Elastic properties of solids
There is a law concerning the elastic properties of materials according to an English Physicist, Robert Hooke. This is today known as Hooke’s Law. A solid substance is said to be elastic if it regains its original shape and size after being deformed or stretched or compressed by a force. Therefore Hooke’s Law states in general that the deformation of an elastic body is directly proportional to the force producing it, provided that the limit of proportionality is not exceeded. Alternatively, Hooke’s Law may be stated, for a wire or spring, as follows: Provided that the elastic limit is not is not exceeded, the extension, e, of a wire is proportional to the load or applied force, F.
In symbols:F e
or F = Ke
Where K is the constant of the spring or wire, known as the stiffness or elastic constant.
If F is in Newtons (N) and e is in metres(m)
K = F/e (N/m or stress)
Young’s modulus of a wire
Suppose a force, F (N) is applied to a wire of cross-sectional area, A (m²), and original length, (m), and this results in an extension, e (m). The parameters of stress and strain on the wire are defined as:
Stress = Force = F…A (N/m²), and
Strain = Extension = e/ (No unit)
It has been proven that stress is always proportional to strain. This is so since F….e, and therefore F/A e/ , A and l… being constants. Hooke’s law may be stated thus in a different way;
In symbols: Stress = F/e
= Y (N/m)
Where Y is a constant known as the Young’s modulus of elasticity for the wire.
The graph of a strained elastic wire
In conclusion, a point is reached where a wire can no longer stand any further increase in load. At this point the wire breaks. Appropriately, this is known as the break point.
Molecular theory and the elasticity of solids
The molecules in a solid are held together by the strong force of cohesion. The molecules in a metal wire are arranged in a crystal lattice and held together by cohesion. When the metal wire is stretched, the molecules are pulled apart as the stretching force overcomes the cohesion. When the force is removed, the molecules return to their original position. If the force is so great that the elastic limit is exceeded, then the molecules are torn apart and they slide over each other. This results in a permanent deformation and the wire breaks.
Energy stored in an elastic wire
Suppose an elastic material, subjected to a force F, extends by a distance e, then, the work done by the force is given by Work = Average force x extension
=1 x e
This work is equal to the energy stored in the elastic material. Also, since F = Ke, by Hooke’s law,
Energy stored = (Ke) x e
= Ke²
Energy stored = Fe = Ke²
