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Help with elasticity/stretching&compression

  1. Sep 10, 2012 #1
    1. The problem statement, all variables and given/known data

    A Force stretches a wire by 1.0mm A second wire of the same material has the same cross section and twice the length. How far will it be stretched by the same force?

    b) A third wire of the same material has teh same length and twice the diameter as teh first. How far will it be stretched by the same force?



    2. Relevant equations

    F = y(delta)L/L0*A Youngs modulus

    3. The attempt at a solution

    1.0mm = 0.01m

    I beleive you have to compare the original youngs mudulus with one that is slightly different... I need some guidelines on how to solve this mathematically please. Also, on a side note, is there a differnence between Youngs modulus/shears modulus/bulk modulus? or all they all aprt of the same idea with different concepts, ie(one uses volume)

    Thanks
     
  2. jcsd
  3. Sep 10, 2012 #2

    CWatters

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    Science Advisor
    Homework Helper

    No the material is the same so the youngs modulus should be the same.

    Try this approach..

    F = -EA0ΔL/L0

    E is the Young's modulus (modulus of elasticity)
    F is the force exerted on an object under tension;
    A0 is the original cross-sectional area through which the force is applied;
    ΔL is the amount by which the length of the object changes;
    L0 is the original length of the object.

    So write two versions of the above one for the short wire (subscript s) and one for the long wire (subscript L). The youngs modulus, the cross sectional area and the force are the same for both lengths of wire..

    F = -EA0ΔLs/Ls

    F = -EA0ΔLL/LL

    Since the force is the same you can equate the two...

    -EA0ΔLs/Ls = -EA0ΔLL/LL

    The youngs modulus and the cross sectional area cancel leaving..

    ΔLs/Ls = ΔLL/LL

    Then rearrange to give...

    ΔLL/ΔLs= LL/Ls

    In other words the amount of stretch (ΔL) increases in the same ratio as the length (L) increases. eg Double the length and the amount of stretch is also doubled (all else being equal).

    If
    LL/Ls = 2
    then
    ΔLL/ΔLs = 2


    Part 2 can be tackled in a similar way. Write two equations with different "A". Note that in this case the length L, the force F and the youngs modulus is the same for both.
     
    Last edited: Sep 10, 2012
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