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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

pressure

volume

tension

compression

elastic, elasticity

brittle

ductile

safety factor

modulus of

elasticity

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

Key Question:

How do you measure the

strength of a solid

material?

*Students read Section 27.1

AFTER Investigation 27.1

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

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?

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

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)

Area (m2)

Stress (N/m2)

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

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

Aluminum alloy tubes

Steel cables

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

Change in

length (m)

Original length (m)

Strain

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)

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)

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

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

— When stretched to its limit, the column reaches a

maximum length of 2.09 m before breaking

Key Question:

What are some implications of Bernoulli’s equation?

*Students read Section 27.2 AFTER Investigation 27.2

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

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.

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.

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

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

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.

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.

Pressure and energy

are related.

Differences in

pressure create

potential energy in

fluids just like

differences in height

create potential

energy from gravity

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

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.

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).

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

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.

Key Question:

How much matter is

in a gas?

*Students read Section 27.3 AFTER Investigation 27.3

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.

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

Original pressure

(N/m2)Final pressure (N/m2)

Final temperature

P1 = P2

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

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

CPO Science Foundations of Physics - WordPress.com · · 2017-05-09ability of an object to hold...

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