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What are the Factors Affecting Elasticity?
From our common experience, we know that when a rubber cord is pulled it increases in length. But in order to increase the length of a steel wire of same diameter by the same amount, a greater force needs to be applied.
When equal and opposite external forces act on a body, the different point masses of the body undergo relative displacements [Fig.]. As a result, the body undergoes a change in its shape or size, or both. In this condition, a reaction force develops inside the body which opposes the change. If this change lies within a definite limit then the body regains its original state once the forces are withdrawn. The property which opposes deformation is present in all materials. This general property of matter is known as elasticity (or the elastic property of matter).
Definition: The property by virtue of which a body resists the deformation in shape or volume or both due to external forces acting on it, and regains its original shape or volume when these external forces are withdrawn is called elasticity.
This property is present in every material, irrespective of whether it is solid liquid or gas.
Elasticity of rubber and steel: From the viewpoint of physics. a body is said to be more elastic if it has a greater ability to resist deformation against the external force. The greater the external force necessary to produce a definite change in the size or shape of a body, the more elastic is the material of the body. As mentioned earlier, in order to produce an equal deformation in a steel wire and a rubber wire of the same dimensions, a greater force is necessary in the case of the steel wire. For this reason, steel is more elastic than rubber.
Factors affecting elasticity:
i) The presence of impurities in a metal changes its elastic property.
ii) If a metal is deformed frequently, then its elasticity decreases. For example, if a thick copper wire is often twisted, it becomes hard and brittle.
iii) The elasticity of a metal changes with temperature. Usually, its elasticity decreases when temperature increases, and vice versa. An exception to this rule occurs in the case of invar—whose elasticity does not change with any change in temperature. Again if a metal is first heated and then cooled, i.e., it is softened, its elasticity gradually decreases.
Some Useful Definitions
Perfectly rigid body: If under the action of any external force, there is no relative displacement among the different parts of a body, i.e., the body does not undergo any deformation, then it is called a perfectly rigid body. In actual practice no substance is perfectly rigid, though diamond and glass are very close approximations of perfectly rigid bodies.
Perfectly elastic body: If after the withdrawal of external forces, a body completely regains its original shape and volume, then it is called a perfectly elastic body. In real life, however, a body cannot be perfectly elastic for all magnitudes of external forces. Up to a certain limiting value of external force, a body behaves as a perfectly elastic body. This limit is known as the elastic limit for the material of the body. Different materials have different elastic limits. For example, the elastic limit of steel is very high while that of rubber is very low.
Perfectly plastic or inelastic body: If a body, elongated (or compressed) by external forces remains in that deformed state even after the withdrawal of these deforming forces, it is called a perfectly plastic or inelastic body. Actually, no material is perfectly inelastic, though clay comes very close to it.
Partly elastic body: If after the withdrawal of external forces, a deformed body only partially regains its original shape and volume then it is called a partly elastic body. Practically all materials are partly elastic.
Strain: Under the influence of external forces, when a body gets deformed, the different parts of the body suffer relative displacements. As a result, the body undergoes a change in length. volume or shape.
Strain of a body is defined as the change of Its length, volume or shape relative to its original length, volume or shape before deformation. So, it is a ratio of two identical quantities and hence it has no unit, i.e., strain is a dimensionless quantity.
Stress: When a body gets deformed under the influence of external forces, a reaction force develops in the body because of elasticity. This force tries to resist the external forces and helps to bring the body back to its unstrained condition after the deforming forces are withdrawn. The reaction force acting per unit area of cross section of the body is called stress.
Since action and reaction are opposite but equal, stress is equal in magnitude to the force applied per unit area of the deformed body.
Stress \(=\frac{\text { applied force }}{\text { area of cross section of the body }}\)
Units and dimension of stress:
Dimension of stress \(=\frac{\text { dimension of force }}{\text { dimension of area }}\) = \(\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}^2}\)
= ML-1T-2
We shall see that the units and dimension of stress is the same as that of pressure.
Normal stress and shearing or tangential stress:
An applied force can act normally or obliquely on the surface of a body [Fig.].
The component of the reaction force perpendicular to a unit area of the surface, is called normal stress. When there is any change in the length of a wire or in the volume of a body, normal stress is developed. The stress associated with an increase in length is called tensile stress and that associated with a decrease is called compressive stress. On the other hands the component of the reaction force parallel to a unit area of the surface is called shearing stress or tangential stress. Usually, shearing stress is developed during any change in the shape of a body.
Breaking load and breaking stress: If the external force exceeds the elastic limit, then a strained body cannot return to its original size or shape even after the deforming force is withdrawn. In such a case, the body gets permanently deformed. If the amount of the external force is increased gradually, then, for a particular value of the applied force, the body breaks or snaps.
The magnitude of force, or load, for which the body breaks or snaps is called the breaking load of that body. In that condition, the maximum reaction force developed per unit area of the surface of the body is called breaking stress. Every material has its characteristic breaking stress.