/m 3 ) Depth (m) Pressure (pa or N/m 2 ) Strength of gravity (9.8 N/kg)

42. 27.2 Calculate pressure  Calculate the pressure 1,000 meters below the surface of the ocean.  The density of water is 1,000 kg/m 3.  The pressure of the atmosphere is 101,000 Pa.  Compare the pressure 1,000 meters deep with the pressure of the atmosphere.

43. 27.2 Properties of liquids and gases  Pressure comes from collisions between atoms or molecules.  The molecules in fluids (gases and liquids) are not bonded tightly to each other as they are in solids.  Molecules move around and collide with each other and with the solid walls of a container.

44. 27.2 Pressure and forces  Pressure creates force on surfaces.  The force is equal to the pressure times the area that contacts the molecules. F =  P A Pressure (N/m 2 ) Area (m 2 ) Force (N)

45. 27.2 Calculate pressure  A car tire is at a pressure of 35 psi.  Four tires support a car that weighs 4,000 pounds.  Each tire supports 1,000 pounds.  How much surface area of the tire is holding up the car?

46. 27.2 Motion of fluids  The study of motion of fluids is called fluid mechanics.  Fluids flow because of differences in pressure.  Moving fluids usually do not have a single speed.

47. 27.2 Properties of liquids and gases  A flow of syrup down a plate shows that friction slows the syrup touching the plate.  The top of the syrup moves fastest because the drag from friction decreases away from the plate surface.

48. 27.2 Properties of liquids and gases  Pressure and energy are related.  Differences in pressure create potential energy in fluids just like differences in height create potential energy from gravity

49. 27.2 Properties of liquids and gases  Pressure does work as fluids expand.  A pressure of one pascal does one joule of work pushing one square meter a distance of one meter.

50. 27.2 Energy in fluids  The potential energy is equal to volume times pressure. E =  P V Pressure (N/m 2 ) Volume (m 3 ) Potential energy (J)

51. 27.2 Energy in fluids  The total energy of a small mass of fluid is equal to its potential energy from gravity (height) plus its potential energy from pressure plus its kinetic energy.

52. 27.2 Energy in fluids  The law of conservation of energy is called Bernoulli’s equation when applied to a fluid.  Bernoulli’s equation says the three variables of height, pressure, and speed are related by energy conservation.

53. 27.2 Bernoulli's Equation  If one variable increases, at least one of the other two must decrease.  If the fluid is not moving (v = 0), then Bernoulli’s equation gives us the relationship between pressure and depth (negative height).

54. 27.2 Properties of liquids and gases  Streamlines are imaginary lines drawn to show the flow of fluid.  We draw streamlines so that they are always parallel to the direction of flow.  Fluid does not flow across streamlines.

55. 27.2 Applying Bernoulli's equation  The wings of airplanes are made in the shape of an airfoil.  Air flowing along the top of the airfoil (B) moves faster than air flowing along the bottom of the airfoil (C).

56. 27.2 Calculating speed of fluids  Water towers create pressure to make water flow.  At what speed will water come out if the water level in the tower is 50 meters higher than the faucet?

57. 27.2 Fluids and friction  Viscosity is caused by forces that act between atoms and molecules in a liquid.  Friction in fluids also depends on the type of flow.  Water running from a faucet can be either laminar or turbulent depending on the rate of flow.

58. 27.3 Properties of Gases Key Question: How much matter is in a gas? *Students read Section 27.3 AFTER Investigation 27.3

59. 27.3 Properties of Gases  Air is the most important gas to living things on the Earth.  The atmosphere of the Earth is a mixture of nitrogen, oxygen, water vapor, argon, and a few trace gases.

60. 27.3 Properties of Gases  An object submerged in gas feels an upward buoyant force.  You do not notice buoyant forces from air because the density of ordinary objects is so much greater than the density of air.  The density of a gas depends on pressure and temperature.

61. 27.3 Boyle's Law  If the mass and temperature are kept constant, the product of pressure times volume stays the same. P 1 V 1 = P 2 V 2 Original volume (m 3 ) Original pressure (N/m 2 ) Final pressure (N/m 2 ) Final volume (m 3 )

62. 27.3 Calculate using Boyle's law  A bicycle pump creates high pressure by squeezing air into a smaller volume.  If air at atmospheric pressure (14.7 psi) is compressed from an initial volume of 30 cubic inches to a final volume of three cubic inches, what is the final pressure?

63. 27.3 Charles' Law  If the mass and volume are kept constant, the pressure goes up when the temperature goes up. Original temperture (k) Original pressure (N/m 2 ) Final pressure (N/m 2 ) Final temperature (K) P 1 = P 2 T 1 T 2

64. 27.3 Calculate using Charles' law  A can of hair spray has a pressure of 300 psi at room temperature (21°C or 294 K).  The can is accidentally moved too close to a fire and its temperature increases to 800°C (1,073 K).  What is the final pressure in the can?

65. 27.3 Ideal gas law  The ideal gas law combines the pressure, volume, and temperature relations for a gas into one equation which also includes the mass of the gas.  In physics and engineering, mass (m) is used for the quantity of gas.  In chemistry, the ideal gas law is usually written in terms of the number of moles of gas (n) instead of the mass (m).

66. 27.3 Gas Constants  The gas constants are different because the size and mass of gas molecules are different.

67. 27.3 Ideal gas law  If the mass and temperature are kept constant, the product of pressure times volume stays the same. P V = m R T Volume (m 3 ) Pressure (N/m 2 ) gas constant (J/kgK) Temperature (K) Mass (kg)

68. 27.3 Calculate using Ideal gas law  Two soda bottles contain the same volume of air at different pressures.  Each bottle has a volume of 0.002 m 3 (two liters).  The temperature is 21°C (294 K).  One bottle is at a gauge pressure of 500,000 pascals (73 psi).  The other bottle is at a gauge pressure of zero.  Calculate the mass difference between the two bottles.

69. Application: The Deep Water Submarine Alvin