A steel bar with a cross-sectional area of 1.00 × 10^-4 m² is heated to 100°C and then it is clamped at both ends with clamps that are 2.0 m apart. When the bar cools to 20°C what is the force exerted by the bar on the clamps? The coefficient of thermal expansion of steel is
12 × 10^-6 K^-1 and Young's modulus for steel is 20 × 10¹⁰ N/m².

Question

Quizplus · Accepted Answer

The change in length of the bar is:$$\Delta L = \alpha L_i \Delta T = (12 	imes 10^{-6} 	ext{ K}^{-1})(2.0 	ext{ m})(100\degree	ext{C} - 20\degree	ext{C}) = 1.92 	imes 10^{-3} 	ext{ m}$$The force exerted by the bar on the clamps is:$$F = Y\frac{\Delta L}{L_i}A = (20 	imes 10^{10} 	ext{ N/m}^2)\frac{1.92 	imes 10^{-3} 	ext{ m}}{2.0 	ext{ m}}(1.00 	imes 10^{-4} 	ext{ m}^2) = 1.92 	imes 10^4 	ext{ N}$$

A Steel Bar with a Cross-Sectional Area of 1