Hooke's law states that the extension of a material is directly proportional to the applied force (load), up to the limit of proportionality .

Define the spring constant k .

The spring constant is a property of a material that measures its stiffness ; the larger the spring constant, the stiffer the material.

On a force-extension graph, what is the significance of the limit of proportionality ?

It is the point beyond which Hooke's law no longer applies, i.e. the extension is no longer proportional to the applied force. It is identified where the line starts to curve .

What is the elastic limit of a material, and how does its position compare to the limit of proportionality?

The elastic limit is the maximum extension a material can undergo and still return to its original length . It always occurs after the limit of proportionality.

On a force-extension graph, the .......... of the straight-line (Hooke's law) region is equal to the spring constant k .

On a force-extension graph, the gradient of the straight-line (Hooke's law) region is equal to the spring constant k .

True or False? On a graph of extension (y-axis) against force (x-axis), the spring constant is equal to the gradient.

False. When extension is plotted on the y-axis and force on the x-axis, the gradient gives Δ x /Δ F , so the spring constant is 1 ÷ gradient , not the gradient itself.

Stress is the applied force per unit cross-sectional area of a material.

Strain is the extension per unit original length . It is a dimensionless quantity, as it is the ratio of two lengths.

Define the Young modulus .

The Young modulus is the ratio of stress to strain for a material undergoing elastic deformation; it measures how stiff a material is.

What are the units of stress, and why does strain have no units?

Stress is measured in N m -2 (Pa), the same unit as pressure. Strain has no units because it is a ratio of two lengths (extension ÷ original length).

On a stress-strain graph, how is the Young modulus found?

The Young modulus is the gradient of the straight-line (linear) part of a stress-strain graph.

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

The ultimate tensile stress is the maximum force per original cross-sectional area a wire can support before it breaks.

True or False? Strain is measured in pascals, the same unit as stress.

False. Stress is measured in pascals (N m -2 ), but strain is the ratio of extension to original length, so it is dimensionless and has no units.

Define the yield point on a force-extension graph.

The yield point is where the material continues to stretch even though no extra force is being applied to it.

What is the difference between elastic deformation 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, and occurs after the yield point

On a force-extension graph, how is compression represented, and how does this compare to how it is used in equations?

Compression is plotted on the graph as a positive, increasing value, even though it can be entered into equations as a negative value.

Why do force-extension and force-compression graphs for the same material differ from one another?

Because materials behave differently under tensile and compressive strain, so their force-extension and force-compression graphs are not the same .

The limit of proportionality is the point .......... which Hooke's law is no longer true.

The limit of proportionality is the point beyond which Hooke's law is no longer true.

True or False? The elastic limit occurs before the limit of proportionality on a force-extension graph.

False. The elastic limit always occurs after the limit of proportionality.

Define breaking stress .

Breaking stress (or fracture stress) is the stress at the point where a material breaks .

What information can be determined from a stress-strain curve?

Up to what stress and strain a material obeys Hooke's law Whether it exhibits elastic and/or plastic behaviour Its Young modulus Its breaking stress

What physically happens to the atoms in a material at the yield point compared to at the breaking stress?

At the yield point , the atoms have started to move relative to each other . At the breaking stress , the atoms separate completely .

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

The Young modulus is found from the gradient of the straight part of the stress-strain graph.

Breaking stress is not the same as .......... tensile stress, which is also marked on many stress-strain graphs.

Breaking stress is not the same as ultimate tensile stress, which is also marked on many stress-strain graphs.

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

False. Breaking stress is the stress at which the material actually fractures, which is not the same as the ultimate tensile stress marked on many graphs.

In Core Practical 3 (investigating the Young modulus of a wire), what are the independent and dependent variables?

Independent variable: the load Dependent variable: the extension

Why is a reference marker placed on the wire during this experiment?

To allow the extension of the wire to be measured accurately as the load is applied.

Give two precautions used in this experiment to reduce uncertainty in the final result.

Take diameter readings at right angles to each other, to check the wire is circular Take six to ten readings and find an average Remove the load and check the wire returns to its original length after each reading (a little creep is acceptable) Use a Vernier scale to measure extension

How is the Young modulus calculated once the gradient of the force-extension graph has been found?

