An aluminum wing on a passenger jet is 38 mlong when its temperature is 23°C.At what temperature would the wing be 2 cm (0.02 m) shorter?

To find the temperature at which the aluminum wing would be 2 cm shorter, we can use the concept of thermal expansion.

The formula for thermal expansion is given by:
ΔL = αLΔT

where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length of the object
ΔT is the change in temperature

In this case, we know the original length of the wing (L = 38 m), the change in length (ΔL = -0.02 m), and the original temperature (23°C). We need to find the change in temperature (ΔT) at which the wing would be 2 cm shorter.

First, we need to find the coefficient of linear expansion (α) for aluminum. The coefficient of linear expansion for aluminum is approximately 23 × 10^(-6) °C^(-1).

Now, let's rearrange the formula to solve for ΔT:
ΔT = (ΔL) / (αL)

Substituting the values, we have:
ΔT = (-0.02 m) / (23 × 10^(-6) °C^(-1) * 38 m)

Calculating this, we find:
ΔT ≈ -18.3 °C

Hence, the aluminum wing would be 2 cm shorter at a temperature approximately 18.3 degrees Celsius below the original temperature of 23°C.