The Young Modulus

1. The Young Modulus Objectives: Define and use the terms stress, strain and Young Modulus Describe an experiment to determine the Young Modulus of a metal wire.

2. The Young Moduls • How elastic or stiff a material is

3. Example • Steel cables over 1 m in diameter support a suspension bridge. • The load of the bridge causes a tensile force in the cable, setting up a tensile stress.  This has the effect of stretching the cable, setting up a tensile strain. • In addition to the cable being elastic and strong, it must be stiff. • The material property (constant) which tells us how stiff it is within its elastic limit is called the Young Modulus, E, where: • E = tensile stress tensile strain • Unit: N m-2 or Pascals (Pa)

4. Stress Stress = Tensile Force cross sect. area Or,  = F/A Units N m-2 or Pascals (Pa) Strain = extension of wire original length No units as it is a ratio

5. Measuring the Young Modulus • Method • Set up the equipment as shown. • Measure the diameter with a micrometer (at 5 places along the wire – then calulate average) • Measure the initial length of the test wire • Add kilogram masses 1 by one and measure the extension using a vernier calliper (or micrometer scale) • Make a table of Tensile Force and extension (make repeat measurements)

6. Analysis • Draw a graph of extension against Tensile Force • Work out the gradient (e/F) • Work out the inverse of the gradient (F/e) • Now use the equation: • Young Modulus = Stress/Strain to work out the Young Modulus • Check with a reference book