ELASTIC PROPERTIES OF SOLID
CONTENT
- Young’s Modulus Law of Elasticity
- Work Done in Springs and Elastic String
- Elastic Potential Energy
Young’s Modulus Law of Elasticity
Suppose a wire of length ℓ (m) and cross-sectional area A (m2) is extended through e (m) by a force F (N).
(a) The ratio of the force to the area, F/A is called the stress or ‘tensile’ of the elastic material.
Stress = \(\frac{F}{A}\)………(1)
(b) The ratio of the extension, e to the original length, ℓ of the wire i.e e is called the tensile strain of the wire.
\ Strain = \(\frac{e}{ℓ}\)……… (2)
From (1) F = stress × A ……….(3)
From (2) e = Strain × ℓ ………(4)
By Hooke’s law, F = ke
\ Stress × A = k × Strain × ℓ
\ \(\frac{Stress}{A}\) = kℓ × strain \(\frac{Stress}{A}\)
\ Stress = k1 strain where k1 =
\(\frac{Constant}{A}\) = kℓ
Stress = k1 ……….(5)
Strain
OR
Stress a Strain
Hence Hooke’s law can also be stated as follows:
The tensile stress of the material is directly proportional to its tensile strain provided the elastic limit is not exceeded
The constant of proportionality, k1 (see equation (5) above) is called.
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