An aluminum wing on a plane is 30.6 m long when the temperature is 20 oC. At what temperature would the wing be 0.06 m shorter
To solve this problem, we can use the formula for thermal expansion:
ΔL = α * L₀ * ΔT
where:
ΔL is the change in length
α is the coefficient of linear expansion
L₀ is the original length of the object
ΔT is the change in temperature
We want to find the temperature at which the wing is 0.06 m shorter, so we need to solve for ΔT.
Given:
L₀ = 30.6 m
ΔL = 0.06 m
ΔT = ?
First, we need to find the coefficient of linear expansion for aluminum. The coefficient of linear expansion for aluminum is approximately 2.3 x 10^-5 /°C.
Substituting the given values into the formula, we have:
ΔL = α * L₀ * ΔT
0.06 m = (2.3 x 10^-5 /°C) * 30.6 m * ΔT
Now we can solve for ΔT:
ΔT = 0.06 m / (2.3 x 10^-5 /°C) * 30.6 m
ΔT ≈ 0.935 °C
So, the wing would be 0.06 m shorter at a temperature approximately 0.935 °C.
To find the temperature at which the aluminum wing is 0.06 m shorter, we need to use the concept of thermal expansion. The formula for linear expansion is:
ΔL = αLΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length
ΔT is the change in temperature
In this case, we know the following information:
L = 30.6 m
ΔL = 0.06 m
To find the change in temperature (ΔT), we can rearrange the equation:
ΔT = ΔL / (αL)
Now, we need the coefficient of linear expansion (α) for aluminum. The coefficient of linear expansion for aluminum is approximately 22 × 10^-6 / oC.
Substituting the known information into the equation:
ΔT = 0.06 m / (22 × 10^-6 / oC * 30.6 m)
Calculating this:
ΔT = 0.06 / (0.000022 * 30.6)
ΔT ≈ 109.89 oC
Hence, the temperature at which the wing would be 0.06 m shorter is approximately 109.89 oC.
-80
(T - 20)*(thermal expansion coeff.)* 30.6 = -0.06
Look up the thermal expansion coefficient of aluminum, and solve for T. It will be less than 20 C.
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thexp.html