PhysicsLab
My Learning
Lesson 10.1 • Competency 10.1Complete Lesson
Back to Unit

Elasticity of Solids & Young’s Modulus

Master tensile stress σ = F/A, tensile strain ε = ΔL/L, Hooke’s law, stress-strain curves for ductile, brittle, and polymeric materials, Young’s modulus Y = (FL)/(AΔL), and strain energy density u = 0.5 Y ε².

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Define tensile stress, tensile strain, proportional limit, elastic limit, yield point, and breaking stress.
  • State Hooke’s Law, calculate Young’s modulus Y, and determine wire elongation ΔL under tensile loading.
  • Derive elastic strain energy U = 0.5 F ΔL and energy density u = 0.5 Y ε² from the stress-strain graph area.

Core Theory & Concepts

When external mechanical forces act on a solid, interatomic bonds deform like microscopic springs. Up to the elastic limit, the material returns fully to its initial length when the load is removed. Hooke’s law states that within the proportional limit, tensile stress is strictly proportional to tensile strain.

Young’s Modulus Formula

Ratio of tensile stress to tensile strain within the proportional limit: Y = (F / A) / (ΔL / L).

Y = \frac{F \cdot L}{A \cdot \Delta L} = \frac{4 F L}{\pi d^2 \Delta L}

Strain Energy Density

The elastic potential energy stored per unit volume equals the area under the linear stress-strain curve.

u = \frac{1}{2} \sigma \epsilon = \frac{1}{2} Y \epsilon^2

Common Misconceptions

Misconception

Breaking stress increases if a wire is made thicker.

Physical Clarification:Breaking force increases with area, but breaking stress (force per unit area) is an intrinsic material property that remains constant.

Syllabus Topic Outline

Competency 10.1
  • 1Interatomic forces and solid elasticity basis
  • 2Stress (σ = F/A) and Strain (ε = ΔL/L) definitions and units
  • 3Stress-strain diagrams: ductile metals, brittle glass, and elastomeric rubber
  • 4Hooke’s Law and Young’s Modulus: Y = (F L) / (A ΔL)
  • 5Elastic potential energy (strain energy) U = 0.5 F ΔL and energy density
  • 6Searle’s apparatus methodology and twin-wire thermal compensation

Practice Problems

1
Competency 10.1 • intermediate

A wire of length 2.0 m and cross-sectional area 1.0e-6 m^2 stretches by 1.0 mm under a load of 100 N. Calculate Young’s modulus Y in Pa.

Pa