aluminum jet wing is 30m long when its temperature is 20deg c.At what temperature would the wing be 5cm(0.05m) shorter
If you’re taking the time to respond why not give a full response? Many of us are stuck at where you left off and don’t know how to continue.
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