sue asked in Science & MathematicsPhysics · 2 months ago

find length of the rod?

A metal rod is 7.39 mm in diameter and 120 mm long before being loaded in tension. When subjected to a force of 1.5 kN, it will undergo 0.1% strain. What is the length of the rod (mm) in this loaded condition?

ps: I think this related to engineering stress and true stress?

2 Answers

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  • 2 months ago
    Favorite Answer

    Long method:

    Strain = (change in length) / (original length)

    In symbols this is:

    ε =  ΔL/L₀

    0.1% is the same as 0.1* 1/100 which is 0.001

    Put these together and we get

    0.001 = ΔL/(120mm)

    ΔL = 0.001*120mm = 0.12mm

    So loaded length is L + ΔL = 120mm + 0.12mm = 120.12mm

    ____________________

    Short method

    Loaded length = 1.001 *120mm = 120.12mm

    Explanation

    To increase something by 7% for example, you multiply it by 1.07

    A strain of 0.1% just means length increases by 0.1%. This is the same as multiplying by 1.001

    ____________________

    Don’t confuse strain and stress. Stress is force/area.

  • 2 months ago

    By Strain (ɛ)  = [ΔL/L]

    =>0.1% =  [ΔL/L] x 100% 

    =>0.1 x 10^-3 = ΔL/(120)

    =>ΔL = 0.012 mm

    =>L(loaded) = L +  ΔL = 12 + 0.012 = 12.012 mm

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