Hooke’s Law

This blog will be a detailed explanation of Hooke’s law. Hooke’s law states that for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the force applied to it. It is a common term used in engineering and physics to describe the relationship between the stress applied to a material and the strain it causes. The law was discovered by an English physicist Robert Hooke and was first published in 1660 in his book called “Micrographia”. The law is one of the oldest working mechanical models used to describe the relationship between stress and strain.

Some Important terms:

Stress:

Stress describes the body’s ability to endure physical weight or pressure without breaking. It is represented as the restoring force per unit area.

Stress = Restoring Force /Area = F / A

Strain:

The change in the configuration (e.g. shape, length, or volume) of the body divided by the original configuration of the object is referred to as Strain.

Strain = Change in length / original length = ∆L / L

Plasticity:

 It is the nature of material to be not able to return to its original dimensions after the removal of deforming forces. In such cases, permanent deformation takes place.

Elasticity: 

Elasticity is the ability of an object to regain its original shape and size after force or stress has been removed. Providing a certain object possesses this quality, it is said to possess elasticity. If the object regains its full dimensions perfectly, it is called a perfectly elastic object.

Hooke’s law equation

Hooke’s equation which can be read in earlier works may apply to many instances and the instances could be of elastic objects. The instances might include the wind blowing on a building or a musician playing the guitar for instance. Such cases are said to be linear-elastic or Hookean, usually for an elastic body and material.

Hooke’s Law Equation of Stress and Strain

Hooke’s Law stipulates that stress is proportional to strain. Here, strain stands as a measure of how far an object or body has been stretched beyond its normal position. In simpler terms, given an object that changes its structure in response to external forces (such as the load) and an object that’s within its elastic limit, Hooke’s Law can be expressed using stress and strain.

Stress α Strain

Stress = Modulus of elasticity × Strain

σ = E ε

Where, σ is the stress, E is the modulus of elasticity, ε is the strain.

In SI units, the spring constant k, and each element of the tensor κ, is measured using units such as newtons per meter (N/m).

For Linear Springs

According to Hooke’s Law, whenever an elastic body is strained, the extension or stretch and tension or pull are linearly related to each other. One of the interesting aspects of this law is that elasticity doesn’t depend on the size of the object or stretch but rather the inherent material properties. The experiment involving stretching a spring with weights hung from it is often used to demonstrate this law because one can see how an extremely small change in length affects the weight suspended from a spring. The change in the length of the spring is proportional to the force of gravity F on the suspended weight. 

All matter is elastic – it tends to return to its original state. This behavior can be visualized by a restoring force that acts in opposition to any deformation; this force tries to maintain the material’s original dimensions. As an example of elasticity within one dimension, we will test Hooke’s law for a spring-mass system where the restoring force is proportional to the magnitude of the deformation (stretch). To get a true representation, we need to know how much force is required for a certain amount of elongation (stretch). With Hooke’s Law and basic math, we can know what change in mass corresponds with an amount of stretch.

The equation is given as,

F = -Kx 

where F is the amount of force applied in Newtons, x is the displacement in meters and k is the spring constant.

Here the force is in the direction opposite that of the displacement, so we have considered the minus sign.

Scalar Springs

Hooke’s spring law applies to elastic material with stochastic complexity so that the stress and deformation are included by two random numbers; it depends on whether the deformation of the surface and stress can be represented by a single number.

To illustrate this, let’s consider a simple rigid object. Take for example a rubber block attached to two parallel plates via springs of small spring constant K. When F is the shearing force and x is the sideways displacement, we observe that the relationship between these variables follows or obeys what’s referred to as Hooke’s law (small deformations).

Application of Hooke’s Law

Spring Scale

What makes spring scales advantageous for fruit and vegetable merchants is their ability to allow for a greater range of high weight. A heavier truck would not be able to be weighed using the conventional weighing method because it can only measure up to 22 pounds, whereas spring scales can have a higher capacity of up to around 100 kg. As you may know, trucks require several people to push together in order to move, while even one person could easily pull along a spring scale and very quickly weigh the contents of a truck! Hooke’s law is what makes this weight measuring mechanism easier in spring scales.

Inflating a Balloon

As air is inflated into a balloon, it starts swelling when air molecules are blasted into it. The molecules which make up the elastomeric nature of the balloon are able to adjust their shape as they’re squeezed further toward one another. Similarly, as air is removed from a previously inflated balloon, it collapses in on itself; therefore, it’s being compressed.Balloons can change the way they look depending on how much air is blown into them. They operate based on Hooke’s law and expand or contract, depending on what forces are exerted upon them.

Disadvantages of Hooke’s law

• Only applicable to solid bodies when force is very small.
• Not a universal law.
• Only applies to materials if they are not stretched past the elastic limit.
• Can be applied only to the elastic regions of the object.

Conclusion:

Hooke’s law was established by Robert Hooke in 1660 and is one of the most fundamental concepts of physics. The law holds for small deformations and states that strain (the deformation of an object) is directly proportional to the applied stress (the force applied to it). We’ve covered a lot of things in this blog post from an explanation of what Hooke’s law is, some important terms associated with it, its equations in different scenarios, applications, and disadvantages. We hope you like it.