A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600 10⁻⁶ m ^3 . The elastic potential energy stored in the wire in stretched condition would be _______ J. (Given Young modulus of copper = 1.1 10¹¹ N/m ^2 )

Step-by-step solution

Given parameters: L = 3 m L = 3 10⁻³ m V = 600 10⁻⁶ m ^3 Y = 1.1 10¹¹ N/m ^2 Strain is given by: Strain = L L = 3 10⁻³ 3 = 10⁻³ Elastic potential energy stored in the wire is: U = 1 2 Stress Strain Volume Since Stress = Y Strain : U = 1 2 Y ( Strain )^2 V Substituting the values: U = 1 2 (1.1 10¹¹) (10⁻³)^2 (600 10⁻⁶) U = 1 2 1.1 10¹¹ 10⁻⁶ 600 10⁻⁶ U = 1 2 1.1 600 10⁻¹ U = 1 2 66 = 33 J Answer: 33