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?

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,

Here,

= Initial Length

= Coefficient of linear expansion of steel

= Change in temperature (Initial and final)

Our values are,

Given that the length of each rail is

Initial temperature is

final temperature is

Coefficient of linear expansion of steel is

Replacing,

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