We explain what Hooke's law is, its formula and its applications in engineering and architecture. Also, how elasticity is calculated.
What is Hooke's law?
Hooke's Law of Elasticity, or simply Hooke's Law, is the physical principle surrounding the elastic behavior of solids. 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 deformation suffered by an object subjected to a force will be directly proportional to the deforming force or load. That is to say, the greater the force, the greater the deformation or displacement or as Hooke himself formulated it in Latin: Ut tension sic vis (“as the extension, so the force”).
Hooke's Law is extremely important in various fields, such as physics and the study of elastic springs (its most frequent demonstration). It is a fundamental concept for engineering and architecture construction and design, as it allows us to predict how a prolonged force or weight will alter the dimensions of objects over time.
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 could 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 the following:
F = -k. ΔL
Where:
- F is the deforming force
- ΔL It is the variation that the length of the spring experiences, whether it is a compression or extension.
- k is the proportionality constant called spring constantgenerally 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 (LF).
See also: Elasticity in physics
Applications of Hooke's law
Hooke's law is extremely useful in all those fields in which full knowledge of the elastic capacity of materials is required. Engineering, architecture and construction are the disciplines in which it is most frequently used.
For example, this law allows predict the effect the weight of cars will have on a bridge and about the materials it is made of (such as 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 development of dynamometers: devices composed 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 elasticity varies whether it is about springs or elastic solids.
To calculate the elasticity of springs, the “spring equation” is applied which is the most general way of stating the formula for Hooke's law (the same one we offered above: F = -k . ΔL).
Knowing the spring constant k and the mass of the object connected to the spring, we can calculate the angular frequency of oscillation of the spring (ω), with the following formula:
ω = √k/m
Instead, To calculate the elasticity of elastic solids, the spring law must be generalized since the distribution of tension 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 form: one-dimensional, three-dimensional isotropic or three-dimensional orthotropic. But these are topics that require much more complex and technical elaboration.
Continue with: Thermodynamics
References
- “Hooke's law of elasticity” on Wikipedia.
- “What is Hooke's Law?” at Khan Academy.
- “Introduction to Hooke's Law” (video) in Flipping Physics.
- “Hooke's Law” on Lumen Learning.
- “Hooke's Law” in The Encyclopaedia Britannica.
