A steel railroad track has a length of 33 m when the temperature is −2 ◦C. What is the increase in the length of the rail on a hot day when the temperature is 39 ◦C? The linear expansion coefficient of steel is 11 × 10−6 ( ◦C)−1 . Answer in units of m.

0.0149 m

Explanation:

When a solid material is heated, it expands; in particular, its length increases according to the equation:

where

is the increase in length

is the linear expansion coefficient

is the original length of the material

is the increase in temperature

In this problem:

is the original length of the steel railroad track

is the linear expansion coefficient of steel

is the change in temperature of the track

Therefore, the increase in length is:

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it