CIE A Level: Stress, Strain, and Young's Modulus in Physics

Tensile Force

Force that increases an object's length.

Compressive Force

Force that decreases an object's length.

Deformation

Change in size or shape of a body.

Natural Length

Length of a spring without applied force.

Extension

Increase in length from natural length.

Compression

Decrease in length from natural length.

Elastic Behaviour

Material returns to original length after force.

Limit of Proportionality

Point where force-extension graph becomes non-linear.

Hooke's Law

Extension is proportional to applied force.

Force-Extension Graph

Graph showing relationship between force and extension.

Spring Constant (k)

Measure of a spring's stiffness in N/m.

F = kx

Equation relating force, spring constant, and extension.

Gradient of Graph

Slope indicating spring constant value.

SI Unit of Spring Constant

Newton per meter (N/m).

Linear Region

Part of graph where Hooke's law applies.

Non-Linear Region

Part of graph where Hooke's law fails.

Extension Calculation

Extended length minus natural length.

Compression Calculation

Natural length minus compressed length.

Material Properties

Unique characteristics affecting force-extension graph.

Tensile Stress (σ)

Tensile stress is the applied force per unit cross-sectional area of a material, given by σ = F / A.

Ultimate Tensile Stress

The maximum force per original cross-sectional area a wire can support at the point it breaks.

Strain (ε)

Strain is the extension per unit length, defined by ε = x / L, where x is extension in metres and L is the original length.

Young Modulus (E)

A measure of the ability of a material to withstand changes in length when a load is added, defined as E = σ / ε.

Stress-Strain Graph

A graph where the gradient of the linear section represents the Young modulus.

Young's Modulus Experiment

An experiment to measure the Young modulus of a metal wire by applying a load and measuring the extension.

Load Force (F)

The force applied to the wire, given as 92 N in the worked example.

Stress Equation

The equation for stress is σ = F / A.

Young Modulus Calculation

E = σ / ε

Cross-Sectional Area Formula

The cross-sectional area A is calculated using A = πd² / 4.

Young Modulus from Gradient

Young modulus can be calculated using E = gradient × L / A.

Load Conversion

Convert the load mass to weight (e.g., 300 g = 0.3 kg = 2.94 N).

Stress-Strain Relationship

For materials demonstrating elastic behavior, stress and strain are directly proportional.