temperature question

Question

An aluminum wing on a passenger jet is 38 m

 long when its temperature is 22°C.

 At what temperature would the wing be 7 cm (0.07 m) shorter?

Answer 1

Background

Materials expand and contract based on the temperature of their surroundings, and the equation that relates this expansion and contraction with Temperature is ΔL = αLΔT, where L is the length of the object, T is the temperature, and α is the linear coefficient of thermal expansion. α measures how much an object contracts or expands per degree of change in temperature. Now we can list our knowns and unknowns.

Knowns

α: 2.3*10-5 meters/(meters*C)

Note: This number was pulled from the internet as this question hasn't given it, but usually, questions will give constants such as the linear coefficient of thermal expansion for various materials)

L = 38 m

ΔL = -7cm = -0.07m

Note, the change in length is negative since the wing gets shorter

Unknowns

ΔT = Final Temperature - Initial Temperature

Initial Temperature = 22C

Solving

Rearranging for ΔT, our equation gives us

ΔT = ΔL/αL

Plugging in the numbers, we get

ΔT = -0.07/(2.3*10^-5*38) = -80.1 C

Now that we know ΔT, we can find the final temperature at which the wing is 7 cm shorter by using this equation

ΔT = Final Temperature - Initial Temperature

Rearranging for Final Temperature, we get

Final Temperature = Initial Temperature + ΔT

Plugging in numbers, we get

Final Temperature = 22 + (-80.1) = -58.1 C

The Temperature at which the wing would be 7cm shorter is -58.1 C