I\'m unsure how to figure out this question: The supersonic aircraft Concorde ha

Question

I'm unsure how to figure out this question:

The supersonic aircraft Concorde has a length of 62.6 when sitting on the ground on a typical day when the temperature is 14.0. The Concorde is primarily made of aluminum. In flight at twice the speed of sound, friction with the air warms the Concorde's skin and causes the aircraft to lengthen by 25.0 . (The passenger cabin is on rollers, so the airplane expands around the passenger cabin.)

Take the coefficient of linear expansion for aluminum to be = 2.40×10-5.


What is the temperature of the Concorde's skin in flight?

Explanation / Answer

The elongation l = l1 T

where l1 is initial length, is coefficient ofthermal expansion and T is increase in temperature.

0.25 = 62.6 X 2.40×105X T
T = 166.4 C
So final temperature is 14 + 166.4 = 180.4 C

(I think that the words "twice the speed of sound" have been givenjust to create some confusion)

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