Hooke’s law explained: An overview

Introduction:

Hooke’s law, also referred to as the law of elasticity, was developed by an English scientist Robert Hooke in 1660, the statement given was, the magnitude of deformation is directly proportional to the deforming force or load for relatively small deformations of an object.  When the load is removed, the item returns to its original shape and dimensions.

Elastic behavior of any solid is put forth by knowing the minimal displacement of atoms, ions, or compounds that an object is built with. This small displacement from their original position is directly proportional to the force that causes the displacement. The deformation of solid can be done by stretching, compressing, squeezing, bending, or twisting any of these forces can be applied.

Hooke’s law was the one to give an explanation on elasticity, that is when an object is subjected to deformation, the material has the tendency to restore back to its original shape.

The ability of the object to return to its original state is called the restoring force. This restoring force is always equal to the “stretch” experienced in terms of Hooke’s law.

Hooke’s law is quite compatible with Newton’s law of static equilibrium. When they are put together to study stress and strain there is more clarity. Using these two laws it’s easier to deduce the relationship between stress and strain for large objects compiled with intrinsic materials.

Definition of Hooke’s law :

A linearly elastic material is one that behaves elastically and has a linear relationship between stress and strain. In this situation stress is directly proportional to strain.

Hooke’s law can be better defined when spoken in terms of spring, when a certain force is applied to the spring to compress, the restoring force is directly proportional to the length compressed.

The strain in the body is found until the stress is removed, once the stress is released the body automatically gets back to its original shape and size. This property of an object or material is called elasticity. Therefore this principle is also called the law of elasticity. 

Hooke’s law formula:

As we know from Hooke’s law, stress is directly proportional to strain.

So in mathematical form,

Stress ∝ strain 

Therefore the proportionality constant = stress / strain.

This proportionality constant is referred to as the modulus of elasticity or young’s modulus.

E = stress / strain or can be denoted as  E = 𝝈 / ε 

SI unit of elasticity = N / m2

The modulus of elasticity mainly depends on the material of the object it is formed and it is independent of the dimensions of the material.

Hooke’s law equation 

As we know according to Hooke’s law that stress and strain are proportional to each other.

The experiment conducted by Robert Hooke, Helped us to understand the behaviour of materials that undergo  Relatively small Deformation. 

The law is better understood by the experimentation of a spring that undergoes the formation when weights are placed, deformation of the spring coil is observed. The change in spring length is proportional to the force of gravity F acting on the suspended weight.

Therefore , F = -K x

F =  force applied to the spring ( N )

x =  the displacement observed in the spring (m)

k =  force constant.

Note: As the force applied is in the opposite direction to that of displacement 

The sign of force is negative.

For scalar springs :

Hooke’s law can be applied to various types of elastic materials or objects of varying complexity. This will, however, be dependent on whether the stress and deformation can be represented by a single number. This number can be both positive or negative.

For example, if we take a rubber block and attach it to two parallel plates, it is distorted because of the shearing force. As a result, the shearing force “Fs” and the lateral displacement of the plates “ Y”  obey Hooke’s law when the deformation is small.

For vector springs:

When we extend or compress a helical spring along its axis, the restoring force, and the elongation or compression that follows, have the same direction. As a result, when Fs and Y are referred to as vectors. Hooke’s equation still appears to be true, stating that the force vector is equal to the elongation vector multiplied by a constant scalar.

Applications of Hooke’s law 

1. Click pens, as we know for the use of click pens we need to use springs that are attached to the cartridge which compresses them then we click, when it is compressed the refill is pushed up and used for writing and one more click it retracts.
2. Recoiling of toy guns, The rear of the toy pistol is connected by a spring. When you pull the trigger on a toy gun, it fires a plastic bullet and recoils immediately due to a spring attached to the base.
3. Manometer, a device used to measure liquid pressure. It is a “U” shaped tube, where the liquid is filled halfway. One end of the tube is open and the other is sealed with elastic rubber. As the pressure increases on one side, there is the displacement of the water molecules to the other side.

Demerits of Hooke’s law 

1. Hooke’s law is applicable only to the elastic region of a material.
2. Hooke’s law is applicable to solid bodies where the scale of deformation is small
3. Hooke’s law isn’t considered a universal law.
4. Hooke’s law can’t be applied to any material that is stretched beyond its limit.

Conclusion:

This law had many important applications in which one example is the invention of the balance wheel, which enabled the development of mechanical clocks, portable timepieces, spring scales, and manometers.

Furthermore, as it helps in estimating for all the solid bodies, Hooke’s law is applied in numerous fields of science and engineering widely. Even in Seismology, molecular mechanics, and acoustics Hooke’s law is utilised.

Hooke’s Law, like any other classical mechanics, can only be applied to a limited set of circumstances. Because no material can be crushed or stretched past a particular minimum size without causing permanent distortion or change of state, it only applies to a certain amount of force or deformation. Many materials, in fact, depart noticeably from Hooke’s rule well before the elastic limits are reached.