Hooke's Law
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 Definition
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 = Force applied (N)
- k = Spring constant (N/m), a measure of stiffness
- x = Displacement (m), amount stretched or compressed
Hooke's law formula
F = kx
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Where:
- F = Force applied on the object (in Newtons, N)
- k = Spring constant or force constant (in Newtons per meter, N/m)
- x = Displacement or extension/compression of the object from its original position (in meters, m)
Hooke's Law Derivation
When a force is applied to an elastic object (like a spring), it deforms — either stretching or compressing.
Observation:
- For small deformations, the amount of stretch or compression (displacement) is directly proportional to the applied force.
Thus,
F∝x
Where:
- F = Applied force
- x = Displacement from the equilibrium (natural) position
To remove the proportionality sign, we introduce a constant k (known as the spring constant or force constant).
Thus,
F=kx
- k depends on the material and geometry of the object (e.g., stiffness of the spring).
- If k is large, the object is stiff; if k is small, the object is flexible.
- Spring constant (k) is defined as the force required to produce a unit displacement (1 meter).
- Units of k = Newton per meter (N/m).
Thus, rearranging:
k = F x/ k
- Car suspensions absorb shocks using spring elasticity.
- Spring mattresses provide comfort based on Hooke’s Law.
2. Construction & Engineering
- Bridges and buildings use Hooke’s Law in stress analysis.
- Engineers calculate forces that materials can safely withstand.
3. Biomechanics & Medical Science
- Human tendons and muscles exhibit elastic behavior explained by Hooke’s Law.
- Prosthetics and orthotic devices are designed based on elasticity principles.
4. Everyday Objects
- Guitar strings vibrate under tension, following Hooke’s Law.
- Trampolines and bungee cords stretch within their elastic limits.
Conclusion
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 FAQs
What is Hooke's Law?
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.
What is the SI unit of Hooke's law?
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).
What is Hooke's Law in A-Level Physics?
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.
What is Hooke's Law Class 11 Physics State?
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.
What are Hooke's Laws? State and explain.
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
How to derive Hooke’s Law?
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.
What is the force constant?
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).
What is Hooke's Law in Strength of Materials?
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.