- What is Hooke's Law?
- Hooke's Law Formula for Springs
- Hooke's law applications
- Hooke's law and elasticity

We explain what Hooke's law is, its formula and its applications in engineering and architecture. Also, how elasticity is calculated.

The greater the load applied to an object, the greater the deformation it undergoes.## What is Hooke's Law?

Hooke's Law of Elasticity, or simply Hooke's Law, is the physical principle around the elastic behavior of solid. It was formulated in 1660 by the British scientist Robert Hooke, a contemporary of the famous Isaac Newton.

The theoretical precept of this law is that the displacement or the deformation suffered by an object subjected to a force, will be directly proportional to the deforming force or the load. That is, the greater the force, the greater the deformation or displacement, or as Hooke himself formulated it in Latin: *Ut tensio sic vis* ("Like the extension, so the force").

Hooke's Law is extremely important in various fields, such as the physical and the study of elastic springs (his most frequent demonstration). It is a fundamental concept for engineering and architecture, construction and design, since it allows to foresee the way in which a prolonged force or a weight will alter the dimensions of the objects in the weather.

This law is said to have been published by Hooke in the form of a mysterious anagram (*ceiiinosssttuv*), from which the Latin statement of his law can be reconstructed, because he was afraid that someone might illegally take possession of his discovery. A couple of years later, however, he made his findings public.

## Hooke's Law Formula for Springs

The most common formula for Hooke's law is as follows:

*F = -k. ΔL*

Where:

*F*is the deforming force*ΔL*is the variation that the length of the spring, either a compression or extension.*k*is the constant of proportionality baptized as*spring constant*, generally expressed in Newtons over meters (N / m).

To calculate ΔL, that is, the deformation of the object, it is necessary to know the initial length (L0) and the final length (Lf).

See also:Elasticity in physics

## Hooke's law applications

Hooke's law predicts the effect of weight on building materials.Hooke's law is extremely useful in all those fields in which the knowledge full of the elastic capacity of materials. Engineering, architecture and construction are disciplines in which it is used most frequently.

For example, this law allows us to predict the effect that the weight of automobiles will have on a bridge and on the materials from which it is made (such as the metal). It also allows calculating the behavior of a bellows or a set of springs, within a specific machine or industrial device.

The best-known application of Hooke's law is the development of dynamometers: devices made up of a spring and a scale that allow forces to be measured scalarly.

## Hooke's law and elasticity

The application of Hooke's law to calculate the elasticity varies whether it is springs, or solid elastic.

To calculate the elasticity of the springs, the “spring equation” is applied, which is the most general way of posing the formula of Hooke's law (the same one that we offered above: F = -k. ΔL).

Knowing the spring constant k and the mass of the object connected to the spring, the angular frequency of oscillation of the spring (ω) can be calculated with the following formula:

ω = √k / m

On the other hand, to calculate the elasticity of elastic solids, the law of springs must be generalized, since the distribution of stress in their bodies is much more complicated than a bellows.

For this, the Lamé-Hooke equations are used, which have specific formulas for each solid according to its specific shape: one-dimensional, three-dimensional isotropic or three-dimensional orthotropic. But these are subjects that require much more complex and technical elaboration.