AQA · A-Level · Physics

    Course version: 7408 · Version from Sept 2016

    M Density, ρ = V Hooke’s law, elastic limit, F = k∆L , k as stiffness and…

    Full specification wording

    Bulk properties of solids: m Density, ρ = V Hooke’s law, elastic limit, F = k∆L , k as stiffness and spring constant.

    Hooke's law states that the extension of a spring or wire is directly proportional to the applied force, provided the limit of proportionality is not exceeded.

    Checked against the AQA 7408 specification (opens in a new tab) on .

    • Point 1 of 8
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Hooke's law states that the extension of a spring or wire is directly proportional to the applied force, provided the limit of proportionality is not exceeded. The constant of proportionality is the stiffness or spring constant k, defined by F = k∆L, where ∆L is the extension. A stiffer spring has a larger k. Density is mass per unit volume, ρ = m/V, so a 2.0 kg block of volume 5.0 × 10⁻⁴ m³ has ρ = 4.0 × 10³ kg m⁻³. The limit of proportionality marks the end of the linear force-extension region. Slightly beyond this lies the elastic limit, the maximum force beyond which the material does not return to its original length when the force is removed, resulting in permanent deformation.

    What earns the marks

    • Density is defined as mass per unit volume and calculated using ρ = m/V, with consistent units such as kg m⁻³.
    • Hooke’s law applies when extension is directly proportional to force, which is true only up to the limit of proportionality.
    • The spring constant k is the force per unit extension, measured in N m⁻¹, and is a measure of stiffness.
    • A force–extension graph is linear through the origin up to the limit of proportionality; the gradient equals k.
    • The elastic limit is distinct from the limit of proportionality; exceeding it causes permanent deformation.

    Common mistakes and how to put them right

    • Using total length instead of extension in F = k∆L.

      Put it right by calculating ∆L = final length − original length before substituting.

    • Conflating the limit of proportionality with the elastic limit.

      Put it right by noting Hooke's law ends at the limit of proportionality, while permanent deformation begins beyond the elastic limit.

    • Confusing stiffness with strength.

      Put it right by stating that k measures resistance to extension, while strength relates to breaking stress.

    Exam tips

    • When calculating density, write the equation, substitute mass and volume with units, and give the answer in kg m⁻³ unless asked otherwise.
    • If a graph is provided, read the gradient to find k and state that the linear region ends at the limit of proportionality, not the elastic limit.

    Try the lesson

    The start of the Bulk properties of solids: m Density, ρ = V Hooke’s law, elastic limit, F = k∆L , k as stiffness and spring constant. lesson, made from checked teaching notes for this specification point.

    Have a go first

    A mass of 300 g is suspended from a vertical spring, which obeys Hooke's law. The spring constant is 150 N m⁻¹. What is the extension of the spring? (Use g = 9.81 m s⁻²)

    Listen

    Hooke's law states that the extension of a spring or wire is directly proportional to the applied force, provided the limit of proportionality is not exceeded. The constant of proportionality is the stiffness or spring constant k, defined by F = k∆L, where ∆L is the extension. A stiffer spring has a larger k. Density is mass per unit volume, ρ = m/V, so a 2.0 kg block of volume 5.0 × 10⁻⁴ m³ has ρ = 4.0 × 10³ kg m⁻³. The limit of proportionality marks the end of the linear force-extension region. Slightly beyond this lies the elastic limit, the maximum force beyond which the material does not return to its original length when the force is removed, resulting in permanent deformation. A strong answer earns marks for these points. Density is defined as mass per unit volume and calculated using ρ = m/V, with consistent units such as kg m⁻³. Hooke’s law applies when extension is directly proportional to force, which is true only up to the limit of proportionality. The spring constant k is the force per unit extension, measured in N m⁻¹, and is a measure of stiffness. A force–extension graph is linear through the origin up to the limit of proportionality; the gradient equals k. A common slip: Using total length instead of extension in F = k∆L. Instead, calculating ∆L = final length − original length before substituting. Exam tip: When calculating density, write the equation, substitute mass and volume with units, and give the answer in kg m⁻³ unless asked otherwise.

    See it

    A flowchart starting with a force applied to a spring or wire, leading to extension being directly proportional to force. From there it branches: one path goes to Hooke's law F = k∆L, then to k as stiffness or spring constant, then to a stiffer spring having a larger k. The other path goes to the limit of proportionality, which leads to the linear force–extension region ending, and also to the elastic limit lying slightly beyond, which leads to permanent deformation beyond the elastic limit.
    It shows how applied force leads to Hooke's law and the spring constant, and how the limit of proportionality and the elastic limit relate to permanent deformation.

    Key words

    Say what each word means before you turn the card.

    Density

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    Hooke's law

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    Spring constant

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    Elastic limit

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    See every definition
    Density
    Mass per unit volume, calculated using ρ = m/V, with consistent units such as kg m⁻³.
    Hooke's law
    The extension of a spring or wire is directly proportional to the applied force, provided the limit of proportionality is not exceeded.
    Spring constant
    The constant of proportionality k, defined by F = k∆L, where ∆L is the extension; a stiffer spring has a larger k.
    Elastic limit
    The maximum force beyond which the material does not return to its original length when the force is removed, resulting in permanent deformation.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A flowchart starting with a force applied to a spring or wire, leading to extension being directly proportional to force. From there it branches: one path goes to Hooke's law F = k∆L, then to k as stiffness or spring constant, then to a stiffer spring having a larger k. The other path goes to the limit of proportionality, which leads to the linear force–extension region ending, and also to the elastic limit lying slightly beyond, which leads to permanent deformation beyond the elastic limit.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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