A horizontal rod with coefficient of linear expansion is attached at its ends to

Question

A horizontal rod with coefficient of linear expansion is attached at its ends to supports a fixed distance L0 apart when at temperature T0 , as shown in the top figure. The rod has a crack 1 3 L0 from the left end, and another crack 1 3 L0 from the right end. While rising to an unknown higher temperature T, the two cracks allow the rod to buckle upward, so the center section of the rod remains horizontal while rising a vertical distance x, as shown in the bottom figure. The three sections of the rod each remain straight. (a) Determine an equation for T in terms of the other given quantities. (b) Calculate the value of T if T0 = 25.0 °C, 6 16.0 10 / C = × , L0 = 1.00 m, and x = 8.00 mm.

I get an answer of 43 degrees Celsius, however that is not the correct answer.

Explanation / Answer

let the initial length = Lo

when temperature raises by temp of DT, length rises by Lo+x

change of length DL = L-L0 = x

from the def of coeffiecnrt of linear expansion of solids

Alpha = DL./(Lo*DT)

so equation DT = DL/(Lo Alpha)   

Final Temperature T2 = T1 + (DL/(Lo Alpha)

T2 = T1 + (x/Lo Alpha)

------------------------------------------------

T2 = 25 + (8e-3*/(6*16 e-6)

T2 = 108.33 deg C

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