aluminum jet wing is 30m long when its temperature is 20deg c.At what temperature would the wing be 5cm(0.05m) shorter

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To determine the temperature at which the aluminum jet wing would be 5 cm shorter, we need to use the coefficient of thermal expansion of aluminum. The coefficient of thermal expansion measures how a material expands or contracts with changes in temperature.

First, we need to find the change in length of the jet wing. This can be calculated using the formula:

ΔL = α * L * ΔT

Where:
ΔL is the change in length
α is the coefficient of thermal expansion
L is the original length
ΔT is the change in temperature

In this case, we are given the original length (L = 30 m) and the change in length (ΔL = 0.05 m). We need to solve for the change in temperature (ΔT) when the wing is 0.05 m shorter.

The formula can be rearranged as:

ΔT = ΔL / (α * L)

Next, we need to find the coefficient of thermal expansion for aluminum. The coefficient of thermal expansion for aluminum is approximately 23 x 10^-6 per degree Celsius.

Plugging in the values into the formula:

ΔT = 0.05 m / (23 x 10^-6 /°C * 30 m)

Calculating the expression:

ΔT = 0.05 m / (0.000023 /°C * 30 m)

Simplifying the units:

ΔT = 0.05 m / (0.00069 /°C)

Dividing:

ΔT ≈ 72.46 °C

Therefore, the aluminum jet wing would be 5 cm shorter at a temperature approximately 72.46 °C higher than the initial temperature of 20 °C.

change in length /length = coef of expansion * change in temp

.05/30 = coef * (20 -T)
look up coefficient for Al, solve for T