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Name: ___________________ Class: _____________________Teacher: _____________________

Thermal physics, materials, and fluids

C2 – Materials in domestic and industrial applications

Learning outcomes Met Signed by teacher

1) Understanding concepts of material properties. Apply material properties to domestic and industrial applications.

2) Define stress, strain, and Young’s modulus qualitatively and quantitatively.Use Hooke’s Law to find the work done in stretching/ compressing a spring.

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1) Material properties

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Elasticity

Stress-strain curves

Elastic limit

Strength

Yield point

Plastic deformation

Creep

Fatigue

Ductility

Brittleness

Malleability

Elastic hysteresis

Strain

Stress Force per unit cross sectional area.

Extension per unit length.


1.1 Elasticity

Solids have a shape and size that does not change unless a sufficient force is applied. As a force is applied, objects behaviour differently depending on their material characteristics but eventually, they all demonstrate the same behaviour:

1.2 Stress-strain curves1.2.1 Stress

1.2.2 Strain

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1. Elastic behaviour – the solid material regains its original size and shape after the applied force is removed, e.g. a spring.

2. Elastic limit – solid materials can bounce back to shape up to a certain limit.

3. Plastic deformation – the shape or size of the object remains the same once the applied force has been removed.

Stress is defined as ___________________________________________________________________________

______.

Stress:

Strain is defined as ___________________________________________________________________________

______.

Strain:


1.2.3 Stress-strain curves

Each material has a unique stress-strain curve. It tells you the amount by which a material is deformed as it experiences a tensile or compressive stress.

These can be used to choose the best material for building bridges, cables for cranes, etc.

Your turn: this is the general shape of a stress strain graph. Label where the material exerts:

Behaves elastically reaches the elastic limit deforms plastically fractures

1.2.4 Young’s modulus

The Young’s modulus can be determined using a stress-strain graph. How?

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Young’s modulus is a measure of the ability of a material to

withstand changes in length when under lengthwise tension

or compression.

Young’s modulus:


1.2.5 Strength

1.2.6 Creep

1.2.7 Fatigue

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Strength – maximum stress that the material can bear. It occurs

just before the material fractures.

Creep – occurs when a material under stress deforms gradually over time, e.g. cardboard boxes

that have been stacked.

Fatigue – material becomes brittle when exposed to applied levels of stress that have been

repeated and relaxed over many cycles, suspension springs.


1.2.8 Brittleness and ductility

1.2.9 Malleability

1.2.10 Elastic hysteresis

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Brittleness – tendency for a material to fracture

under stress.

Ductility – can be drawn into new shapes, e.g.

wires (copper).

Malleability – ability to be shaped by means of

compressive forces – rolling, hammering, stamping.

Elastic hysteresis – occurs in materials like rubber, where

internal friction between large molecules dissipates heat

energy.


Your task: you have been given many materials with different facts about them. You must read the facts and determine the material properties of each material.

Material Properties Reasons

Gold

Lead

Copper

Glass

Diamond

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Materials summary – complete this for homework

Stress Strain

Elasticity Strength

Stress-strain curves Elastic limit

Yield point Plastic deformationCreep Fatigue

Ductility Malleability

Elastic hysteresis

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Brittleness2) Stress, strain, and Young’s modulus

2.1 Density

Recap of density

How do you calculate the volume of:

a) A regular shape? (e.g. cube)

b) An irregular shape? (e.g. cork)

Experiment: determine the density of both regular and irregular objects.

Object Mass (g) Volume (mm³) Density (g/mm³)

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2.2 Conversion of units

Your turn – convert these units using the rules above the help you:

1) Convert 34.5 mm³ into m³

2) Convert 7.657 cm³ into m³

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mm cm m

× 10 × 100

÷ 100÷ 10

mm³ cm³ m³

÷ 1,000,000

× 1,000,000

× 1000

÷ 1000


3) Comvert 4 m³ into cm³

2.3 Tensile/compressive stress

Stress depends on the force being applied, F, across a cross-sectional area, A.

