DEFINITIONS

• Stress is the force per unit cross sectional area on a wire, and hence has units of N m^-2 or Pascals.
• Strain is the extension divided by the original length, and hence has no units.
• Young's modulus is is given by tensile stress divided by tensile strain. E = ^{tensile stress} / _{tensile strain} Youngs modulus E is a constant for the same range over which Hooke`s law can be applied. Infact the costant of proportionality in Hooke`s law (known as the spring constant) is equal to ^{E A}/ _r, where r is length without a force applied and A is the crosssectional area.
• Tensile means along its the direction it is in tension.

MEASURING YOUNGS MODULUS

By using two wires suspended from the same beam, errors due to changes in environment and deformation of the beam can be avoided. The attachement on the bottom which could well have a vernier scale allows extention in the second wire which has weight added to it, to be measured to quite a high degree of accuracy. The force causing this can of course be determined from the mass of the weights multiplied by gravity. This is known as Searles apparatus.

STRAIN ENERGY
During the deformation of a material obeying Hooke's law, the deforming force will move through a distance and hence work will be done, this energy is stored as strain energy. To find the energy we integrate the force with respect to distance and hence it is equal to ¹/₂ k x², where k is the spring constant and x is the extension. It should be noticed that as F = k x, this could also be written as W = ¹/₂ F x, which can be separated into ^F / _A, stress and ^x / _L. Hence, Strain Energy equals ¹/₂ stress multiplied by strain.

GRAPHS
For a ductile material such as copper wire, there are 3 main points on graph of stress against strain. These are

• E - the elastic limit, above this point Hooke`s law can now longer be applied.
• P - the plastic limit, above this point the material no longer returns to its original shape once the force is remove. e.g. the point a will contract online the dotted line parallel to the original slope.
• D - the breaking stress, where the wire finally snaps.