Elastic Behaviour Of Solids, Elasticity, Important Topics For JEE 2024

Elastic Behaviour of Solids : The properties of material under the action of external deforming forces are very essential, for an engineer, to enable him, in designing him all types of structures and machines. Whenever a load is attached to a thin hanging wire it elongates and the load moves downwards (sometimes through a negligible distance). The amount by which the wire elongates depends upon the amount of load and the nature of wire material.

Cohesive force, between the molecules of the hanging wire offer resistance against the deformation, and the force of resistance increases with the deformation. The process of deformation stops when the force of resistance is equal to the external force (i.e. the load attached). Sometimes the force of resistance offered by the molecules is less than the external force. In such a case, the deformation continues until the wire breaks.

Thus, we may conclude that if some external deforming force is applied to a body it has two effects on it, namely:

(i) deformation of the body,

(ii) internal resistance (restoring) forces are developed.

The States Of Matter

The States Of Matter : Matter is usually classified into one of three states or phases: solid, liquid, or gas. Because they can flow easily, both liquids and gases are called fluids.

• A solid has a fixed shape which it tends to retain, whereas fluids have no fixed shape.
• A liquid sinks to the bottom of its container, and a gas expands to fill the available volume.
• T he atoms in a solid vibrate about fixed equilibrium positions, whereas the atoms or molecules in a liquid move about relatively freely and collide frequently with each other.

Elasticity

Elasticity : We have used the concept of a rigid solid body in which the distance between any two particles is always fixed. Real solid bodies do not exactly fulfil this condition. When external forces are applied, the body may get deformed. When deformed, internal forces develop which try to restore the body in its original shape. The extent to which the shape of a body is restored when the deforming forces are removed varies from material to material.

The property to restore the natural shape or to oppose the deformation is called elasticity . If a body completely gains its natural shape after the removal of the deforming forces, it is called a perfectly elastic body. If a body remains in the deformed state and does not even partially regain its original shape after the removal of the deforming forces, it is called a perfectly inelastic or plastic body. Quite often, when the deforming forces are removed, the body partially regains the original shape.

In other words, Whenever a single force (or a system of forces) acts on a body it undergoes some deformation and the molecules offer some resistance to the deformation. When the external force is removed, the force of resistance also vanishes and the body returns back to its original shape. But it is only possible if the deformation is within a certain limit. Such a limit is called elastic limit. This property of materials of returning back to their original position is called the elasticity.

A body is said to be perfectly elastic if it returns back completely to its original shape and size after removing the external force. If a body remains in the deformed state and does not even partially regain its original shape after the removal of the deforming forces, it is called a perfectly inelastic or plastic body. Quite often, when the external forces are removed, the body partially regains the original shape.

Such bodies are partially elastic. If the force acting on the body is increased and the deformation exceeds the elastic limit, the body loses to some extent, its property of elasticity. In this case, the body will not return to its original shape and size even after removal of the external force. Some deformation is left permanently.

Now we have observed that a spring returns to its original shape when the force compressing or stretching it is removed. In fact, all materials change their shape in some way when they are squeezed or stretched, and many of them, such as rubber, return to their original shape when the action on the material is stopped.

Such materials are said to be "elastic." From an atomic viewpoint, elastic behaviour has its origin in the forces that atoms exert on each other. Atoms in a solid are held in place by forces between atoms termed as interatomic forces that can be modelled as springs. It is because of these atomic-level "springs" that a material tends to return to its initial shape once the forces that cause the deformation are removed. The interatomic forces that hold the atoms of a solid together are particularly strong, so considerable force has to be applied to stretch or compress a solid object.

In nature all rigid objects are somewhat elastic, even though they do not appear to be, compressing, pulling or twisting can deform a rigid object. If a rigid object is deformed by a small amount, it will return to its original size and shape when the deforming force is removed. If a rigid object is deformed past a point called its elastic limit, it will not return to its original size and shape but will remain permanently deformed and will break if the applied force continues.

When external forces are applied on a body, which is not free to move, there is a change in its dimensions. When these forces are removed, the body tends to regain its original shape and size. The property by virtue of which a body tends to regain its original shape and size when the external deforming forces are removed, is called elasticity. The property of the material body by virtue of which it does not regain its original configuration when the external force is removed is.

Deforming Force

Deforming Force : An external force applied to a body which changes its size or shape or both is called deforming force.

Perfectly Elastic Body

Perfectly Elastic Body : A body is said to be perfectly elastic when it completely regains its original configuration on the removal of deforming forces. Since no material can regain completely its original form so the concept of perfectly elastic body is only an ideal concept. A quartz fibre is the nearest approach to the perfectly elastic body.

Perfectly Plastic Body

A body is said to be perfectly plastic if it does not regain its original form even slightly when the deforming force is removed. Since every material partially regains its original form on the removal of deforming forces, so the concept of perfectly plastic body is also an ideal concept. Paraffin wax, wet clay are the nearest approach to a perfectly plastic body.

Cause Of Elasticity

Cause Of Elasticity : In a solid, atoms and molecules are arranged in such a way that each molecule is acted upon by the forces due to the neighbouring molecules. These forces are known as intermolecular forces. When no deforming force is applied on the body, each molecule of the solid (i.e. body) is in its equilibrium position and the inter molecular forces between the molecules of the solid are maximum.

On applying the deforming force on the body, the molecules either come closer or go far apart from each other. As a result of this, the molecules are displaced from their equilibrium position. In other words, intermolecular forces get changed and restoring forces are developed on the molecules. When the deforming force is removed, these restoring forces bring the molecules of the solid to their respective equilibrium positions and hence the solid (or the body) regains its original form.

Basically, A solid body is composed of a great many molecules or atoms arranged in a particular fashion. Each molecule is acted upon by the forces due to the neighbouring molecules. The solid takes such a shape that each molecule finds itself in a position of stable equilibrium. When the body is deformed, the molecules are displaced from their original positions of stable equilibrium. The intermolecular distances change and restoring forces start acting on the molecules which drive them back to their original positions and the body takes its natural shape.

One can compare this situation to a spring-mass system. Consider a particle connected to several particles through springs. If this particle is displaced a little, the springs exert a resultant force which tries to bring the particle towards its natural position. In fact, the particle will oscillate about this position. In due course, the oscillations will be damped out and the particle will regain its original position.