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A change in length ratio question

  1. Mar 20, 2007 #1
    This may be common sense, but my brain just isnt working at the moment.

    If I am taking a length, L, and effectively stretching it to a new
    length, L+dL. I am interested in the ratio dL/L

    Let us say for example L is 2 mm long, and a stretched length of 2+0.2
    mm is 2.2 mm. The total ratio of change, dL/L, is 0.2/2, or 0.1

    If I take a portion of that length, lets say, between 1.2 and 1.6, and
    examine only the length where L is now 0.4. If the same stretching is
    applied, does the ratio of dL/L remain the same no matter where I am
    looking at a portion of the length?

  2. jcsd
  3. Mar 20, 2007 #2
    Probably- yes. It depends on how you stretch the line.

    Under a uniform stretch- x'=ax. dx=x'-x=(a-1) x, dx/x=a-1
  4. Mar 20, 2007 #3


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    Science Advisor

    If you are looking at this as a physical (Physics - Mechanics) problem then the answer is yes. A thing called Hookes Law states that dL/L is proportional to the pressure (Force per unit CrossSection) in the member. So if the member is of uniform cross-sectional area then the pressure (tensile pressure if stretching and compressive pressure if contracting) is constant along its length and therefore so is dL/L.
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