Steven W. answered • 09/25/16

Physics Ph.D., *professional*, easygoing, 4000+ hours tutoring physics

Hi Shish!

There is a little bit of an ambiguity in this problem. It seems set up to work with one-dimensional thermal expansion (since we are only told about the length of the bridge). However, we are not told at which temperature the bridge is 518 m. I might guess it would be designed to be some minimum length at the coldest conceivable temperature, since it might be very dangerous to have a bridge contract too much. So I will assume that 518 m is the bridge's original length when it is - 20 C.

[NOTE: as an alternative, we could compute the

*fractional*change in the bridge's length between -20 C and 35 C, but then we would not need to know what the -20 C length of the bridge was).The formula for one-dimensional thermal expansion is:

ΔL = L

_{o}αΔTwhere

ΔL = change in length of the bridge over indicated temperature change

L

_{o}= original length of bridge at starting temperatureΔT = temperature change (usually in deg C or K)

α = coefficient of thermal expansion (temp units must match ΔT)

The coefficient of thermal expansion is an empirical quantity, measured experimentally, that you can look up in tables for various materials, such as steel. It is technically temperature dependent, but relatively constant over a fairly wide range of everyday temperatures (a value at 20 C is usually quoted in fundamental problems). For steel, I find a tabular value of α =12 x 10

^{-6}per K)With this, we can calculate:

ΔL = (518 m)(12 x 10

^{-6}per K)(35 C - (-20 K)) = 518(12 x 10^{-6})(55) = 0.34 mI am not sure if an engineering class is going to ask for more details; but, with the information given, this is a result suitable for a fundamental problem.

I hope this helps! Just let me know if you have more questions or information about this.