Question

Older railroad tracks in the U.S. are made of 12-m-long pieces of steel. When the tracks are laid, gaps are left between the sections to prevent buckling when the steel thermally expands.
1.If a track is laid at 16°C, how large should the gaps be if the track is not to buckle when the temperature is as high as 50°C?

Answer 1

To solve this problem we will apply the concepts related to linear expansion in bodies when there is a temperature difference. For this case, this linear relationship is given by the function,

$\Delta L = L_0 \alpha \Delta T$

Here,

$L_ 0$= Initial Length

$\alpha$ = Coefficient of linear expansion of steel

$\Delta T$ = Change in temperature (Initial and final)

Our values are,

Given that the length of each rail is $L = 12.0 m$

Initial temperature is $T_i = 16\°C$

final temperature is $T_f = 50\°C$

Coefficient of linear expansion of steel is $\alpha = 12*10^{-6} /\°C$

Replacing,

$\Delta L = L_0 \alpha \Delta T$

$\Delta L = (12.0m)(12*10^{-6})(50-16)$

$\Delta L = 0.004896m$

$\Delta L = 4.896mm$

Therefore the gaps will be 4.896mm langer than its initial length.