Elasticity
Stress, strain, Hooke's law, Young's, bulk and rigidity moduli, and elastic potential energy. (Physics › Properties of Bulk Matter, NEET UG syllabus.)
What is Elasticity?
The property of a material body by virtue of which it regains its original shape and size after the removal of deforming forces.
Key formula / rule: Stress
Key points
- Define and differentiate between stress and strain, including their types and units.
- State Hooke's Law and explain the concept of the elastic limit.
- Define and apply Young's Modulus, Bulk Modulus, and Rigidity Modulus in problem-solving.
- Calculate the elastic potential energy stored in a deformed body.
Common exam trap
Confusing stress with pressure: Stress is an internal restoring force, while pressure is an external normal force.
Definitions
- Term
Elasticity
- Meaning
The property of a material body by virtue of which it regains its original shape and size after the removal of deforming forces.
- Term
Stress
- Meaning
The internal restoring force developed per unit cross-sectional area of a deformed body. It is a measure of the intensity of internal forces acting within a deformable body.
- Term
Strain
- Meaning
The fractional change in the dimensions of a body produced by deforming forces. It is a measure of deformation.
- Term
Hooke's Law
- Meaning
Within the elastic limit, the stress developed in a body is directly proportional to the strain produced in it.
- Term
Elastic Limit
- Meaning
The maximum stress a material can withstand without undergoing permanent deformation. Beyond this limit, the material does not return to its original state.
- Term
Young's Modulus
- Meaning
The ratio of longitudinal stress to longitudinal strain, characterizing a material's resistance to changes in length.
- Term
Bulk Modulus
- Meaning
The ratio of normal stress (pressure) to volumetric strain, characterizing a material's resistance to changes in volume.
- Term
Rigidity Modulus
- Meaning
The ratio of tangential stress to shearing strain, characterizing a material's resistance to changes in shape.
Learning objectives
Define and differentiate between stress and strain, including their types and units.
State Hooke's Law and explain the concept of the elastic limit.
Define and apply Young's Modulus, Bulk Modulus, and Rigidity Modulus in problem-solving.
Calculate the elastic potential energy stored in a deformed body.
Analyze stress-strain curves for different materials.
Understand the factors affecting the elasticity of materials.
Formulae
- Name
Stress
- Note
F is the applied force, A is the cross-sectional area. SI unit: N/m² or Pascal (Pa).
- Expression
σ = F/A
- Name
Longitudinal Strain
- Note
ΔL is the change in length, L is the original length. Dimensionless.
- Expression
εL = ΔL/L
- Name
Volumetric Strain
- Note
ΔV is the change in volume, V is the original volume. Dimensionless.
- Expression
εV = ΔV/V
- Name
Shearing Strain
- Note
Δx is the relative displacement of parallel layers, h is the distance between layers. Also represented as the angle of shear in radians. Dimensionless.
- Expression
θ = Δx/h
- Name
Young's Modulus
- Note
Ratio of longitudinal stress to longitudinal strain. SI unit: Pa.
- Expression
Y = (F/A) / (ΔL/L)
- Name
Bulk Modulus
- Note
Ratio of normal stress (pressure P) to volumetric strain. The negative sign indicates that an increase in pressure causes a decrease in volume. SI unit: Pa.
- Expression
B = -P / (ΔV/V)
- Name
Rigidity Modulus
- Note
Ratio of tangential stress to shearing strain. SI unit: Pa.
- Expression
G = (Ftangential/A) / θ
- Name
Elastic Potential Energy (Stored in a stretched wire)
- Note
Energy stored when a body is deformed within its elastic limit. SI unit: Joule (J).
- Expression
U = (1/2) × F × ΔL = (1/2) × Y × (strain)² × Volume
- Name
Elastic Potential Energy Density
- Note
Energy stored per unit volume. SI unit: J/m³.
- Expression
u = (1/2) × Stress × Strain
Prerequisites
Basic understanding of force, area, and volume.
Concepts of pressure and density.
Knowledge of work and energy.
Common mistakes
Confusing stress with pressure: Stress is an internal restoring force, while pressure is an external normal force.
Incorrectly applying units: Stress and moduli have units of N/m², strain is dimensionless.
Forgetting the elastic limit: Hooke's Law is only valid within this limit.
Using incorrect formulas for different types of strain or moduli.
Misinterpreting 'more elastic': A material is more elastic if it resists deformation more strongly for a given stress (i.e., has a higher modulus of elasticity).
Keywords
Elasticity
Stress
Strain
Hooke's Law
Elastic Limit
Young's Modulus
Bulk Modulus
Rigidity Modulus
Elastic Potential Energy
Deforming Force
Practice preview
What is the SI unit of stress?…
easy
Which of the following materials is generally considered the most elastic?…
easy
The energy stored per unit volume in a stretched wire is given by:…
medium