Question
Calculate the compressional force required to prevent the metallic rod of length $l \mathrm{~cm}$ and cross-sectional area $A \mathrm{~cm}^{2}$ when heated through $t^{\circ} \mathrm{C}$, from expanding along lengthwise. The Young's modulus of elasticity of the metal is $E$ and mean coefficient of linear expansion is $\alpha$ per degree celsius:(a) EA\alphat(b) $\frac{E \text { A\alphat }}{(1+\alpha t)}$(c) $\frac{E A \alpha t}{(1-\alpha t)}$(d) El\alphat
Step 1
Step 1: The linear thermal expansion can be written as: \[L' = L(1 + \alpha t)\] where \(L'\) is the final length, \(L\) is the original length, \(\alpha\) is the coefficient of linear expansion, and \(t\) is the temperature difference. Show more…
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