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

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1 CPO Science Foundations of Physics Unit 8, Chapter 27

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

3 Chapter 27 Objectives 1. Perform calculations involving the density of solids, gases, and liquids. 2. Apply the concepts of force, stress, strain, and tensile strength to simple structures. 3. Describe the cause and some consequences of thermal expansion in solids, liquids, and gases. 4. Explain the concept of pressure and calculate pressure caused by the weight of fluids. 5. Explain how pressure is created on a molecular level. 6. Understand and apply Bernoulli s equation to flow along a streamline. 7. 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 Most engineers and scientists use the greek letter rho (ρ) to represent density. Density (kg/m 3 ) r = m V Mass (kg) Volume (m 3 or L)

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 ). Stress (N/m 2 ) s = F A Force (N) Area (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 = m 2 Tensile strength = 600 Mpa

18 27.1 Evaluate Design #2 Aluminum alloy tubes Cross section = 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. Strain e = Dl l Change in length (m) Original length (m)

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: Stress (Mpa) s = -E e Modulus of elasticity (pa) Strain

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 Change in length (m) Dl = a (T 2 -T 1 ) l Coefficient of thermal expansion Change in temperature ( o C) Original 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 Classwork: Stress and Strain Find the modulus of elasticity for a 2-meter long cylindrical column made of a mystery material, assuming: The radius of the column is 10 cm. The maximum stress force it can withstand is 300 kpa When stretched to its limit, the column reaches a maximum length of 2.09 m before breaking

33 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

34 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.

35 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

37 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 Pressure

38 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.

39 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.

40 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.

41 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.

42 27.2 Pressure in liquids The pressure at the same depth is the same everywhere in any liquid that is not moving. Pressure (pa or N/m 2 ) P = r g d Density (kg/m 3 ) Depth (m) Strength of gravity (9.8 N/kg)

43 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.

44 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.

45 27.2 Pressure and forces Pressure creates force on surfaces. The force is equal to the pressure times the area that contacts the molecules. Pressure (N/m 2 ) Force (N) F = P A Area (m 2 )

46 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?

47 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.

48 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.

49 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

50 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.

51 27.2 Energy in fluids The potential energy is equal to volume times pressure. Pressure (N/m 2 ) Potential energy (J) E = P V Volume (m 3 )

52 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.

53 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.

54 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).

55 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.

56 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).

57 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?

58 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.

59 27.3 Properties of Gases Key Question: How much matter is in a gas? *Students read Section 27.3 AFTER Investigation 27.3

60 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.

61 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.

62 27.3 Boyle's Law If the mass and temperature are kept constant, the product of pressure times volume stays the same. Original pressure (N/m 2 ) Final pressure (N/m 2 ) P 1 V 1 = P 2 V 2 Original volume (m 3 ) Final volume (m 3 )

63 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?

64 27.3 Charles' Law If the mass and volume are kept constant, the pressure goes up when the temperature goes up. Original pressure (N/m 2 ) Final pressure (N/m 2 ) Original temperture (k) P 1 = P 2 T 1 T 2 Final temperature (K)

65 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?

66 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).

67 The gas constants are different because the size and mass of gas molecules are different Gas Constants

68 27.3 Ideal gas law If the mass and temperature are kept constant, the product of pressure times volume stays the same. Pressure (N/m 2 ) P V = m R T gas constant (J/kgK) Volume (m 3 ) Mass (kg) Temperature (K)

69 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 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.

70 Application: The Deep Water Submarine Alvin

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