A steel rod is clamped rigidly at both ends. At 20^ C , the rod experiences zero tension. If the temperature increases to 100^ C , determine the force exerted by the rod on one of the clamps. The cross-sectional area of the rod is 2.00 mm ^2 . The coefficient of linear expansion of steel is 12.0 10⁻⁶ ^ C⁻¹ and the Young's modulus of steel is 2.00 10¹¹ N m ⁻² .

Step-by-step solution

The thermal stress developed in a rigidly clamped rod due to a change in temperature is given by = Y T . The force exerted by the rod on the clamps is F = A = Y A T . Substituting the given values Y = 2.00 10¹¹ N m ⁻² , A = 2.00 10⁻⁶ m ^2 , = 12.0 10⁻⁶ ^ C ⁻¹ , and T = 100^ C - 20^ C = 80^ C : F = (2.00 10¹¹) (2.00 10⁻⁶) (12.0 10⁻⁶) 80 F = 4 12 80 10⁻¹ F = 384 N