AQA A Level Physics复习笔记4.8.1 The Young Modulus

• The Young modulus is the measure of the ability of a material to withstand changes in length with an added load
  • This gives information about the stiffness of a material
  • This is useful for engineers to make sure the materials they are using can withstand sufficient forces

   

• The Young Modulus is defined as the ratio of tensile stress and tensile strain

• Where:
  • F = force (N)
  • L = original length (m)
  • A = cross-sectional area (m2)
  • ΔL = extension (m)

   

• Since strain is dimensionless, the units of the Young Modulus is pascals (Pa)
• The Young Modulus of a material is typically a very large number, in the order of GPa

Table of the Young's Modulus for Materials

• The Young Modulus is equal to the gradient of a stress-strain graph when it is linear (a straight line)
  • This is the region in which Hooke's Law is obeyed

   

• The area under the graph in this region is equal to the energy stored per unit volume of the material

A stress-strain graph is a straight line with its gradient equal to the Young modulus

Step 1: Determine the stress and strain where the linear region ends

The Young Modulus is the gradient of the linear region of a stress-strain graph

Step 2: Calculate the gradient of the graph in this region