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20 April, 17:40

the steel bed of a suspension bridge is 200m long at 20 C. If the extremes of temperature to which it might be exposed are - 30 C to 40 C, how much will it contract and expand

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  1. 20 April, 18:00
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    The steel bed will contract by 0.13 m, and expand by 0.052 m

    Explanation:

    For contraction,

    α = ΔL / (LΔθ) ... Equation 1

    Where α = Linear expansivity of steel, ΔL = decrease in length / Increase in length, L = Original length, Δθ = Change in temperature

    make ΔL the subject of the equation

    ΔL = α (LΔθ) ... Equation 2

    Given: α = 13*10⁻⁶/C, L = 200 m, Δθ = - 30-20 = - 50 °C

    Substitute into equation 2

    ΔL = 13*10⁻⁶ (200) (-50)

    ΔL = - 0.13 m

    Similarly, For expansion,

    Using equation 2

    ΔL = α (LΔθ)

    Given: α = 13*10⁻⁶/C, L = 200 m, Δθ = 40-20 = 20 °C

    Substitute into equation 2

    ΔL = 13*10⁻⁶ (200) (20)

    ΔL = 0.052 m.

    Hence the steel bed will contract by 0.13 m, and expand by 0.052 m
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