Physics Problem Help!?

Question

A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 15.700 m when the temperature is 21.2°C, what is the measured length when the temperature rises to 31.4°C? (Note: Do not neglect the expansion of the steel tape. Give your answer to three decimal places.)

Answer 1

aluminum support column. If the measured length is 15.700 m when the temperature is 21.2°C, what is the measured length when the temperature rises to 31.4°C?

Al: 23.1 µm/mK

steel:11.0 ~ 13.0 10-6/K, use average of 12

∆T = 31.4 - 21.2 = 10.2 C

differential expansion difference is 23-12 = 11 µm/mK

15.7m x 11 µm/mK x 10.2 C = 1761 e-6 m

total length = 15.700 + 0.001761 = 15.702 m

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Answer 2

What you need to do is look up the coefficients of linear thermal expansion of steel and also of aluminum.  The aluminum column will increase in length by an amount equal to a(Al) x dT, where a(Al) is the coefficient of linear expansion of aluminum and dT is the temperature change, in this case 10.2 C.

Then, remember that the steel tape will also increase an amount given by a(Steel) x 10.2, where a(Steel) is the coefficient of linear expansion of steel.  

Knowing these two numbers should make it easy to determine what measured length you will get.