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.