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Tensile stress –

Compressive stress -


2.4 Tensile/ compressive strain

Strain depends on the original length of the wire, L, and the extension of the wire when the load is applied, Δx.

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Tensile strain –

Compressive strain -


Practice questions – show all your working out!

These are provided so that you become more confident with the quantities involved, and with the large and small numbers.

Hint: you will need the formula for the area of a circle, A=π d2

4.

A strip of rubber originally 75 mm long is stretched until it is 100 mm long.

1. What is the tensile strain?

2. Why has the answer no units?

3. The greatest tensile stress which steel of a particular sort can withstand without breaking is

about 109 N m-2. A wire of cross-sectional area 0.01 mm2 is made of this steel. What is the greatest force that it can withstand?

4. Find the minimum diameter of an alloy cable, tensile strength 75 MPa, needed to support a load of 15 kN.

5. Calculate the tensile stress in a suspension bridge supporting cable, of diameter of 50 mm, which pulls up on the roadway with a force of 4 kN.

6. Calculate the tensile stress in a nylon fishing line of diameter 0.36 mm which a fish is pulling with a force of 20 N

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2.5 Young’s modulus

Proof

The gradient of the stress-strain graph gives you the Young’s modulus for that material.

Harder question – you will need to use the equations for stress and strain.

7. A large crane has a steel lifting cable of diameter 36 mm. The steel used has a Young modulus of 200 GPa. When the crane is used to lift 20 kN, the unstretched cable length is 25.0 m. Calculate the extension of the cable.

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Young’s modulus -


Exam question

1. The table below shows the results of an experiment where a force was applied to a sample of metal.

(a)     On the axes below, plot a graph of stress against strain using the data in the table.

 

Strain / 10–3

0 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Stress /108 Pa 0 0.90 2.15 3.15 3.35 3.20 3.30 3.50 3.60 3.60 3.50

(3)

(b)     Use your graph to find the Young modulus of the metal.

 

 

 

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answer = ...................................... Pa

(2)

(c)     A 3.0 m length of steel rod is going to be used in the construction of a bridge. The tension in the rod will be 10 kN and the rod must extend by no more than 1.0mm. Calculate the minimum cross-sectional area required for the rod.

Young modulus of steel = 1.90 × 1011 Pa

 

 

 

 

 

answer = ...................................... m2

(3)

(Total 8 marks)

Progress check:

😊 😐 ☹

Material properties

Density

Unit conversions

Stress

Strain

Young’s modulus

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2.6 Hooke’s Law

Experiment – add weights onto the end of a spring, noting down the force and extension after every addition. Using these results, plot a force-extension graph, and find the spring constant.

Mass (kg) Force (N) Original length (mm)

Extended length (mm)

Extension (mm)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

*Extension: once you have found the spring constant, find the work done by the spring. Hint: it is the area under the force-extension plot.

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Hooke’s Law –


Task: try this exam question combining material properties, stress, strain, Young’s modulus, and Hooke’s law.

          2. (a)     (i)      Describe the behaviour of a wire that obeys Hooke’s law.

.............................................................................................................

.............................................................................................................

(ii)     Explain what is meant by the elastic limit of the wire.

.............................................................................................................

.............................................................................................................

(iii)     Define the Young modulus of a material and state the unit in which it is measured.

.............................................................................................................

.............................................................................................................

(5)

(Total 5 marks)

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2.7 Work done in stretching/compressing a spring

When a spring is stretched or compressed, energy is transferred – i.e. work is done. There are 2 ways of calculating this work done.

1. This equation comes from finding the area beneath a force-extension graph (shaded region).

2. This equation comes from substituting Hooke’s law into the equation above:

Task:

If you haven’t already, find the work done stretching the spring from your force-extension graph on page 13. Show your working out and remember the units.

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