Question

a) A thermo gate consists of a 6061-T6-aluminum plate ($\alpha = 24 \times 10^{-6} / \text{C}$, E = 68.9 GPa) from A-B and a Am-1004-T61-magnesium plate ($\alpha = 26 \times 10^{-6} / \text{C}$, E = 44.7 GPa) from C-D. Each have a width of 15 mm and are fixed at their ends. If the gap between them is 1.5 mm when the temperature is $T_1 = 25^\circ \text{C}$, determine the temperature required to just close the gap. b) What is the axial force in each plate if the temperature becomes $T_2 = 100^\circ \text{C}$?

          a) A thermo gate consists of a 6061-T6-aluminum plate ($\alpha = 24 \times 10^{-6} / \text{C}$, E = 68.9 GPa) from
A-B and a Am-1004-T61-magnesium plate ($\alpha = 26 \times 10^{-6} / \text{C}$, E = 44.7 GPa) from C-D. Each
have a width of 15 mm and are fixed at their ends. If the gap between them is 1.5 mm when
the temperature is $T_1 = 25^\circ \text{C}$, determine the temperature required to just close the gap.
b) What is the axial force in each plate if the temperature becomes $T_2 = 100^\circ \text{C}$?

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a) A thermo gate consists of a 6061-T6-aluminum plate (α = 24 × 10^-6 / C, E = 68.9 GPa) from
A-B and a Am-1004-T61-magnesium plate (α = 26 × 10^-6 / C, E = 44.7 GPa) from C-D. Each
have a width of 15 mm and are fixed at their ends. If the gap between them is 1.5 mm when
the temperature is T1 = 25^∘C, determine the temperature required to just close the gap.
b) What is the axial force in each plate if the temperature becomes T2 = 100^∘C?

Added by Anthony C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sparsha S

Step 1

The change in length for the aluminum plate can be calculated using the formula: ΔL = αLΔT where ΔL is the change in length, α is the coefficient of thermal expansion, L is the original length, and ΔT is the change in temperature. For the aluminum Show more…

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A thermo gate consists of a 6061-T6-aluminum plate (Î± = 24x10-6 / Â°C, E = 68.9 GPa) from A-B and an AM-1004-T61-magnesium plate (Î± = 26x10-6 / Â°C, E = 44.7 GPa) from C-D. Each has a width of 15 mm and is fixed at their ends. If the gap between them is 1.5 mm when the temperature is T1 = 25Â°C, determine the temperature required to just close the gap. b) What is the axial force in each plate if the temperature becomes T2 = 100Â°C? 10 mm 10 mm B D 600 mm 400 mm -1.5 mm

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