Calculate the wire's cross-sectional area from its diameter, then find the Young modulus using the gradient of the force-extension graph and the original length and cross-sectional area of the wire.

Safety glasses should be worn during this experiment in case the .......... snaps.

Safety glasses should be worn during this experiment in case the wire snaps.

True or False? A large amount of 'creep' after removing the load is acceptable, as it does not affect the results.

False. Only a little creep is acceptable; a large amount indicates the wire's elastic limit has been exceeded, which affects the validity of the results.

Define elastic strain energy .

Elastic strain energy is the work done in stretching a material, stored while the material obeys Hooke's law (before its elastic limit).

How is elastic strain energy found from a force-extension graph, and is this true for materials that don't obey Hooke's law?

Elastic strain energy is the area under the force-extension graph . This is true whether or not the material obeys Hooke's law .

For a non-linear (non-Hookean) region of a force-extension graph, how is the area under the graph calculated?

Split the graph into geometric shapes and sum their areas, then count the remaining squares , converting each square's value using the axis scales before adding it to the total.

For the linear region of a force-extension graph, the work done is the area of a .......... triangle under the graph.

For the linear region of a force-extension graph, the work done is the area of a right-angled triangle under the graph.

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

False. The area under a force-extension graph gives the work done (elastic strain energy) whether or not the material obeys Hooke's law ; only the shape of the area used to calculate it differs.

International A Level (IAL)PhysicsEdexcelFlashcards1. Mechanics & MaterialsStretching Materials

Stretching Materials (Edexcel International A Level (IAL) Physics): Flashcards

Exam code: YPH11

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FrontHooke's Law
Define Hooke's law.
FrontHooke's Law
State the Hooke's law equation and define each term.
BackHooke's Law
$Δ F = k Δ x$
F = applied force (N)
k = spring constant (N m^-1)
Δx = extension (m)

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Cards in this collection (38)

