An aluminum wing on a passenger jet is 30 m long when its temperature is 20°C. At what temperature would the wing be 5 cm (0.05 m) shorter?

To solve this problem, we can use the concept of thermal expansion. When an object, such as the aluminum wing, undergoes a change in temperature, its dimensions can change.

The formula for linear thermal expansion is given by:
ΔL = α * L * ΔT

Where:
ΔL is the change in length
α is the coefficient of linear expansion of the material (in this case, aluminum)
L is the original length of the object
ΔT is the change in temperature

We can rearrange the formula to solve for the change in temperature (ΔT):
ΔT = ΔL / (α * L)

To solve for the change in temperature required for the wing to be 5 cm (0.05 m) shorter, we need to substitute the given values:
ΔL = -0.05 m (negative sign indicates a decrease in length)
L = 30 m (original length of the wing)

The coefficient of linear expansion for aluminum is approximately 2.3 × 10^(-5) °C^(-1). So, substituting the values in the formula, we get:
ΔT = -0.05 m / (2.3 × 10^(-5) °C^(-1) * 30 m)
≈ -0.05 m / (6.9 x 10^(-4) °C^(-1) m)
≈ -72.46 °C

Therefore, the wing would need to be at a temperature approximately 72.46°C lower for it to be 5 cm (0.05 m) shorter.