State Hooke’s law. Define elastic limit and modulus of elasticity.

Hooke's Law states that the extension or deformation of an elastic material is directly proportional to the applied force or load, as long as the elastic limit of the material is not exceeded. Mathematically, it can be expressed as:

F = k * ΔL

Where:
F is the applied force or load,
k is the spring constant or stiffness of the material,
ΔL is the change in length or deformation of the material.

Elastic Limit:
The elastic limit is the maximum stress or load that a material can withstand while still returning to its original shape once the applied stress is removed. If the stress or load exceeds the elastic limit, the material may experience permanent deformation or even fracture. The elastic limit is different for different materials and is an important consideration in engineering applications.

Modulus of Elasticity:
The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness or rigidity of a material. It quantifies the relationship between stress and strain in a material under elastic deformation. It is defined as the ratio of the stress applied to a material to the resulting strain produced. Mathematically, it can be expressed as:

E = σ / ε

Where:
E is the modulus of elasticity,
σ is the stress applied to the material,
ε is the resulting strain in the material.

The modulus of elasticity is a material property and provides information about how a material will deform under applied stress. It allows engineers to design and analyze structures by predicting the behavior of materials under different loading conditions.