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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.

User SpamapS
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1 Answer

1 vote

Answer:

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

User Pavel Kostenko
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