A steel wire with a cross-sectional area of 0.5 mm ^2 is secured between two fixed supports. The wire is just taut at 20^ C . Calculate the tension in the wire when the temperature drops to 0^ C . The coefficient of linear expansion for steel is 1.2 10⁻⁵ ^ C ⁻¹ and its Young's modulus is 2.0 10¹¹ N m ⁻² .

Step-by-step solution

The thermal stress developed in the wire due to a change in temperature is given by F A = Y T The tension in the wire is F = Y A T Given: Y = 2.0 10¹¹ N m ⁻² A = 0.5 mm ^2 = 0.5 10⁻⁶ m ^2 = 1.2 10⁻⁵ ^ C ⁻¹ T = 20^ C - 0^ C = 20^ C Substituting the values: F = (2.0 10¹¹) (0.5 10⁻⁶) (1.2 10⁻⁵) 20 F = 1.0 10^5 1.2 10⁻⁵ 20 F = 1.2 20 = 24 N