8.0 INTRODUCTION TO ELASTICITY
Elasticity is the ability of a deformed material body to return to its original shape and size when the forces causing the deformation are removed. A body with this ability is said to behave (or respond) elastically.
ELASTIC LIMIT: The maximum stress that a material can withstand without permanent deformation. Beyond this limit, the material will not return to its original shape.
YIELD POINT: The point at which a material begins to deform plastically. At this stage, the material will not return to its original shape even after the stress is removed.
BREAKING POINT: The point at which a material fails and breaks under stress. This is the ultimate tensile strength of the material.
8.1 HOOKE’S LAW OF ELASTICITY
It states that the force exerted by a spring is directly proportional to the extension of the spring from its equilibrium position, provided that the elastic limit is not exceeded.
Mathematically,
F = ke
Where: F is the force,
k is the spring constant, and
e is the displacement or extension.
SPRING BALANCE AS A DEVICE FOR MEASURING FORCE: A device used to measure force or weight based on Hooke’s Law. It consists of a spring fixed at one end with a hook at the other end to hold the object being weighed.
WORK DONE PER UNIT VOLUME IN SPRINGS AND ELASTIC STRINGS: The work done on a spring is stored as potential energy.
Mathematically, the work done:
W = ½ke² or W = ½Fe
Where: k is the spring constant,
e is the extension,
F is the force applied.
8.2 STRESS AND STRAIN
STRESS: It is defined as the force applied per unit area of a material.
Mathematically,
Stress (σ) = Force (F) / Area (A)
Units of stress are Pascals (Pa) or N/m².
STRAIN: It is defined as the deformation or displacement of a material compared to its original length.
Mathematically,
Strain (ε) = Change in Length (ΔL) / Original Length (L₀)
Strain is a dimensionless quantity (no units).
8.3 YOUNG’S MODULUS
RELATIONSHIP BETWEEN STRESS AND STRAIN
Stress and strain are related through Young’s Modulus (E).
Young’s Modulus is defined as:
E = Stress / Strain
E = (F/A) / (ΔL/L₀)
Where: F is the force,
A is the cross-sectional area,
ΔL is the change in length, and
L₀ is the original length.
This relationship holds true within the elastic limit of the material.
Young’s Modulus: A measure of the stiffness of a solid material. It is defined as the ratio of tensile stress to tensile strain.
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