Elasticity, Stress & Strain

# Elasticity, Stress & Strain | Physics Class 11 - NEET PDF Download

 Table of contents Elastic Behaviour of Solids Terms Related to Elasticity Stress Strain Hooke’s Law Stress-Strain Curve Summary

Till now we have learned that solids have fixed shapes and dimensions i.e. they are rigid. You must have observed that if a weight is hung from the end of a vertically hung steel spring, it gets stretched. When the weight is removed, it goes back to its original shape and size. This shows that steel spring has some elastic behavior!

Stretching of Springs

In this document, we will be studying the Elasticity of solids in detail.

## Elastic Behaviour of Solids

The property of the body to regain its original configuration (length, volume, or shape) when the deforming forces are removed, is called elasticity.

Spring-ball model for the illustration of elastic behavior of solids

• In a solid, atoms and molecules are arranged in such a way that each molecule is acted upon by the forces due to the neighboring molecules. These forces are known as intermolecular forces.  For instance, assume the atoms or molecules of solid as the balls in the image below and the springs represent the interatomic or intermolecular forces. This is called the spring-ball model of solids.
• In this system, if any ball is displaced from its equilibrium position, the ball attached to it will be stretched or compressed. Due to this, restoring forces will come into play and force the ball to come back to its original position. This leads to elastic behavior in solids.
• The change in the shape or size of a body when external forces act on it is determined by the forces between its atoms or molecules. These short-range atomic forces are called elastic forces.

Question for Elasticity, Stress & Strain
Try yourself:
What is the definition of stress?

1. Deforming force

A force that when applied changes the normal position of the molecules thus resulting in the change of configuration of the body.

2. Elastic body

A body that regains its original configuration immediately and completely after the removal of deforming force from it is called a perfectly elastic body. Quartz and phosphorus bronze are examples of nearly perfectly elastic bodies.

Elastic Materials

3. Plastic body
The inability of a body to return to its original size and shape even on removal of the deforming force is called plasticity and such a body is called a plastic body.

Plastic Materials

Question for Elasticity, Stress & Strain
Try yourself:The ability of the material to deform without breaking is called:

## Stress

Stress is defined as the ratio of the internal force F, produced when the substance is deformed, to the area A over which this force acts.

In equilibrium, this force is equal in magnitude to the externally applied force. In other words,

The SI Unit of stress is newton per square meter (Nm-2).In CGS units, stress is measured in dyne cm-2. The dimensional formula of stress is ML-1T-2

### Stress is of two types:

1. Normal stress: It is defined as the restoring force per unit area perpendicular to the surface of the body. Normal stress is of two types, tensile stress and compressive stress.

Tensile and compressive stress

2. Tangential stress: When the elastic restoring force or deforming force acts parallel to the surface area, the stress is called tangential stress or shear stress.

Tangential Stress

Question for Elasticity, Stress & Strain
Try yourself:A 20kg load is suspended by a wire of cross section 0.4mm2. The stress produced in N/m2 is :

## Strain

It is defined as the ratio of the change in size or shape to the original size or shape. It has no dimensions, it is just a number.

### Strain is of three types:

1. Longitudinal strain: If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain or tensile strain.
It is given as:

Longitudinal strain

2. Volumetric strain: If the deforming force produces a change in volume alone, the strain produced in the body is called volumetric strain. It is given as:

Volumetric strain3. Shear strain: The angle tilt caused in the body due to tangential stress expressed is called shear strain. It is given as:

Shear strain

The maximum stress to which the body can regain its original status on the removal of the deforming force is called the elastic limit.

Question for Elasticity, Stress & Strain
Try yourself:Shearing strain is expressed by

## Hooke’s Law

Hooke’s law states that, within elastic limits, the ratio of stress to the corresponding strain produced is a constant.

This constant is called the modulus of elasticity. Thus,

## Stress-Strain Curve

Stress-strain curves are useful to understand the tensile strength of a given material. The given figure shows a stress-strain curve of a given metal.

Stress-strain curve

• The curve from O to A is linear. In this region, Hooke’s Proportional limit law is obeyed.
• In the region from A to B stress and strain are not proportional. Still, the body regains its original dimension, once the load is removed.
• Point B in the curve is the yield point or elastic limit and the corresponding stress is known as yield strength of the material.
• The curve beyond B shows the region of plastic deformation.
• The point D on the curve shows the tensile strength of the material. Beyond this point, additional strain leads to fracture, in the given material.

## Summary

• Elasticity is a measure of the deformation of an object when a force is applied. Objects that are very elastic like rubber have high elasticity and stretch easily.
• Stress is force over an area.
• Strain is the change in length over the original length.
• Most objects behave elastically for small strains and return to their original shape after being bent.
• If the strain on an object is greater than the elastic limit of the object, it will permanently deform or eventually fracture. Fracture strength is a measure of the force needed to break an object.
The document Elasticity, Stress & Strain | Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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## FAQs on Elasticity, Stress & Strain - Physics Class 11 - NEET

 1. What is elasticity and why is it important in the study of solids?
Ans. Elasticity is the ability of a material to regain its original shape and size after the removal of an external force. It is important in the study of solids because it helps in understanding how materials respond to applied forces and how they deform under stress.
 2. What is stress and how is it related to elasticity?
Ans. Stress refers to the force applied per unit area on a material. In the context of elasticity, stress is directly related to the deformation or change in shape of a solid material. The amount of stress a material can withstand before permanent deformation occurs is a measure of its elasticity.
 3. What is strain and how is it measured?
Ans. Strain is a measure of the deformation or change in shape of a material in response to an applied stress. It is typically expressed as the ratio of the change in length or size of the material to its original length or size. Strain can be measured using various techniques such as strain gauges or extensometers.
 4. What is Hooke's Law and how does it relate to elasticity?
Ans. Hooke's Law states that the deformation of a material is directly proportional to the applied force, as long as the material remains within its elastic limit. This means that for small deformations, the stress is directly proportional to the strain. Hooke's Law is a fundamental principle in the study of elasticity and is used to calculate the elastic modulus of a material.
 5. What is a stress-strain curve and what information does it provide?
Ans. A stress-strain curve is a graphical representation of the relationship between stress and strain for a material. It shows how the material responds to applied forces and provides important information about its mechanical properties, such as its elastic modulus, yield strength, and ultimate strength. The curve can be used to determine the material's behavior under different loading conditions and to evaluate its suitability for various applications.

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