The extension of a material is directly proportional to the applied force (load), up to the limit of proportionality .

Define the spring constant .

A measure of the stiffness of a material — the force needed per unit extension, with units N m -1 . The larger the spring constant, the stiffer the material.

On a force-extension graph, the .......... is the point beyond which the extension is no longer proportional to the applied force.

On a force-extension graph, the limit of proportionality is the point beyond which the extension is no longer proportional to the applied force.

Where is the elastic limit located relative to the limit of proportionality on a force-extension graph?

The elastic limit always comes after the limit of proportionality. It is the maximum amount a material can be stretched and still return to its original length once the force is removed.

How is the spring constant found from a force-extension graph?

It is the gradient of the straight (Hooke's law) region of the graph.

True or False? The spring constant is always equal to the gradient of a force-extension graph.

False. The spring constant equals the gradient only when force is on the y-axis and extension on the x-axis. If the axes are swapped, the spring constant is the reciprocal of the gradient (1 ÷ gradient).

The applied force per unit cross-sectional area of a material. Units: N m -2 (pascals, Pa).

The extension per unit length — the ratio of extension to original length. Strain is dimensionless and has no units.

What is the ultimate tensile stress of a wire?

The maximum force per original cross-sectional area a wire can support before it breaks.

Define the Young modulus .

The ratio of stress to strain for a material behaving elastically — a measure of how stiff a material is. Unit: Pa .

The .......... of the linear region of a stress-strain graph is equal to the Young modulus.

The gradient of the linear region of a stress-strain graph is equal to the Young modulus.

True or False? Strain has the unit metres.

False. Strain is the ratio of two lengths (extension ÷ original length), so it is dimensionless and has no unit.

Define the limit of proportionality .

The point beyond which Hooke's law no longer applies — the extension is no longer proportional to the applied force. On a graph it is where the line starts to curve.

Define the elastic limit .

The point before which a material will return to its original length or shape when the deforming force is removed. It always lies after the limit of proportionality.

What is the yield point on a force-extension graph?

The point at which the material continues to stretch even though no extra force is applied to it.

.......... is a change of shape where the material will not return to its original shape once the load is removed.

Plastic deformation is a change of shape where the material will not return to its original shape once the load is removed.

What is the difference between elastic and plastic deformation?

Elastic deformation — the material returns to its original shape when the load is removed. Plastic deformation — the material does not return to its original shape when the load is removed (occurs after the elastic limit).

What does a straight line through the origin on a force-extension graph show?

That the material obeys Hooke's law over that region — extension is proportional to force. The spring constant k is the gradient of that straight line.

True or False? A material's force-compression graph is always identical to its force-extension graph.

False. Materials behave differently under tensile and compressive strain, so a material's force-compression graph is not the same as its force-extension graph.

What material properties can be read from a stress-strain curve?

up to what stress and strain the material obeys Hooke's law whether it shows elastic and/or plastic behaviour its Young modulus (gradient of the linear region) its breaking stress

Define breaking stress .

The stress at the point where the material breaks (fractures) . Also called fracture stress — at this point the atoms separate completely.

How is the Young modulus found from a stress-strain graph?

From the gradient of the straight (linear) part of the graph.

At the .......... , the atoms in a material start to move relative to each other, and at the breaking stress they separate completely.

At the yield point , the atoms in a material start to move relative to each other, and at the breaking stress they separate completely.

True or False? Breaking stress and ultimate tensile stress are the same thing.

False. Breaking stress (fracture stress) is the stress at which the material breaks. Ultimate tensile stress is the maximum stress the material can support, marked separately on many graphs. They are not the same.

What is the yield point on a stress-strain graph?

The point beyond which the material continues to strain (stretch) without any additional stress being applied.

What are the independent and dependent variables in Core Practical 5: Investigating Young Modulus?

Independent: the load (force) Dependent: the extension of the wire

How is the diameter of the wire measured in this practical?

With a micrometer screw gauge or digital calipers , taking pairs of readings at right angles to each other to check the wire is circular.

A .......... is placed on the wire so that the extension can be measured accurately as the load is added.

A reference marker is placed on the wire so that the extension can be measured accurately as the load is added.

