A load of 10 kg is suspended by a metal wire that is 3 m long and possesses a cross-sectional area of 4 mm ^2 . Determine the strain. The Young modulus of the metal is 2.0 10¹¹ N/m ^2 .

Step-by-step solution

The force applied on the wire is the weight of the load: F = mg = 10 9.8 = 98 N The cross-sectional area is: A = 4 mm ^2 = 4 10⁻⁶ m ^2 The formula for Young's modulus is: Y = Stress Strain = F / A Strain Rearranging for strain: Strain = F A Y Substituting the given values: Strain = 98 4 10⁻⁶ 2.0 10¹¹ Strain = 98 8 10^5 Strain = 12.25 10⁻⁵ = 1.225 10⁻⁴