The mass of a material per unit volume, ρ = m/V, measured in kg m⁻³.

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

What is the spring constant?

The force per unit extension, k = F/ΔL, in N m⁻¹. It measures stiffness.

What is the elastic limit?

The point beyond which a material no longer returns to its original length when the force is removed.

Define tensile stress.

The tensile force per unit cross-sectional area, σ = F/A, in pascals (N m⁻²).

Define tensile strain.

The extension per unit original length, ε = ΔL/L. It has no unit.

What is the breaking stress?

The stress at which the material breaks.

What is plastic deformation?

Permanent deformation: the material does not return to its original shape when the force is removed.

What is a brittle material?

One that breaks suddenly at a small strain with no plastic deformation.

What is a ductile material?

One that deforms plastically and extends a lot before it breaks, such as copper.

Density, Hooke's law and stress-strainAQA A-Level Physics: Flashcards

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Define density.

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Define density.: The mass of a material per unit volume, ρ = m/V, measured in kg m⁻³.
How many m³ are there in 1 cm³?: 10⁻⁶ m³.
State Hooke's law.: The extension of a material is proportional to the applied force, up to the limit of proportionality.
What is the spring constant?: The force per unit extension, k = F/ΔL, in N m⁻¹. It measures stiffness.
What does the gradient of a force-extension graph give for a spring that obeys Hooke's law?: The spring constant k.
What is the elastic limit?: The point beyond which a material no longer returns to its original length when the force is removed.
Define tensile stress.: The tensile force per unit cross-sectional area, σ = F/A, in pascals (N m⁻²).
Define tensile strain.: The extension per unit original length, ε = ΔL/L. It has no unit.
What is the breaking stress?: The stress at which the material breaks.
What is plastic deformation?: Permanent deformation: the material does not return to its original shape when the force is removed.
What is a brittle material?: One that breaks suddenly at a small strain with no plastic deformation.
What is a ductile material?: One that deforms plastically and extends a lot before it breaks, such as copper.
What is the cross-sectional area of a wire of diameter d?: A = πd²/4 = π(d/2)².

Exam questions on Density, Hooke's law and stress-strain

A solid rectangular block of metal measures 4.0 cm by 5.0 cm by 2.0 cm and has a mass of 108 g.
A second block is made from the same metal and has the same outside dimensions, but it contains a hollow cavity. Its mass is 80 g. Calculate the volume of the cavity.2 marks
A student hangs masses from a helical steel spring. A load of 4.0 N produces an extension of 0.080 m. The spring obeys Hooke's law up to its elastic limit, which is reached at a load of 6.0 N.
A load of 9.81 N is hung from the spring, which is greater than the elastic limit. Describe two ways in which the behaviour of the spring differs from its behaviour at loads below the limit.2 marks
A steel wire of length 2.50 m and diameter 0.50 mm hangs from a fixed support. A load of 80 N is hung from its lower end, and the wire extends by 3.0 mm. The wire is within the region where it obeys Hooke's law.
Define tensile stress and tensile strain, and state the unit of tensile stress.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).