Question

A steel bar is 10 mm diameter and 2 m long. It stretched with a force of 20 kN and extends by 0.2 mm. Calculate the stress and strain. What is the Young’s modulus of the steel bar?

Answer 1

Answer:

2.5 * 10^12 Nm-2

Explanation:

Stretching force = 20 * 10^3 N

diameter = 10 * 10^-3 m

extension = 0.2 * 10^-3 m

length of bar = 2m

Young Modulus = stress/strain

stress = Force/Area

Strain = extension/length

Young Modulus = Force/Area/extension/length

But area = πr^2 = 3.142 * (5 *10^-3)^2 = 7.9 * 10^-5 m^2

Stress = 20 * 10^3/7.9 * 10^-5  = 2.5 * 10^8 Nm-2

Strain = 0.2 * 10^-3/2 = 1 * 10^-4

Young Modulus = 2.5 * 10^8/1 * 10^-4  

Young Modulus =  2.5 * 10^12 Nm-2