Question

Consider the program dimension program above: 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?

a) 15.9°C
b) 17.8°C
c) 19.3°C
d) 20.5°C

Answer 1

To calculate the change in temperature needed for the aluminum wing to be 1 mm shorter, we can use the concept of thermal expansion. From ebook table 5.2, we can find the coefficient of linear expansion for aluminum, which is approximately 24 x 10^-6 °C^-1.

Step-by-step explanation:

To calculate the change in temperature needed for the aluminum wing to be 1 mm shorter, we can use the concept of thermal expansion. From ebook table 5.2, we can find the coefficient of linear expansion for aluminum, which is approximately 24 x 10-6 °C-1. We can set up the equation:

ΔL = αLΔT

Where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature. We can solve for ΔT:

ΔT = ΔL / (αL)

Plugging in the given values, ΔL = 1 mm = 0.001 m, α = 24 x 10-6 °C-1, and L = 26 m, we can calculate ΔT:

ΔT = 0.001 m / (24 x 10-6 °C-1 * 26 m) ≈ 1.92 °C

Therefore, the temperature at which the wing would be 1 mm shorter is approximately 1.92 °C higher than the original temperature of 17.1 °C. Adding these values together, we get approximately 19.02 °C.