# Hooke’s law

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 orIons 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: