# Elastic Behavior of Solids

## What is Elasticity?

Elasticity is defined as an attribute of rigid bodies to restore its original shape.

Consider a spring hanging at one end through a rod at the top and the other end of it is left free.

If I stretch this free end, the spring starts vibrating back and forth. It means the potential energy stored inside it transforms into kinetic energy; the spring is in solid form, so there is a tiny space between the successive atoms. Due to the force of attraction between them, they try to come back to their lattice points.

This is how an interatomic force of attraction comes into play.

So soon the stage comes when restoring force acting in the opposite direction to the applied force brings the spring into its natural state.

Hence, the condition in which the body rolls back to its initial form. Such a condition is elasticity.

### Explain Elastic Behavior of Solids

Solid is one of the three states of matter composed of many molecules or atoms arranged in a particular form.

Here, each molecule is acted upon by the forces because of neighboring molecules.

The solids take such a shape that each molecule finds itself in a position of stable equilibrium.

The rigid bodies when stretched with an external force restore their original shape after the removal of this force. It means they are in an elastic limit. So, until the elastic limit, the body resists the changes.

Therefore, we can say that the body is perfectly elastic.

Thus, the elastic behavior of solids can be explained very well by observing the microscopic nature of the solids.

### Elastic Behavior of Solids

When a solid body is deformed, the atoms or molecules inside it are displaced from their fixed points or lattice points (equilibrium positions) causing a change in interatomic and intermolecular distances.

When this force is removed, the interatomic force tries to bring back the body into its original position. Thus, the body comes to its original shape.

### Mechanical Properties of Solids

The restoring mechanism can be visualized through a model of a spring ball system.

Here, the ball represents atoms and spring represents the interatomic force of attraction between the balls or atoms.

Fig.2

Initially, these atoms are in their respective lattice points as shown in Fig.2. When they are displaced from their points,  the interatomic force of attraction brings the system to its original shape.

Deformation: The phenomenon of change in the shape of a body under the effect of applied force.

Deforming Force: The external force that is responsible for deformation in the shape of the system is called the deforming force.

Restoring Force: The opposite force that works in the way the frictional force does in a moving body. This force acts in the opposite direction, and it is a property of a body to come back to its original position after an external force is removed.

### Important Points on Elastic Behavior of Solids

The attribute of a matter or a body under which a body regains its original configuration is called elasticity.

Let us understand this through an experiment:

On stretching a rubber band, we observe that there is a change in its shape and size. On releasing the band, the rubber regains its original length.

The force applied to the rubber band is the deforming force. Therefore, the force that restores the elongated body to its original shape, and size is called the restoring force.

### Applications of Elastic Behavior of Materials

Elastic materials are those materials that can be used in places where the long-term usage of such material is required.

We may find applications of elastic materials outlined below:

1. Used in the construction of bridges, beams, columns, pillars: while constructing these materials, in-depth knowledge of the strength of the materials used in the construction is of prime importance.

2. Construction of cranes: Cranes are used to lift the loads. Therefore, great care is taken into consideration that the extension of the rope does not exceed the elastic limit of the rope.

3. In engineering, it is of utmost importance to know the elastic behavior of materials being used.

The bridges are designed in such a way that they don’t get deformed or break under a load of heavy traffic, or due to the force of strongly blowing wind, and its weight.

Let’s consider a bar of length L and breadth d. Let Y be the young's modulus of the material of the bar. When a load ‘W’ is attached at its middle point,  the depression δ produced at its middle point is given by,

δ = Wl3/4Ybd3

The metallic parts of the machinery are designed in such a way that when they are subjected to stress beyond the elastic limit, they will get permanently deformed.

Q1: What is Hooke’s Law of Elasticity?

Ans: Hooke’s law states that the extension produced in the wire is directly proportional to the load applied within the elastic limit.

We know within the elastic limit:

Stress α Strain

Or,             Stress  = E x Strain

Where E is known as the modulus of elasticity of the body.

Q2: What is the formula for Elasticity in Physics?

Ans: According to the equation of Hooke’s law, F = kΔL, where ΔL is the amount of extension in the length of the material. So, elasticity is a measure of how difficult it is to stretch an object. In other words, it is a measure of how small the value of k is. The materials like rubber have a small k. Hence, they stretch a lot, even with a little force.

Q3: What are Elasticity Stress and Strain?

Ans: The stress acting on an object is directly proportional to the strain caused in the body within an elastic limit. It is represented as Stress α Strain.

Q4: Which is more elastic Steel or Rubber?

Ans: Steel is more elastic than the rubber because when it is stretched, steel regains its position earlier than rubber.