Let’s solve numerical problems based on the Young modulus formula.
Young’s Modulus is the ratio of Longitudinal Stress and Longitudinal Strain. If it’s designated with Y then
Y = Longitudinal Stress / Longitudinal Strain = (F/A)/( ΔL /L) = (FL)/(A ΔL )
Numerical Problem based on Young modulus with solution
A force of 250N is applied to a steel wire of length 1.5m and diameter 0.60 mm.
Calculate the extension of the wire.
(Young modulus for mild steel = 2.1 x 1011 Pa)
Diameter = d = 0.6 mm = 0.6 x 10-3 m
Cross-sectional area of the wire A= π.(d/2)2= (22/7) . ( 0.6 x 10-3/2)2 = 2.83 x 10-7 m2
Force F = 250 N
L = 1.5 m
extension of the wire = ΔL = ?
Young modulus Y = 2.1 x 1011 Pa
Using the formula of Young modulus:
Y= (FL)/(A ΔL)
ΔL = (FL)/(A Y)
ΔL = (250 x 1.5)/( 2.83 x 10-7 x 2.1 x 1011 ) = 6.3 x 10-3 m = 6.3 mm
Hence, the extension of the wire = 6.3 mm