# Hooke’s Law Formula

## Hooke’s Law Formula

The Hookes Law Formula, which asserts that the displacement or change in the position of the spring relative to its rest proportion is directly proportional to the load applied to the spring, was put forth by the English scientist Robert Hooke in 1660. The Hookes Law Formula is one of the fundamental principles in the field of Physics.

As a result, when the load is removed under the required conditions, the item resumes its original shape and dimensions. These tiny displacements of the material’s component molecules, atoms, or ions occur from their normal places. According to Hookes Law Formula equation, they are proportional to the force that causes the displacement, exemplifying the elastic behaviour of solids.

### What is Hooke’s Law?

According to Hookes Law Formula, for relatively minor deformations of an object, the displacement or magnitude of the deformation is directly proportional to the deforming force or load.

Hooke’s law governs the opposing force created by a spring. Robert Hooke, an English scientist, created Hooke’s law of elasticity. It does not matter what kind of material is deformed, or how much. Hooke’s law only applies to elastic materials in the elastic area (up to the proportionate limit). This means that Hooke’s law will not hold true if any elastic material is stretched or compressed above the proportionate limit.

### Derivation of Hooke’s law

Hookes Law Formula has been mathematically explained using the following equation: F = kx. Here, F stands for the applied force and is constant in this equation, while K stands for a constant equal to k times the Displacement or change in length of an item denoted by x. F stands for the applied force, k stands for the Displacement constant, and x stands for the lengthening of the object.

The elastic constant k is affected by the nature of the object’s material, size, and shape. When a significant force is applied, the elastic material deforms much more than the quantity suggested by Hookes Law Formula. On the other hand, the material remains elastic and returns to its original size when the applied force is removed, and it retains its shape when the force is removed. Hookes Law Formula equation is sometimes expressed as follows:

A spring’s restoring force equals the Spring constant multiplied by its displacement from its usual position. F = -kx, Where F is the spring’s restoring force (Newtons, N), k is the spring constant (N/m), and x is the spring’s Displacement (m).

The negative sign indicates the applied force’s direction. According to tradition, F= -kx contains the minus or negative sign. Hookes Law Formula states that the restoring force F is proportionate to the Displacement x. The coordinate for Displacement x is negative when the spring is squeezed. The spring’s normal length results in zero. When the spring is expanded, the result is positive.

### Hooke’s Law Example

Students can check the Hookes Law Formula examples on the Extramarks website and make their conceptual understanding more strong for their exams.

## 1. Does the real substance uphold Hookes Law Formula?

No, some substances do not adhere to Hookes Law Formula. Others are made of mud, rubber, or plastic. Hooke’s law only applies to little elastomeric material deformation.

## 2. What does the slope of the graph of stress against strain for elastic material within proportionate limit represent?

The stress and strain are directly inversely proportional within the proportional limit. The slope is a representation of Hooke’s law’s stiffness constant. It is also known as the elasticity modulus.

## 3. What exactly is the elastic limit?

Due to its inherent flexibility, every solid substance has the propensity to resist changing in shape. Therefore, when a force is applied to a body, the item initially deforms, and some energy is created inside it. It has been found that if a force is applied up to a certain point, the body returns to its original shape, but if it exceeds that point, the deformation is irreversible. Therefore, the region in which Hooke’s law is applicable is the Elastic Limit.

## 4. What exactly is elastomeric potential energy?

The energy created in a material due to elongation or suppression from its normal state due to applying an external force is known as elastomeric potential energy. Every substance in the cosmos has a structure made up of atoms and molecules. When an object’s shape changes because of the intrinsic packing of these particles in the structure, energy is created inside it to return it to its original state.