Hooke's Law and Elastic Limit
States that within the elastic limit, stress is directly proportional to strain.
What is Hooke's Law and Elastic Limit?
Internal restoring force per unit area developed in a body when it is deformed by an external force.
Key formula / rule: Hooke's Law
Key points
- Define stress and strain.
- State and explain Hooke's Law.
- Identify and explain the concept of the elastic limit.
- Understand the relationship between stress, strain, and the modulus of elasticity.
Common exam trap
Applying Hooke's Law beyond the elastic limit.
Definitions
- Term
Stress
- Meaning
Internal restoring force per unit area developed in a body when it is deformed by an external force.
- Term
Strain
- Meaning
The ratio of change in dimension to the original dimension; it is a dimensionless quantity.
- Term
Elastic Limit
- Meaning
The maximum stress that a material can withstand without undergoing permanent deformation.
- Term
Modulus of Elasticity
- Meaning
The constant of proportionality between stress and strain within the elastic limit, representing the stiffness of the material.
Learning objectives
Define stress and strain.
State and explain Hooke's Law.
Identify and explain the concept of the elastic limit.
Understand the relationship between stress, strain, and the modulus of elasticity.
Formulae
- Name
Hooke's Law
- Note
Where σ is stress, ε is strain, and E is the modulus of elasticity. Valid only within the elastic limit.
- Expression
σ = Eε
- Name
Stress
- Note
F is the applied force, A is the cross-sectional area over which the force acts.
- Expression
σ = F/A
- Name
Strain (Longitudinal)
- Note
ΔL is the change in length, L₀ is the original length.
- Expression
ε = ΔL/L₀
Prerequisites
Understanding of Force and Motion
Concept of Deformation
Basic understanding of Area
Common mistakes
Applying Hooke's Law beyond the elastic limit.
Confusing stress and strain.
Incorrectly calculating the modulus of elasticity.
Assuming Hooke's Law applies to all deformations, regardless of magnitude.
Keywords
Hooke's Law
Elastic Limit
Stress
Strain
Young's Modulus
Modulus of Rigidity
Bulk Modulus
Elasticity
Plasticity
Deformation
Practice preview
According to Hooke's Law, within the elastic limit, the stress is directly proportional to:…
easy
The elastic limit is the point up to which:…
easy
A spring is stretched by 2 cm when a force of 10 N is applied. If the spring obeys Hooke's Law, what force is required to stretch it by 5 cm?…
medium