CPO Science Foundations of Physics Unit 8, Chapter 27 Unit

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Unit 8, Chapter 27
CPO Science Foundations of Physics
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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

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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 Bernoullis equation to flow
  along a streamline.
• Apply the gas laws to simple problems involving
  pressure, temperature, mass, and volume.

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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

• Boyles law
• streamline
• laminar flow
• turbulent flow
• Bernoullis equation
• pascal (Pa)
• Charles law
• gas constant (R)
• composite material
• thermal expansion

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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
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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.

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27.1 Density

• Most engineers and scientists use the greek
  letter rho (?) to represent density.

Mass (kg)
r m V
Density (kg/m3)
Volume (m3 or L)
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27.1 Densities of Common Materials

• Which materials are less dense than water?

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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.

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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/m2).

Force (N)
s F A
Stress (N/m2)
Area (m2)
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27.1 Properties of Solids
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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.

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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.

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27.1 Tensile strength
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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.

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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.

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27.1 Evaluate Design 1

• High strength steel tubes
• Cross section 0.015 m2
• Tensile strength 600 Mpa

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27.1 Evaluate Design 2

• Aluminum alloy tubes
• Cross section 0.015 m2
• Tensile strength 290 Mpa

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27.1 Evaluate Design 3

• Steel cables
• Cross section 0.03 m2
• Tensile strength 400 Mpa

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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.

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27.1 Strain

• The Greek letter epsilon (e) is usually used to
  represent strain.

Change in length (m)
e Dl l
Strain
Original length (m)
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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.

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27.1 Modulus of Elasticity
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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

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

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27.1 Thermal Expansion
Coefficient of thermal expansion
Change in length (m)
Dl a (T2-T1) l
Change in temperature (oC)
Original length (m)
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27.1 Thermal Expansion

• Which substances will expand or contract the most
  with temperature changes?

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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.

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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.

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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.

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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.

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27.2 Properties of Liquids and Fluids

• Key Question
• What are some implications of Bernoullis
  equation?

Students read Section 27.2 AFTER Investigation
27.2
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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.

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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.

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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/m2 means a force of one newton
  acts on each square meter.

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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.

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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.

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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.

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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.

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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/m2)
Density (kg/m3)
P r g d
Depth (m)
Strength of gravity (9.8 N/kg)
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27.2 Calculate pressure

• Calculate the pressure 1,000 meters below the
  surface of the ocean.
• The density of water is 1,000 kg/m3.
• The pressure of the atmosphere is 101,000 Pa.
• Compare the pressure 1,000 meters deep with the
  pressure of the atmosphere.

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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.

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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/m2)
Force (N)
F P A
Area (m2)
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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?

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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.

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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.

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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

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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.

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27.2 Energy in fluids

• The potential energy is equal to volume times
  pressure.

Pressure (N/m2)
Potential energy (J)
E P V
Volume (m3)
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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.

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27.2 Energy in fluids

• The law of conservation of energy is called
  Bernoullis equation when applied to a fluid.
• Bernoullis equation says the three variables of
  height, pressure, and speed are related by energy
  conservation.

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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
  Bernoullis equation gives us the relationship
  between pressure and depth (negative height).

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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.

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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).

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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?

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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.

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27.3 Properties of Gases

• Key Question
• How much matter is in a gas?

Students read Section 27.3 AFTER Investigation
27.3
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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.

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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.

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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/m2)
Final pressure (N/m2)
P1V1 P2V2
Final volume (m3)
Original volume (m3)
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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?

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27.3 Charles' Law

• If the mass and volume are kept constant, the
  pressure goes up when the temperature goes up.

Original pressure (N/m2)
Final pressure (N/m2)
Original temperture (k)
Final temperature (K)
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27.3 Calculate using Charles' law

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

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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).

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27.3 Gas Constants

• The gas constants are different because the size
  and mass of gas molecules are different.

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27.3 Ideal gas law

• If the mass and temperature are kept constant,
  the product of pressure times volume stays the
  same.

gas constant (J/kgK)
Pressure (N/m2)
P V m R T
Temperature (K)
Volume (m3)
Mass (kg)
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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 m3 (two
  liters).
• The temperature is 21C (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.

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Application The Deep Water Submarine Alvin