The **Hooke ‘s law** refers to the law of **elasticity** which was discovered by the English scientist **Robert ****Hooke** in 1660, which states that for relatively small deformations that occur in an object, the **displacement** or size of the **deformation** it is directly **proportional** to the deformation **force** or load. In these situations, the object returns to its original shape and size by discarding the load. The elastic behavior of solids according to Hooke’s law can be explained by the fact that small displacements of their constituent **molecules** , **atoms** or**Ions** from normal positions are also proportional to the **force** causing the **displacement** .

**Unit:**Newtons / Meters**Symbol:**K**Formula:**K = N / m

## What is Hooke’s Law?

Hooke’s law is the law that states that the **deformation** suffered by a certain **elastic** material is directly **proportional** to the **force** that has been applied to it and that has caused the deformation.

- Who Proposed Hooke’s Law
- History
- Statement
- Hooke’s law formula
- Units
- Explanation
- What is Hooke’s law for?
- Applications
- Curiosities
- Conclusions
- Examples of Hooke’s law

## Who Proposed Hooke’s Law

The law was proposed by **Robert Hooke** , who was an English physicist who was born in Freshwater, on the Isle of Wight, on July 18, 1635, and who died in London on March 3, 1703. He had a very important role thanks to his great contributions in **science** , **astronomy** , **physics** , **mathematics** , **biology** and **chemistry** .

## History

Robert Hooke was in charge of studying, among other things, the **spring** . His law allows associating a **constant** to each spring. In 1678 he published the law known as Hooke’s Law: “The force that returns a spring to its equilibrium position is proportional to the value of the distance it travels from that position.”

## Statement

The statement of Hooke’s Law tells us that: ** “The force that returns a spring to its equilibrium position is proportional to the value of the distance it travels from that position** .

**F = D ㆍ D**

*”*## Hooke’s law formula

Deformation force can be applied to a **solid** either through **stretching** , **compression** , **bending,** or **twisting** . Mathematically, Hooke’s law states that the applied force F equals a constant k multiplied by the **displacement** or change in **length** x, or F = kx. The value of k depends not only on the type of elastic material considered, but also on its dimensions and shape. The formula is as follows:

**K = N / m**

Where:

- F is the modulus of the
**force**that we apply on the spring and due to this, we must never introduce a negative value of this variable in Newtons into the formula. - k is the
**elasticity constant of**the material with which the spring or spring has been made - x is the
**length**of the spring after it has been stretched - x0 is the
**measure**of the spring before it has been stretched

## Units

We will express the force by means of **Newtons** (N) and the elongation of the body will be measured in **meters** (m). Therefore, the units used to express Hooke’s law is in Newtons / Meters.

## Explanation

The simplest explanation of Hooke’s law tells us that if the deforming **force** of the object exceeded a certain **value** , then the body would acquire a certain permanent **deformation** that would prevent it from recovering its original shape or size. This minimum stress necessary to produce a permanent deformation was called the **elasticity limit** .

## What is Hooke’s law for?

Hook’s law is used to elaborate studies on the cases of **longitudinal stretching** , since it establishes that the unit **elongation** that an elastic material has is directly proportional to the applied **force** .

In other words, it works to be able to make measurements of the **elongation** of a material, usually **springs,** and it tells us that the elongation of the material is directly proportional to the **force** that produces it, this means that the more force is performed, the more the elongation is stretched. dock.

## Applications

One of the main applications of Hooke’s law is in **dynamometers** , which are instruments used to make measurements and whose calibrations are made based on the law proposed by Hooke. In general, dynamometers are composed of a **spring** and a **scale** where it is possible to indicate the force that is associated with its deformation.

They are also applied to **springs** , which is one of the most important uses because when exerting force they deform and then return to the position they had at the beginning. It is also applied to the mechanics of **elastic solids** in the distribution of stresses.

## Curiosities

- The
**chroniclers**of his time called him with words like**despicable**,**distrustful**and**jealous**. **Isaac Newton**abhorred him so much that after his death he had the only existing portrait of him burned.- Hooke improved the precision of the microscope by adding a
**screw focusing**mechanism and a**light source**. Before this, to focus something under a microscope you had to move what you were looking at until you could see it correctly.

## Conclusions

Some conclusions that have been reached with Hooke’s law are the following:

- The
**deformations**that a spring undergoes and its period of**oscillation**are proportional to the**mass**. - It is concluded that when a solid object is
**deformed**, this object presents a natural**opposition**as a reaction and that it is explicitly manifested when the force that deforms it stops as it will try to return to its**natural state**. - The
**deformation**and the**force**needed to produce this deformation is directly proportional, as long as the deformation is not excessive.

## Examples of Hooke’s law

Some examples in which we can see Hooke’s law applied are the following:

- Springs that lengthen and then return to their normal state.
- Torsion springs.
- The springboards.