Question

If a 41 m steel footbridge experiences extreme temperatures between ?11?C and 41?C, what is the range in size of this bridge if it measures exactly 41 m at 24?C? (Steel has a coefficient of linear expansion of 1.1 × 10?5 /?C) Answer in units of m.

Answer 1

The size range is 40,994 to 41,008 m

Step-by-step explanation:

This is a thermal expansion exercise, which has as an equation

ΔL = L α ΔT = L α (
`T_(f)` - T₀)

Where ΔL and ΔT are the variation of length and temperature, respectively, L is the initial length and α is the coefficient of thermal expansion

For our problem we must calculate the bridge length for maximum temperature

ΔL = 41 1.1 10⁻⁵ (41-24)

ΔL = 7.667 10⁻³ m

`T_(f)`-L₀ = 7.667 10⁻³ m

`T_(f)`= L₀ + 7.667 10⁻³ m

`T_(f)`= 41 + 0.007667 m

`T_(f)` = 41.0077 m

We repeat the calculation for the minimum temperature

ΔL = 41 1.1 10⁻⁵ (11-24)

ΔL = -5.863 10⁻³ m

`T_(f)` = 41 - 5,863 10⁻³

`T_(f)` = 40.994 m

The size range is 40,994 to 41,008 m