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By Karan Singh Bisht
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Updated on 21 Apr 2025, 17:23 IST
In the 17th century, while exploring the behavior of springs and the nature of elasticity, English scientist Robert Hooke observed that many materials displayed a consistent pattern under stress.
He found that within a certain range, the force needed to stretch or compress a material was directly proportional to its extension or compression. This fundamental principle came to be known as Hooke’s Law. In this article, we will explore Hooke’s Law in detail, including its principles, formula, and applications.
Hooke's Law states that the force applied to elongate or compress an elastic body is directly proportional to the displacement or deformation of the body, provided the elastic limit of the material is not exceeded.
Mathematical Expression of Hooke’s Law
F = kx
F = kx
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Where:
When a force is applied to an elastic object (like a spring), it deforms — either stretching or compressing.
Observation:
Thus,
F∝x
Where:
To remove the proportionality sign, we introduce a constant k (known as the spring constant or force constant).
Thus,
F=kx
Thus, rearranging:
k = F x/ k
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3. Biomechanics & Medical Science
4. Everyday Objects
Hooke’s Law plays a critical role in understanding material behavior and designing safe structures. From car suspensions to medical devices, it prevents mechanical failures and enhances technological innovations across multiple fields.
Hooke's Law states that the force needed to extend or compress a spring by some distance is directly proportional to that distance, provided the material's elastic limit is not exceeded. Mathematically:
F=kx,
where F is the force applied, k is the spring constant, and x is the displacement.
The SI unit associated with Hooke’s law is the unit of force, which is the Newton (N). For the spring constant (k), the SI unit is Newton per meter (N/m).
In A-Level Physics, Hooke's Law explains how materials behave elastically. It states that the extension of a spring or elastic material is proportional to the force applied, up to the elastic limit. The relationship is linear and reversible within this limit, forming the foundation of studying material properties like elasticity and stiffness.
In Class 11 Physics, Hooke’s Law is stated as: "Within the elastic limit, the stress applied to a body is directly proportional to the strain produced in it."
In formula form: Stress ∝S train or Stress= E× Strain
where E is the modulus of elasticity.
Hooke’s Law states that for small deformations, the force (or stress) is directly proportional to the displacement (or strain) in elastic materials.
Directly proportional means doubling the force doubles the extension.
Elastic limit: Beyond a certain point, materials no longer follow Hooke’s law and undergo permanent deformation.
Thus,
F=kx
or
Stress = Elastic modulus × Strain
The derivation of Hooke's Law is simple:
Apply a small force F on a spring.
Measure the displacement x produced.
Experimentally, F ∝ x for small stretches.
Introducing a constant of proportionality k (spring constant):
F=kx
where k = F/x, depending on the material's stiffness.
The force constant (k), also known as the spring constant, is a measure of the stiffness of a spring. It is defined as the force required to produce a unit extension or compression in the spring.
Mathematically:
k= x/F
Unit of force constant = Newton per meter (N/m).
In Strength of Materials, Hooke’s Law describes the linear relationship between stress and strain within the elastic limit. It helps engineers calculate how much a material will deform under various loads and ensures that constructions like bridges and buildings are safe.