S.
Contents
No.
1. Title Page
2. Certificate
3. Acknowledgement
4. Index
5. Introduction
6. Objective of the Project
7. Theory of Elasticity
8. Stress and Its Types
9. Strain and Its Types
10. Hooke’s Law
11. Young’s Modulus
12. Bulk and Shear Modulus
13. Stress-Strain Curve
14. Poisson’s Ratio
15. Factors Affecting Elasticity
16. Real-Life Applications
Experiment: Determining Young’s
17. Modulus of a Wire
18. Observations and Calculations
19. Result and Conclusion
20. Precautions
21. Bibliography
Introduction
Elasticity is the ability of an object or
material to resume its normal shape after
being stretched or compressed. It is one of
the most important physical properties of
solids. The study of elasticity explains how
forces applied to objects cause them to
deform and how they return to their original
state when the force is removed.
It plays a critical role in fields such as civil
engineering, materials science, and even
biomechanics. Structures like bridges,
buildings, and machines rely on materials
that behave predictably under stress and
strain.
[Image Placeholder]
Leave space here for an image showing a
stretched spring or elastic band.
Objective of the Project
• To study the basic principles of elasticity.
• To understand stress, strain, and their
relationship.
• To analyze different types of moduli:
Young’s, Bulk, and Shear.
• To practically determine the Young’s
Modulus of a wire using weights and
measurements.
Theory of Elasticity
When a body is subjected to external force, it
undergoes deformation. If the body regains
its original shape and size after the removal
of the force, it is said to be elastic.
Within the elastic limit, the deformation is
reversible. Beyond that, the material enters
the plastic region, where it gets permanently
deformed.
Stress and Its Types
Stress is the restoring force per unit area
developed in the body.
Formula: Stress = Force / Area
Unit: Pascal (Pa)
Types of Stress:
• Tensile Stress – Pulling the material apart
• Compressive Stress – Pushing the
material together
• Shear Stress – Forces act tangentially
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Leave space for a diagram showing tensile,
compressive, and shear stress.
Strain and Its Types
Strain is the measure of deformation and is
dimensionless.
Formula: Strain = Change in dimension /
Original dimension
Types of Strain:
• Longitudinal Strain – ΔL / L
• Volumetric Strain – ΔV / V
• Shear Strain – Angular deformation
Hooke’s Law
According to Hooke’s Law, within the elastic
limit, stress is directly proportional to strain.
Mathematical Form:
Stress ∝ Strain
Or, σ = E × ε, where:
σ = stress, ε = strain, E = Young’s Modulus
The law is valid only up to the proportional
limit of the material.
[Image Placeholder]
Leave space for a stress-strain graph
showing Hooke’s Law.
Young’s Modulus
Young’s modulus measures stiffness in a
material when it is stretched or compressed.
Formula:
E = (Stress) / (Strain) = (F × L) / (A × ΔL)
Where:
F = Force applied,
L = Original length,
A = Area of cross-section,
ΔL = Change in length
Unit: Pascal (Pa)
Bulk Modulus and Shear Modulus
Bulk Modulus (K):
Resistance to uniform compression.
Formula:
K = -ΔP / (ΔV / V)
High bulk modulus = less compressible
Shear Modulus (G):
Resistance to tangential forces.
Formula:
G = Shear Stress / Shear Strain
Stress-Strain Curve
The stress-strain curve reveals the behavior
of a material when loaded:
1. Proportional Limit – Linear, obeys
Hooke’s Law
2. Elastic Limit – Last point of elasticity
3. Yield Point – Begins to deform plastically
4. Ultimate Stress – Maximum stress
5. Breaking Point – Failure
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Leave space for a labeled stress-strain curve.
Poisson’s Ratio
Poisson’s Ratio (ν): Ratio of lateral strain to
longitudinal strain
Formula:
ν = Lateral Strain / Longitudinal Strain
Typical value for metals: 0.25–0.35
Factors Affecting Elasticity
• Material type: Metals are more elastic
• Temperature: Increases reduce elasticity
• Impurities: Reduce elasticity
• Time of force applied: Gradual force
preserves elasticity better
Applications of Elasticity
• Design of bridges, buildings, springs
• Sports equipment
• Biomedical: tendons and ligaments
• Vehicle suspensions
• Mechanical sensors and measuring tools
Experiment: Determining Young’s Modulus of
a Wire
Aim:
To determine the Young’s modulus of a
metallic wire using Searle’s apparatus.
Apparatus Required:
• Searle’s apparatus
• Micrometer screw gauge
• Vernier calipers
• Meter scale
• Weights and hanger
• Metallic wire (copper or steel)
Theory:
Young’s modulus is given by:
E = (MgL) / (πr² × ΔL)
Where:
M = Mass added
g = Gravity (9.8 m/s²)
L = Length of wire
r = Radius of wire
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Leave space for diagram of experimental
setup.
Observations and Calculations
• Length of wire (L): 1.5 m
• Radius of wire (r): 0.25 mm = 0.25 × 10⁻³ m
• Area of cross-section (A): πr² = 1.96 × 10⁻⁷
m²
• Extension (ΔL): 1 mm = 1 × 10⁻³ m
• Weight added (M): 1 kg
Using formula:
E = (1 × 9.8 × 1.5) / (1.96 × 10⁻⁷ × 1 × 10⁻³)
E ≈ 7.5 × 10¹⁰ Pa
Result and Conclusion
• The Young’s modulus of the given wire is
approximately 7.5 × 10¹⁰ Pascal.
• The experiment successfully
demonstrated the linear relationship
between stress and strain in the elastic
region.
Precautions
• Wire should be free from kinks.
• Take all readings without parallax error.
• Use uniform weights.
• The wire should be hung vertically and
kept taut.
Bibliography
1. NCERT Physics Class XI
2. H.C. Verma – Concepts of Physics
3. Physicslab.org
4. Khan Academy
5. School Physics Practical Manual
