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Young's Modulus Question: stretch of a wire

  1. Apr 27, 2016 #1
    1. The problem statement, all variables and given/known data
    A force stretches a wire by 2mm. A second wire of the same material and with the same area of cross-section and twice the length is also stretched by the same force. What will its stretch be?

    2. Relevant equations
    F= (YA/L)ΔL

    3. The attempt at a solution

    F, Y, and A are all equal

    First wire:
    F =(YA/L1)*2 mm

    Second wire:
    F =(YA/2L1)ΔL

    1. I set them equal to each other to solve for ΔL
    (YA/2L1)ΔL = (YA/L1)*2

    2. I cancelled out YA
    ΔL/2L1 = 2/L1

    3. I multiplied both sides by 2L1 to isolate ΔL

    ΔL = 4 mm


    Did I do this correctly? I'm unsure because I've received notes from a friend and they got a different answer for the same problem. Thanks in advance.
     
  2. jcsd
  3. Apr 28, 2016 #2

    haruspex

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    You did it right.
    An easier route to the answer considers the longer wire as two copies of the first wire end to end. Each copy is subject to the same tension as the original, so each stretches 2mm.
     
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