produced in a body is directly proportional to the stress that produces it. It can be verified in a simple way by stretching a thin straight wire (stretches like spring) of length L and uniform cross- sectional area A suspended from a fixed point O. A pan and a pointer are attached at the free end of the wire as shown in Figure . (a).
The extension produced on the wire is measured using a vernier scale arrangement. The experiment shows that for a given load, the corresponding stretching force is F and the elongation produced on the wire is ΔL. It is directly proportional to the original length L and inversely proportional to the area of cross section A. A graph is plotted using F on the X- axis and ΔL on the Y- axis.
This graph is a straight line passing through the origin as shown in Figure . (b). Figure . (a) Experimental verification of Hooke’s law weight Pan Pointer Wire Scale Support - - - - Unit Properties of matter In this section, we shall define the elastic modulus of a given material.
There are three types of elastic modulus. (a) Young’s modulus (b) Rigidity modulus (or Shear modulus) (c) Bulk modulus Young’s modulus: When a wire is stretched or compressed, then the ratio between tensile stress (or compressive stress) and tensile strain (or compressive strain) is defined as Young’s modulus. Young modulus of a material = Tensilestressorcompressivestress Tensilestrainorcompressivestrain Y= σ ε t t or Y= σ ε c c ( . ) EXAMPLE .
Within the elastic limit, the stretching strain produced in wires A, B, and C due to stress is shown in the figure. Assume the load applied are the same and discuss the elastic property of the material. Stress Strain O B C Write down the elastic modulus in ascending order. Solution Here, the elastic modulus is Young modulus and due to stretching, stress is tensile stress and strain is tensile strain.
(a) Portion OA: In this region, stress is very small such