Describe how the Young modulus is obtained from the measurements in Core Practical 5.

plot a graph of force against extension and find its gradient calculate the cross-sectional area from the wire's diameter combine the gradient, original length and cross-sectional area to find the Young modulus

State two ways to reduce the uncertainty in this experiment.

use a long wire and measure long distances to reduce percentage error take repeat readings (six to ten) and find an average use a Vernier scale to measure the extension take diameter readings at right angles to check the wire is circular

True or False? Using a short, thick wire gives the most accurate value for the Young modulus.

False. A long, thin wire is better: it extends more for a given load, so the extension can be measured with a smaller percentage uncertainty .

Why is the load removed after each reading to check the wire returns to its original length?

To confirm the wire has not exceeded its elastic limit . A little 'creep' is acceptable, but a large amount means the elastic limit has been exceeded.

State one safety precaution for this practical.

Wear safety glasses in case the wire snaps, and cushion the floor and feet beneath the weights in case they fall.

Define elastic strain energy .

The energy stored in a material when work is done to stretch or compress it. Below the elastic limit (while Hooke's law is obeyed), all the work done is stored as elastic strain energy.

What does the area under a force-extension graph represent?

The work done in stretching the material, which equals the elastic strain energy stored. This is true whether or not the material obeys Hooke's law.

For the region where a material obeys Hooke's law, the work done is the area of a .......... under the force-extension graph.

For the region where a material obeys Hooke's law, the work done is the area of a right-angled triangle under the force-extension graph.

How do you find the work done from a non-linear force-extension graph?

Find the full area under the graph: split it into geometric shapes (triangles, rectangles, trapeziums), then count the leftover squares and convert them using the axis values before adding everything together.

True or False? The area under a force-extension graph gives the work done only if the material obeys Hooke's law.

False. The area under the graph gives the work done (elastic strain energy) whether or not the material obeys Hooke's law. For non-linear graphs you find the full area under the curve.

A LevelPhysicsEdexcelFlashcards4. MaterialsStretching Materials

Stretching Materials (Edexcel A Level Physics): Flashcards

Exam code: 9PH0

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FrontHooke's Law
Define Hooke's Law.

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Cards in this collection (41)

