12.5. Elasticity - 1

A wire of length 2 m and area of cross section 10^-4 m² is stretched by a load 102 kg. The wire will stretched by 0.1 cm

Calculate

a.     Longitudinal stress

b.     Longitudinal strain

c.      Young’s modulus of wire

Given-

Original length                  =       L        = 2m

Area of cross section         =       A       = 10^-4 m²

Load attached                    =       M      = 102 kg

Change in length               =       l         = 0.1 cm     = 0.1 X 10^-2 m

 Longitudinal stress           =       ?

Longitudinal strain            =       ?       

Young’s modulus of wire   =       ?

Stress

The stress can be defined as internal elastic restoring force per unit cross sectional area of body.

Or in other words,

Applied force per unit cross sectional area of body.

Longitudinal Stress = ( applied force ) / (area of cross section )

Longitudinal Stress = F / A

Longitudinal Stress = ( M g ) / (π r²)

Longitudinal Stress = ( 102 X 9.8 ) / ( 10^-4 )

Longitudinal Stress = 1 X 10⁷ N / m²

Strain

The strain can be defined as change in dimension per unit original dimension.

 Longitudinal strain

Longitudinal strain is the ratio of change in length to original length

Longitudinal strain = (change in length ) / ( original length )

Longitudinal strain = l / L

Longitudinal strain = ( 0.1 X 10^-2 ) / 2

Longitudinal strain = 5 X 10^-4

Young’s modulus

Young’s modulus is defined as the ratio of longitudinal stress to longitudinal strain.

Young’s modulus =       Y       = ( Longitudinal Stress ) / (Longitudinal Strain )

Young’s modulus =       Y       = (1 X 10⁷ ) / (5 X 10^-4)

Young’s modulus =      Y       = 2 X 10¹⁰ N / m²