# A classical mechanics problem by Jaber Al-arbash

At a temperature of $$60 ^\circ F$$, a 0.04 in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [ $$\alpha = 12.5 \times 10^{-6} / ^\circ F$$ ] bar with a width of 3 in and a thickness of 0.75 in. Bar (2) [ $$\alpha = 9.6 \times 10^{-6} / ^\circ F$$ ] bar with a width of 2 in and a thickness of 0.75 in.

Assume the supports at $$A$$ and $$C$$ are rigid. What is the lowest temperature at which the two bars contact each other?

Equations to be used:

a) Elongation or lengthening $$\delta = \alpha \Delta TL$$.

b) $$\delta_1 + \delta_2 =0.04$$.

Note: Since there is a gap of 0.04 in between the two bars, the sum of the elongations of bar (1) and (2) is given as shown in equation (b).

Symbols:

$$\alpha$$: Thermal expansion of a bar

$$L$$: Length

$$T$$: Temperature

$$\delta$$: Elongation.

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