First slide

Stress and strain

Question

When an elastic material with Young's modulus Y is subjected to a stretching stress s, the elastic energy stored per unit volume of the material

Moderate

A

Y s / 2
B

s² Y/2
C

s² / 2y
D

s / 2y

Solution

E = Energy stored per unit volume
$= \frac{1}{2} \times stress \times strain = \frac{1}{2} \times s \times strain$
Further. strain $= \frac{stress}{Y} = \frac{s}{Y}$
$∴ E = \frac{1}{2} \times s \times \frac{s}{Y} = \frac{s^{2}}{2 Y}$

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