Question

An aluminum wing on a passenger jet is 25 m long when its temperature is 21°C. At what temperature would the wing be 6 cm (0.06 m) shorter?

Answer 1

The temperature at which the wing would be shorter is
`- 80.69^(\circ)C`

Solution:

The original length of the Aluminium wing,
`l_(w) = 25 m`

Temperature, T =
`21^(\circ)C`

Change in the wing's length,
`\Delta l_(w) = 0.06 m`

Also, for Aluminium, at temperature between
`20^(\circ)C` to
`100^(\circ)C`, the linear expansion coefficient,
`\alpha = 23.6* 10^(- 6)/^(\circ)C`

Now, Change in length is given by:

`\Delta l_(w) = l_(w)\alpha \Delta T`

`0.06 = 25* 23.6* 10^(- 6)\(T - T')`

`(0.06)/(5.9* 10^(- 4)) = 21^(\circ)C _ T'`

`T' = - 80.69^(\circ)C`