Verified answer

An aluminum wing is 30 m long when its 20ºC.

At what temp. would the the wing be 5 cm shorter?

You have not provided enough information. You have to have some function that relates the

original length of the material, the expansion (or contraction) amount, and the temperature

difference. A constant of proportionality should a part of the function, as well. This constant

of proportionality is called the coefficient of linear expansion and is indicated by the Greek

letter α (alpha).

The general expansion formula can be expressed as:

e = αL∆t

Where:

e = expansion

L = original length

∆t = change in temperature

Given:

e = -5 cm = -0.05 m

α = 22.2 x 10^-6 (for aluminum)

L = 30 m

∆t = ?

We have to find the change in temperature in order to determine the temperature that will

cause the wing to shrink by 5 cm. Therefore, we have to rearrange the equation to make

∆t the unknown.

∆t = e/αL = -0.05/(22.2 x 10^-6)(30) = -75

∆t = -75°C

The temperature that will cause the wing to contract by 5 cm is

is given by 20°C - 75°C = -55°C

New t = -55°C

Lt = L0*(1 + a*t) where a = coefficient of linear expansion and t = difference in temperature in °C to a first approximation. Lt = 30 - 0.05 = 29.95 and L0 = 30;

a = 23.1 x 10^-6

29.95/30 = 1 + 0.0000231*t

t = - 72 °C.

This temperature is relevant because at high altitudes, the temperature is low and around - 78 °C--I remember that I did see this on a Gulf Air flight.