Answer to Question #241169 in Physics for ren

Question

A steel railroad track has a length of 30 m when the temperature is 0 oC. (a) What is its length on a hot day when the temperature is 40 oC. (b) Suppose the track is nailed down so that it can’t expand. What stress results in the track due to the temperature change?

Answer 1

The length on a hot day is

$$L=L_0(1+\alpha T)=\\=30(1+(12·10^{-6})40)=30.0144\text{ m}.$$

The stress the track would experience if not allowed to expand is

$$\sigma=E\epsilon=E·\frac{L-L_0}{L_0}=\\\space\\ =(200·10^{9})·\frac{30.0144-30}{30}=96·10^{6}\text{ Pa}.$$