Define Hooke's law.
Hooke's law states that the extension of a material is directly proportional to the applied force (load), up to the limit of proportionality.
Define the spring constant k.
The spring constant is a property of a material that measures its stiffness; the larger the spring constant, the stiffer the material.
State the Hooke's law equation and define each term.
$Δ F = k Δ x$
- F = applied force (N)
- k = spring constant (N m^-1)
- Δx = extension (m)
On a force-extension graph, what is the significance of the limit of proportionality?
It is the point beyond which Hooke's law no longer applies, i.e. the extension is no longer proportional to the applied force. It is identified where the line starts to curve.
What is the elastic limit of a material, and how does its position compare to the limit of proportionality?
The elastic limit is the maximum extension a material can undergo and still return to its original length. It always occurs after the limit of proportionality.
On a force-extension graph, the .......... of the straight-line (Hooke's law) region is equal to the spring constant k.
On a force-extension graph, the gradient of the straight-line (Hooke's law) region is equal to the spring constant k.
True or False?
On a graph of extension (y-axis) against force (x-axis), the spring constant is equal to the gradient.
False.
When extension is plotted on the y-axis and force on the x-axis, the gradient gives Δx/ΔF, so the spring constant is 1 ÷ gradient, not the gradient itself.
Define stress.
Stress is the applied force per unit cross-sectional area of a material.
Define strain.
Strain is the extension per unit original length. It is a dimensionless quantity, as it is the ratio of two lengths.
Define the Young modulus.
The Young modulus is the ratio of stress to strain for a material undergoing elastic deformation; it measures how stiff a material is.
What are the units of stress, and why does strain have no units?
Stress is measured in N m^-2 (Pa), the same unit as pressure. Strain has no units because it is a ratio of two lengths (extension ÷ original length).
On a stress-strain graph, how is the Young modulus found?
The Young modulus is the gradient of the straight-line (linear) part of a stress-strain graph.
The .......... tensile stress is the maximum force per original cross-sectional area a wire can support before it breaks.
The ultimate tensile stress is the maximum force per original cross-sectional area a wire can support before it breaks.
True or False?
Strain is measured in pascals, the same unit as stress.
False.
Stress is measured in pascals (N m^-2), but strain is the ratio of extension to original length, so it is dimensionless and has no units.
Define the yield point on a force-extension graph.
The yield point is where the material continues to stretch even though no extra force is being applied to it.
What is the difference between elastic deformation 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, and occurs after the yield point
On a force-extension graph, how is compression represented, and how does this compare to how it is used in equations?
Compression is plotted on the graph as a positive, increasing value, even though it can be entered into equations as a negative value.
Why do force-extension and force-compression graphs for the same material differ from one another?
Because materials behave differently under tensile and compressive strain, so their force-extension and force-compression graphs are not the same.
The limit of proportionality is the point .......... which Hooke's law is no longer true.
The limit of proportionality is the point beyond which Hooke's law is no longer true.
True or False?
The elastic limit occurs before the limit of proportionality on a force-extension graph.
False.
The elastic limit always occurs after the limit of proportionality.
Define breaking stress.
Breaking stress (or fracture stress) is the stress at the point where a material breaks.
What information can be determined from a stress-strain curve?
- Up to what stress and strain a material obeys Hooke's law
- Whether it exhibits elastic and/or plastic behaviour
- Its Young modulus
- Its breaking stress
What physically happens to the atoms in a material at the yield point compared to at the breaking stress?
At the yield point, the atoms have started to move relative to each other. At the breaking stress, the atoms separate completely.
How is the Young modulus determined from a stress-strain graph?
The Young modulus is found from the gradient of the straight part of the stress-strain graph.
Breaking stress is not the same as .......... tensile stress, which is also marked on many stress-strain graphs.
Breaking stress is not the same as ultimate tensile stress, which is also marked on many stress-strain graphs.
True or False?
Breaking stress and ultimate tensile stress are always the same value.
False.
Breaking stress is the stress at which the material actually fractures, which is not the same as the ultimate tensile stress marked on many graphs.
In Core Practical 3 (investigating the Young modulus of a wire), what are the independent and dependent variables?
- Independent variable: the load
- Dependent variable: the extension
Why is a reference marker placed on the wire during this experiment?
To allow the extension of the wire to be measured accurately as the load is applied.
Give two precautions used in this experiment to reduce uncertainty in the final result.
- Take diameter readings at right angles to each other, to check the wire is circular
- Take six to ten readings and find an average
- Remove the load and check the wire returns to its original length after each reading (a little creep is acceptable)
- Use a Vernier scale to measure extension
How is the Young modulus calculated once the gradient of the force-extension graph has been found?
Calculate the wire's cross-sectional area from its diameter, then find the Young modulus using the gradient of the force-extension graph and the original length and cross-sectional area of the wire.
Safety glasses should be worn during this experiment in case the .......... snaps.
Safety glasses should be worn during this experiment in case the wire snaps.
True or False?
A large amount of 'creep' after removing the load is acceptable, as it does not affect the results.
False.
Only a little creep is acceptable; a large amount indicates the wire's elastic limit has been exceeded, which affects the validity of the results.
Define elastic strain energy.
Elastic strain energy is the work done in stretching a material, stored while the material obeys Hooke's law (before its elastic limit).
How is elastic strain energy found from a force-extension graph, and is this true for materials that don't obey Hooke's law?
Elastic strain energy is the area under the force-extension graph. This is true whether or not the material obeys Hooke's law.
Give the two equations used to calculate elastic strain energy for a material obeying Hooke's law.
$Δ E_{e l} = \frac{1}{2} F Δ x$
$Δ E_{e l} = \frac{1}{2} k (Δ x)^{2}$
For a non-linear (non-Hookean) region of a force-extension graph, how is the area under the graph calculated?
Split the graph into geometric shapes and sum their areas, then count the remaining squares, converting each square's value using the axis scales before adding it to the total.
For the linear region of a force-extension graph, the work done is the area of a .......... triangle under the graph.
For the linear region of a force-extension graph, the work done is the area of a right-angled triangle under the graph.
True or False?
The area under a force-extension graph only gives the work done if the material obeys Hooke's law.
False.
The area under a force-extension graph gives the work done (elastic strain energy) whether or not the material obeys Hooke's law; only the shape of the area used to calculate it differs.

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