Define Hooke's Law.
The extension of a material is directly proportional to the applied force (load), up to the limit of proportionality.
What is the equation for Hooke's Law?
$F = k Δ x$
Where F = applied force (N), k = spring constant (N m^-1) and Δx = extension (m).
Define the spring constant.
A measure of the stiffness of a material — the force needed per unit extension, with units N m^-1. The larger the spring constant, the stiffer the material.
On a force-extension graph, the .......... is the point beyond which the extension is no longer proportional to the applied force.
On a force-extension graph, the limit of proportionality is the point beyond which the extension is no longer proportional to the applied force.
Where is the elastic limit located relative to the limit of proportionality on a force-extension graph?
The elastic limit always comes after the limit of proportionality. It is the maximum amount a material can be stretched and still return to its original length once the force is removed.
How is the spring constant found from a force-extension graph?
It is the gradient of the straight (Hooke's law) region of the graph.
True or False?
The spring constant is always equal to the gradient of a force-extension graph.
False.
The spring constant equals the gradient only when force is on the y-axis and extension on the x-axis. If the axes are swapped, the spring constant is the reciprocal of the gradient (1 ÷ gradient).
Define stress.
The applied force per unit cross-sectional area of a material. Units: N m^-2 (pascals, Pa).
Define strain.
The extension per unit length — the ratio of extension to original length. Strain is dimensionless and has no units.
What is the ultimate tensile stress of a wire?
The maximum force per original cross-sectional area a wire can support before it breaks.
Define the Young modulus.
The ratio of stress to strain for a material behaving elastically — a measure of how stiff a material is. Unit: Pa.
What is the equation for the Young modulus?
$E = \frac{stress}{strain}$
Since strain has no units, the Young modulus has the same unit as stress: Pa.
The .......... of the linear region of a stress-strain graph is equal to the Young modulus.
The gradient of the linear region of a stress-strain graph is equal to the Young modulus.
True or False?
Strain has the unit metres.
False.
Strain is the ratio of two lengths (extension ÷ original length), so it is dimensionless and has no unit.
Define the limit of proportionality.
The point beyond which Hooke's law no longer applies — the extension is no longer proportional to the applied force. On a graph it is where the line starts to curve.
Define the elastic limit.
The point before which a material will return to its original length or shape when the deforming force is removed. It always lies after the limit of proportionality.
What is the yield point on a force-extension graph?
The point at which the material continues to stretch even though no extra force is applied to it.
.......... is a change of shape where the material will not return to its original shape once the load is removed.
Plastic deformation is a change of shape where the material will not return to its original shape once the load is removed.
What is the difference between elastic and plastic deformation?
Elastic deformation — the material returns to its original shape when the load is removed.
Plastic deformation — the material does not return to its original shape when the load is removed (occurs after the elastic limit).
What does a straight line through the origin on a force-extension graph show?
That the material obeys Hooke's law over that region — extension is proportional to force. The spring constant k is the gradient of that straight line.
True or False?
A material's force-compression graph is always identical to its force-extension graph.
False.
Materials behave differently under tensile and compressive strain, so a material's force-compression graph is not the same as its force-extension graph.
What material properties can be read from a stress-strain curve?
- up to what stress and strain the material obeys Hooke's law
- whether it shows elastic and/or plastic behaviour
- its Young modulus (gradient of the linear region)
- its breaking stress
Define breaking stress.
The stress at the point where the material breaks (fractures). Also called fracture stress — at this point the atoms separate completely.
How is the Young modulus found from a stress-strain graph?
From the gradient of the straight (linear) part of the graph.
At the .........., the atoms in a material start to move relative to each other, and at the breaking stress they separate completely.
At the yield point, the atoms in a material start to move relative to each other, and at the breaking stress they separate completely.
True or False?
Breaking stress and ultimate tensile stress are the same thing.
False.
Breaking stress (fracture stress) is the stress at which the material breaks. Ultimate tensile stress is the maximum stress the material can support, marked separately on many graphs. They are not the same.
What is the yield point on a stress-strain graph?
The point beyond which the material continues to strain (stretch) without any additional stress being applied.
What are the independent and dependent variables in Core Practical 5: Investigating Young Modulus?
Independent: the load (force)
Dependent: the extension of the wire
How is the diameter of the wire measured in this practical?
With a micrometer screw gauge or digital calipers, taking pairs of readings at right angles to each other to check the wire is circular.
A .......... is placed on the wire so that the extension can be measured accurately as the load is added.
A reference marker is placed on the wire so that the extension can be measured accurately as the load is added.
Describe how the Young modulus is obtained from the measurements in Core Practical 5.
- plot a graph of force against extension and find its gradient
- calculate the cross-sectional area from the wire's diameter
- combine the gradient, original length and cross-sectional area to find the Young modulus
State two ways to reduce the uncertainty in this experiment.
- use a long wire and measure long distances to reduce percentage error
- take repeat readings (six to ten) and find an average
- use a Vernier scale to measure the extension
- take diameter readings at right angles to check the wire is circular
True or False?
Using a short, thick wire gives the most accurate value for the Young modulus.
False.
A long, thin wire is better: it extends more for a given load, so the extension can be measured with a smaller percentage uncertainty.
Why is the load removed after each reading to check the wire returns to its original length?
To confirm the wire has not exceeded its elastic limit. A little 'creep' is acceptable, but a large amount means the elastic limit has been exceeded.
State one safety precaution for this practical.
Wear safety glasses in case the wire snaps, and cushion the floor and feet beneath the weights in case they fall.
Define elastic strain energy.
The energy stored in a material when work is done to stretch or compress it. Below the elastic limit (while Hooke's law is obeyed), all the work done is stored as elastic strain energy.
What does the area under a force-extension graph represent?
The work done in stretching the material, which equals the elastic strain energy stored. This is true whether or not the material obeys Hooke's law.
For a material obeying Hooke's law, what are the two equations for elastic strain energy?
$Δ E_{e l} = \frac{1}{2} F Δ x$
or, using F = kΔx:
$Δ E_{e l} = \frac{1}{2} k (Δ x)^{2}$
For the region where a material obeys Hooke's law, the work done is the area of a .......... under the force-extension graph.
For the region where a material obeys Hooke's law, the work done is the area of a right-angled triangle under the force-extension graph.
How do you find the work done from a non-linear force-extension graph?
Find the full area under the graph: split it into geometric shapes (triangles, rectangles, trapeziums), then count the leftover squares and convert them using the axis values before adding everything together.
True or False?
The area under a force-extension graph gives the work done only if the material obeys Hooke's law.
False.
The area under the graph gives the work done (elastic strain energy) whether or not the material obeys Hooke's law. For non-linear graphs you find the full area under the curve.

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