Question

4) Uma barra de ferro, coeficiente de dilatação linear 12.10 −6 °C −1, possui um comprimento de 10 m a 10°C, se a barra é aquecida até 200°C, determine: a) A dilatação sofrida pela barra; b) O comprimento final da barra

Answer 1

$\mathrm{Seja\ uma\ barra\ de\ ferro\ tal\ que}\ \ell_0=10\ \text{m}.$

$\mathrm{Sua\ temperatura\ \acute{e}\ variada\ de\ 10^{\circ}C\ a\ 200^{\circ}C.}$

$\text{Sabe-se que}\ \alpha=12\times10^{-6}^{\circ}\mathrm{C^{-1}}.$

$\mathbf{a)}\ \mathbf{Dilata\c{c}\tilde{a}o\ da\ barra}\text{:}$

$\boxed{\Delta\ell=\ell_0\alpha\Delta\theta}\Longrightarrow \Delta\ell=10(12\times10^{-6})(200-10)$

$\Longrightarrow \Delta\ell=2.28\times10^{4}\times10^{-6}\ \therefore\ \boxed{\Delta\ell=0.0228\ \text{m}}$

$\mathbf{b)}\ \mathbf{Comprimento\ final\ da\ barra}\text{:}$

$\boxed{\ell=\ell_0+\Delta\ell}\Longrightarrow \ell=10+0.0228\ \therefore\ \boxed{\ell=10.0228\ \text{m}}$