An aluminum wing on a passenger jet is 40m long when it's temperature is 15 degrees C. At what temperature would the wing be 3cm (0.03m) shorter? The coefficient of linear expansion for aluminum being used is (25 * 10^-6). I keep plugging this into an equation for thermal expansion, but I am not getting numbers that look right. [change in L (0.03) = (25 * 10^-6)(40)(change in T, T-15)]
Since change in length = dL = L0*alpha*dT
given, dL = L(0.03) = -0.03 (negative signs represents decrease in length)
L0 = 40 m
alpha = 25*10^-6
dT = T - T0 = T - 15 degC
So, -0.03 = 40*(25*10^-6)*(T - 15)
T - 15 = -0.03/(40*25*10^-6) = -30
T = -30+15
T = -15 degC
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