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 sections to prevent buckling when the steel termally expands. 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: ∆L = 0.49cm ≈ 0.50cm

Therefore there should be 0.5 cm gap between each piece of steel.

Explanation:

Thermal expansion of steel is the increase in size of steel as a result of increased temperature. It can be represented by the mathematical expression:

∆L = L (k) ∆T ... 1

Where;

∆L is the change in length

L is the initial length

∆T is the change in temperature

k is the specific Linear expansion coefficient.

Given;

L = 12m

∆T = 50°C - 16°C = 34°C

k (for steel) = 1.2 * 10^-6 / C

Substituting the values into the equation 1

∆L = 12 * 34 * 12*10^-6

∆L = 4896 * 10^-6 m

∆L = 0.49cm ≈ 0.50cm

Therefore there should be 0.5 cm gap between each piece of steel.

Answer: gap required in track =

5.39millimeter{5.39mm}

Explanation: This is a linear expansivity problem.

Coefficient of Linear expansivity = {gap in lenght}/{{original lenght*.

{change in temperature}}

But coefficient of linear expansivity of steel = 13.2*EXP{-6}/degree Celsius.

Making change in lenght or gap subject of formula we have,

Gap = coefficient of linear expansivity*{{original lenght*{change in temperature}}

But,

Original lenght = 12m

Change in temperature = 50 - 16 = 34 degree Celsius.

Therefore,

Gap in lenght = 13.2*EXP{-6}*12*34=

=5.39*EXP{-3}meter

= 5.39mm