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.

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

Explanation:

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

      ΔL = L α ΔT = L α  ( - 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

       -L₀ = 7.667 10⁻³ m

        = L₀ + 7.667 10⁻³ m

       = 41 + 0.007667 m

        = 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

      = 41 - 5,863 10⁻³

      = 40.994 m

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

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