# Hooke’s Law - Definition, formula, Graph, Applications

By Mohit Uniyal|Updated : May 4th, 2022

In the 19th-century, while studying springs and elasticity, Robert Hooke, an English scientist noticed that numerous materials exhibited an analogous property when the stress-strain correlation was studied. Robert Hooke formulated a mathematical expression for the same, termed Hooke's law.

There was a linear region where the force required to extend the material was proportional to the extension of the material. This is referred to as Hooke's Law. In this article, let us learn about Hooke’s law thoroughly.

## What is Hooke’s Law?

Stress and strain take completely different forms in, unlike situations. Normally, for tiny deformations, the stress and strain are proportional to each other, and this is referred to as Hooke’s Law. Steel displays linear-elastic behaviour in most engineering applications; Hooke's law is valid for it throughout its elastic span. For some other materials, such as aluminium, Hooke's law is only valid for a part of the elastic range.

### Hooke’s Law Definition

“Hooke’s law defines that the strain of the substance is proportional to the applied stress within the elastic limit of that substance.”

When the elastic materials are stretched or compressed, the atoms and molecules disfigure until the force is applied, and when the force is removed, they return to their previous state.

### Hooke’s law Formula

Mathematically, within the proportional limit of a material the Hooke’s law formula is expressed as follows-

### σ = Eε

Where, in SI units

• σ is the stress; Pa
• E is the modulus of elasticity or Young’s modulus, Pa (Normally GPA)
• ε is the strain, dimensionless

## Hooke’s Law Graph

The figure below shows the stress-strain curve for mild steel.

The material shows elastic behaviour up to the proportional limit, Beyond that the material loses elasticity and shows plasticity.

From the emergence to the proportional limit nearing yield strength, the straight line suggests that the material follows Hooke’s law. Beyond the elastic limit between proportional limit and yield strength, the material no longer has its elasticity and shows plasticity. The area under the curve from emergence to the proportional limit falls under the elastic span. The area under the curve from a proportional limit to the fracture point/rupture falls under the plastic span.

The material’s ultimate strength is described based on the maximum ordinate value given by the stress-strain curve (from emergence to rupture). The value gives the rupture strength at a point of rupture.

## Hooke’s Law Applications

Hooke’s Law is used in all branches of science and engineering; For understanding the behaviour of elastic materials there is no replacement for Hooke's law. Following are some of the applications of Hooke’s Law:

• It is used as a fundamental principle behind the manometer, spring scale, and the balance wheel of the clock.
• Hooke’s law sets the foundation for seismology, acoustics and molecular mechanics.

Even though Hooke’s law is used widely in Engineering, it’s not a universal principle. The law is not applicable as soon as the elastic limit of a material is surpassed. Usually, for solid particles, Hooke’s law provides precise results when the deformations are small. Numerous materials deviate from Hooke’s law even well before reaching the elastic limit. Following are some of the disadvantages of Hooke’s Law:

• Hooke’s law comes to an end when applied beyond the elastic limit of a material.
• Hooke’s law is correct just for solid bodies if the forces and deformations are small.
• Hooke’s law isn’t a universal principle and solely applies to the materials as long as they aren’t stretched well past their capacity.

If you are preparing for ESE/ GATE or other PSU Exams, then avail Online Classroom Program for ESE and GATE:

### Comprehensive Preparation for GATE & ESE

Attempt online mock tests of ESE & GATE 2023 at BYJU'S Exam Prep to improve the exam score in all disciplines.

Thanks

write a comment

## FAQs on Hooke’s Law

• Hooke’s law applies to any elastic entity of random complexity, as long as a single number can convey the deformation and the stress. Hooke’s law is applicable within the proportional limit.

• Hooke’s Law is linear. It states that the restoring force is proportional to the displacement within its proportional limit.  If shown on a graph, the line depicting force as a function of displacement should show a direct variation.

• Hooke’s law applies to a perfectly elastic material. It does not apply beyond the elastic limit of any substance. So we can state that Hooke's law holds good up to proportional limit.

• Objects that quickly regain their original shape after being deformed by a force, often obey Hooke's law. Hooke's law only holds good for some materials under definite loading conditions. Steel obeys Hooke's law throughout its elastic span. For aluminium, Hooke's law is only valid for a portion of the elastic span.

• Hooke’s Law is crucial because it helps us to acknowledge how an elastic object will behave when stretched or compacted within its proportional limit. It is important to enhance the technology by understanding the material behaviour properties.

### Related Posts

GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com