ELASTIC PROPERTIES OF SOLID

CONTENT

1. Young’s Modulus Law of Elasticity
2. Work Done in Springs and Elastic String
3. 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.