AQA · A-Level · Physics

    Course version: 7408 · Version from Sept 2016

    Bulk properties of solids: Tensile strain and tensile stress.

    Tensile stress is the force applied per unit cross-sectional area, σ = F/A, measured in pascals (Pa), where 1 Pa = 1 N m⁻².

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

    • Point 2 of 8
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Tensile stress is the force applied per unit cross-sectional area, σ = F/A, measured in pascals (Pa), where 1 Pa = 1 N m⁻². Tensile strain is the extension per unit original length, ε = ∆L/L, and has no unit because it is a ratio of two lengths. For example, a wire of original length 2.00 m that extends by 4.0 mm has strain ε = 0.0040 m / 2.00 m = 2.0 × 10⁻³. If the same wire has cross-sectional area 1.0 × 10⁻⁶ m² and carries a force of 20 N, the stress is σ = 20 N / 1.0 × 10⁻⁶ m² = 2.0 × 10⁷ Pa. Stress and strain allow comparison of materials independent of sample size, and their ratio gives the Young modulus.

    What earns the marks

    • Tensile stress is defined as force per unit cross-sectional area, σ = F/A, with the force perpendicular to the area.
    • The unit of stress is the pascal, Pa, equivalent to N m⁻².
    • Tensile strain is defined as extension divided by original length, ε = ∆L/L, and is dimensionless.
    • Extension ∆L must be the change in length, not the total length, and original length L must be used in the denominator.
    • Stress and strain are proportional in the linear region of a force–extension graph, which is the region where Hooke’s law applies.
    • The ratio of tensile stress to tensile strain gives the Young modulus, E = σ/ε, for a material obeying Hooke’s law.

    Common mistakes and how to put them right

    • Using total length instead of extension when calculating strain.

      Put it right by using ∆L = final length − original length.

    • Forgetting to convert area from mm² or cm² to m².

      Put it right by converting to m² before dividing force by area.

    • Mixing up stress and strain.

      Put it right by remembering stress is force per area and strain is extension per original length.

    • Omitting units for stress or giving strain a unit.

      Put it right by stating stress in Pa and strain as a dimensionless ratio.

    Exam tips

    • Write the defining equation for stress or strain before substituting values, and show the conversion of any non-SI units.
    • For strain, ensure the extension and original length are in the same unit so the ratio is dimensionless.
    • When comparing materials, calculate stress and strain separately and then use E = σ/ε if the Young modulus is required.
    • Check that the force used in stress calculations is the tensile force along the material, not a perpendicular or compressive force.

    Try the lesson

    The start of the Bulk properties of solids: Tensile strain and tensile stress. lesson, made from checked teaching notes for this specification point.

    Have a go first

    A wire of original length 2.5 m is stretched by an extension of 1.5 mm. What is the tensile strain of the wire?

    Listen

    Tensile stress is the force applied per unit cross-sectional area, σ = F/A, measured in pascals (Pa), where 1 Pa = 1 N m⁻². Tensile strain is the extension per unit original length, ε = ∆L/L, and has no unit because it is a ratio of two lengths. For example, a wire of original length 2.00 m that extends by 4.0 mm has strain ε = 0.0040 m / 2.00 m = 2.0 × 10⁻³. If the same wire has cross-sectional area 1.0 × 10⁻⁶ m² and carries a force of 20 N, the stress is σ = 20 N / 1.0 × 10⁻⁶ m² = 2.0 × 10⁷ Pa. Stress and strain allow comparison of materials independent of sample size, and their ratio gives the Young modulus. A strong answer earns marks for these points. Tensile stress is defined as force per unit cross-sectional area, σ = F/A, with the force perpendicular to the area. The unit of stress is the pascal, Pa, equivalent to N m⁻². Tensile strain is defined as extension divided by original length, ε = ∆L/L, and is dimensionless. Extension ∆L must be the change in length, not the total length, and original length L must be used in the denominator. A common slip: Using total length instead of extension when calculating strain. Instead, using ∆L = final length − original length. Exam tip: Write the defining equation for stress or strain before substituting values, and show the conversion of any non-SI units.

    See it

    A flowchart running from top to bottom. One branch starts with a node for tensile force F and cross-sectional area A, leading to tensile stress σ = F/A, then to its unit, the pascal, Pa = N m⁻². A second branch starts with extension ∆L and original length L, leading to tensile strain ε = ∆L/L, then to the note that it is a dimensionless ratio. Both the stress node and the strain node feed into a node stating that the ratio of stress to strain gives the Young modulus E = σ/ε, which then leads to a final node saying this allows comparison of materials independent of sample size.
    It shows how tensile stress and tensile strain are each defined and calculated, and how their ratio gives the Young modulus for comparing materials.

    Key words

    Say what each word means before you turn the card.

    Tensile stress

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    Tensile strain

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    Pascal

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    Young modulus

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    See every definition
    Tensile stress
    The force applied per unit cross-sectional area, σ = F/A, measured in pascals (Pa), where 1 Pa = 1 N m⁻².
    Tensile strain
    The extension per unit original length, ε = ∆L/L, which has no unit because it is a ratio of two lengths.
    Pascal
    The unit of stress, Pa, equivalent to N m⁻².
    Young modulus
    The ratio of tensile stress to tensile strain, E = σ/ε, for a material obeying Hooke’s law.

    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 running from top to bottom. One branch starts with a node for tensile force F and cross-sectional area A, leading to tensile stress σ = F/A, then to its unit, the pascal, Pa = N m⁻². A second branch starts with extension ∆L and original length L, leading to tensile strain ε = ∆L/L, then to the note that it is a dimensionless ratio. Both the stress node and the strain node feed into a node stating that the ratio of stress to strain gives the Young modulus E = σ/ε, which then leads to a final node saying this allows comparison of materials independent of sample size.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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