Question

An aluminum wing on a passenger jet is 26 m long when the temperature is 17.1 degrees Celsius. Using eBook table 5.2, at what temperature (in degrees Celsius) would the wing be 1 mm shorter?

Answer 1

To determine the temperature at which the aluminum wing would be 1 mm shorter, we can use the concept of thermal expansion. By rearranging the equation for linear expansion and plugging in the given values, we find that the wing would be 1 mm shorter at a temperature of approximately 170.89°C.

Step-by-step explanation:

To determine the temperature at which the aluminum wing would be 1 mm shorter, we can use the concept of thermal expansion. The equation for linear expansion is ΔL = αLΔT, where ΔL is the change in length, α is the linear coefficient of expansion, L is the original length, and ΔT is the change in temperature.

In this case, we want to find the temperature at which the wing is 1 mm shorter, so we rearrange the equation to solve for ΔT: ΔT = ΔL / (αL)

Now we can substitute the given values: ΔL = 0.001 m, α = 2.3 x 10^-5 /°C, and L = 26 m. Plugging these values into the equation, we find: ΔT = (0.001 m) / (2.3 x 10^-5 /°C * 26 m) = 170.89°C. Therefore, the wing would be 1 mm shorter at a temperature of approximately 170.89°C.