(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A bimetallic strip is made of metal which has coefficient of thermal expansion is equal to α_{1}and the other's is equal to α_{2}at the temperature of T_{0}. The temperature is increased to T_{0}+ ΔT (ΔT > 0). The strip curves as shown in the figure. If both strip have the same width of d. Find r_{1}measured from the center of the curve to the center of the strip as shown in the figure

2. Relevant equations

1) radian is (Length of the curve)/(Radius)

2) Using the following estimation

(1 + x)^{-1}≈ 1-x and (1 + ax)(1+bx) ≈ 1+(a+b)x for x << 1

3. The attempt at a solution

α_{1}strip expansion is L_{0}(1 + α_{1}ΔT) for the length

and d(1 + α_{1}ΔT) for the width

α_{2}strip expansion is L_{0}(1 + α_{2}ΔT) for the length

and d(1 + α_{2}ΔT) for the width

Multiplying radian with radius, the result should be the curve length

r_{1}θ = L_{0}(1 + α_{1}ΔT)

r_{2}θ = L_{0}(1 + α_{2}ΔT)

r_{2}= r_{1}+ d(2 + α_{1}ΔT + α_{2}ΔT)/2

Is that correct?

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# Homework Help: Thermal expansion of bimetallic strip

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