Bimetallic strip

A metal strip of length \(l_0 = 20 \,\text{cm}\) consists of a layer of iron (Fe) and a layer of zinc (Zn), which are welded together with each having a thickness of \(d = 2\,\text{mm}\). At a temperature of \(T = 0\, ^\circ\text{C}\), the bimetallic strip is completely straight.

What is the radius of the curvature \(r\) of the strip at a temperature of \(T = 100\, ^\circ\text{C}?\)

The respective thermal expansion coefficients of zinc and iron are

\[\alpha_\text{Zn} = 3\cdot 10^{-5}/^\circ\text{C},\quad \alpha_\text{Fe} = 1\cdot 10^{-5}/^\circ\text{C}.\]

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