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Unit 8, Chapter 27 CPO Science Foundations of Physics
Unit 8, Chapter 27
CPO Science
Foundations of Physics
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
Chapter 27 Objectives1. 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.
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
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
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.
27.1 Density
r = m
V
Mass (kg)
Volume (m3 or L)
Density (kg/m3)
Most engineers and scientists use the greek letter
rho (ρ) to represent density.
27.1 Densities of Common Materials
Which materials are less dense than water?
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.
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).
s = F
A
Force (N)
Area (m2)
Stress (N/m2)
27.1 Properties of Solids
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.
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.
27.1 Tensile strength
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.
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.
27.1 Evaluate Design #1
High strength steel tubes
Cross section = 0.015 m2
Tensile strength = 600 Mpa
27.1 Evaluate Design #2
Aluminum alloy tubes
Cross section = 0.015 m2
Tensile strength = 290 Mpa
27.1 Evaluate Design #3
Steel cables
Cross section = 0.03 m2
Tensile strength = 400 Mpa
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.
27.1 Strain
The Greek letter epsilon (ε) is usually used to
represent strain.
e = Dl
l
Change in
length (m)
Original length (m)
Strain
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.
27.1 Modulus of Elasticity
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:
s = -E e
Modulus of
elasticity (pa)
Strain
Stress (Mpa)
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.
27.1 Thermal Expansion
Dl = a (T2-T1)
l
Change in
temperature (oC)
Original length (m)
Coefficient of thermal expansionChange in
length (m)
27.1 Thermal Expansion
Which substances
will expand or
contract the most
with temperature
changes?
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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.
27.2 Pressure in liquids
The pressure at the same depth is the same
everywhere in any liquid that is not moving.
P = r g d
Density (kg/m3)
Depth (m)
Pressure
(pa or N/m2)
Strength of gravity
(9.8 N/kg)
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.
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.
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/m2)
Area (m2)Force
(N)
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?
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.
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.
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
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.
27.2 Energy in fluids
The potential energy is equal to volume times
pressure.
E = P V
Pressure (N/m2)
Volume (m3)Potential
energy
(J)
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.
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.
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).
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.
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).
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?
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.
27.3 Properties of Gases
Key Question:
How much matter is
in a gas?
*Students read Section 27.3 AFTER Investigation 27.3
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.
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.
27.3 Boyle's Law
If the mass and temperature are kept constant, the
product of pressure times volume stays the same.
P1V1 = P2V2
Original volume (m3)
Original pressure
(N/m2)Final pressure (N/m2)
Final volume (m3)
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?
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/m2)Final pressure (N/m2)
Final temperature
(K)
P1 = P2
T1 T2
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?
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).
27.3 Gas Constants
The gas
constants are
different because
the size and
mass of gas
molecules are
different.
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 (m3)
Pressure
(N/m2)
gas constant (J/kgK)
Temperature (K)
Mass (kg)
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 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.
Application: The Deep Water
Submarine Alvin
