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Stress and elongation problem

  1. Dec 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Two wires are made of the same metal but have different dimensions. Wire 1 is 4 times longer and twice the diameter of wire 2. If they are both under the same load, compare (a) the stresses in the two wires and (b) the elongations of the two wires.

    2. Relevant equations
    stress = F/A
    elongation = ΔL/L

    3. The attempt at a solution

    For the first part I did
    F/A
    F/((x/2)^2*3.14)
    2F/3.14x^2

    F/A
    F/((x/4)^2*3.14)
    16F/3.14x^2

    So it should be that the thinner wire experiences 8 times as much stress as the thicker wire. However the correct answer is that the thinner wire experiences 4 times as much stress.
     
  2. jcsd
  3. Dec 14, 2014 #2

    PhanthomJay

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    You forgot to square the 2 in your first equation .
    Elongation is change in length. You have written the equation for strain.
     
  4. Dec 24, 2014 #3
    Ok I figured it out. Thanks!
     
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