Unit 1: Materials

This guide covers sub-topic 1.4 Materials, completing Unit 1: Mechanics and Materials, from the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics (YPH11), Issue 3 specification (first teaching September 2018, first assessment January 2019). This topic is commonly studied using applications such as food testing, engineering materials and spare-part surgery for joint replacement.

Before studying this

This topic follows sub-topic 1.3, Mechanics, and assumes familiarity with force, and with rearranging and using equations involving ratios and graphs of experimental data.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 1.4

Candidates will be assessed on their ability to: use the equation density ρ = m/V; understand how to use the relationship upthrust = weight of fluid displaced; use the equation for viscous drag (Stokes’ law), F = 6πηrv, and understand that this equation applies only to small spherical objects moving at low speeds with laminar flow (or in the absence of turbulent flow), and that viscosity is temperature dependent; CORE PRACTICAL 2: use a falling-ball method to determine the viscosity of a liquid; use the Hooke’s law equation, ΔF = kΔx, where k is the stiffness of the object; understand how to use the relationships (tensile or compressive) stress = force/cross-sectional area, (tensile or compressive) strain = change in length/original length, and Young modulus = stress/strain; draw and interpret force-extension and force-compression graphs, and understand the terms limit of proportionality, elastic limit, yield point, elastic deformation and plastic deformation and be able to apply them to these graphs; draw and interpret tensile or compressive stress-strain graphs, and understand the term breaking stress; CORE PRACTICAL 3: determine the Young modulus of a material; and calculate the elastic strain energy Eel in a deformed material sample, using the equation Eel = ½FΔx, and from the area under the force-extension graph.

Density, upthrust and viscosity

Density is mass per unit volume: ρ = m/V. When an object is immersed in a fluid, it experiences an upthrust equal to the weight of fluid it displaces (Archimedes’ principle) — this is why objects appear to weigh less, and can float, in a fluid.

Viscous drag on a small sphere moving slowly through a fluid is given by Stokes’ law:

F = 6πηrv

where η is the fluid’s viscosity, r is the sphere’s radius and v is its speed. This equation applies only to small spherical objects moving at low speeds with laminar flow (i.e. in the absence of turbulence), and viscosity itself depends on temperature — typically decreasing as a liquid warms. CORE PRACTICAL 2 uses a falling-ball method (dropping small spheres through a viscous liquid and timing their fall at terminal velocity) to determine a liquid’s viscosity, applying Stokes’ law together with the object’s weight and the upthrust acting on it.

Hooke’s law and the Young modulus

Hooke’s law states that the extension of a material is proportional to the applied force, up to its limit of proportionality:

ΔF = kΔx

where k is the stiffness of the object (in N/m). To compare materials independently of their sample’s dimensions, physicists use stress and strain:

stress = force / cross-sectional area
strain = change in length / original length

The Young modulus is the ratio of stress to strain within the region where a material obeys Hooke’s law:

Young modulus = stress / strain

CORE PRACTICAL 3 determines the Young modulus of a material, typically a wire, by measuring extension against applied force and calculating stress and strain from the wire’s known cross-sectional area and original length.

Force-extension and stress-strain graphs

A force-extension graph for a material shows a straight line through the origin up to the limit of proportionality, beyond which the graph curves. The elastic limit is the point beyond which the material no longer returns to its original shape when the force is removed. Beyond the elastic limit, some materials show a yield point, where the material extends significantly with little or no increase in force. Deformation up to the elastic limit is elastic deformation (fully reversible); deformation beyond it is plastic deformation (permanent).

A stress-strain graph shows the same underlying behaviour normalised for the sample’s dimensions, allowing direct comparison between different samples of the same or different materials, and identifies the breaking stress — the maximum stress a material can withstand before it fractures.

Elastic strain energy

The elastic strain energy stored in a deformed material sample — equal to the work done in stretching it, provided the material obeys Hooke’s law — is:

Eel = ½FΔx

This is also equal to the area under a force-extension graph up to the point of interest, which remains valid even beyond the limit of proportionality (where the graph is no longer a straight line and the area must instead be found graphically).

Worked example. A wire of natural length 2.00 m and cross-sectional area 1.5 × 10⁻⁷ m² extends by 3.0 mm when a force of 45 N is applied, within its limit of proportionality. Find (a) the stress, (b) the strain, and (c) the Young modulus of the wire.

(a) stress = force / area = 45 / (1.5 × 10⁻⁷) = 3.0 × 10⁸ Pa

(b) strain = extension / original length = 0.0030 / 2.00 = 1.5 × 10⁻³ (no units — strain is a ratio)

(c) Young modulus = stress / strain = (3.0 × 10⁸) / (1.5 × 10⁻³) = 2.0 × 10¹¹ Pa

Common mistakes

Confusing stress (force per unit area, in Pa) with force itself, or strain (a dimensionless ratio) with extension itself (in metres). Applying Stokes’ law to objects that are not small, spherical, or moving slowly enough for laminar flow — the equation does not apply once flow becomes turbulent. Assuming a material returns to its original shape after any deformation — this is only true up to the elastic limit; beyond it, deformation is plastic and permanent. Forgetting that elastic strain energy is the area under a force-extension graph, not a force-time or stress-strain graph, and that ½FΔx only applies within the region of Hooke’s-law behaviour.

Quick revision checklist

• Use ρ = m/V and the upthrust = weight of fluid displaced relationship.
• State and apply Stokes’ law, F = 6πηrv, and its conditions of validity.
• Describe CORE PRACTICAL 2 (falling-ball method for viscosity).
• Use Hooke’s law, ΔF = kΔx, and define stiffness.
• Calculate stress, strain and the Young modulus from force-extension data.
• Interpret force-extension and stress-strain graphs, identifying the limit of proportionality, elastic limit, yield point, elastic and plastic deformation, and breaking stress.
• Describe CORE PRACTICAL 3 (determining the Young modulus of a material).
• Calculate elastic strain energy using Eel = ½FΔx and from the area under a force-extension graph.

Related resources

• Unit 1: Mechanics — the previous sub-topic
• Unit 2: Waves and Particle Nature of Light — the next unit
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.