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Homework Help: Find depression in wire with hanging mass

  1. Mar 15, 2010 #1
    Hello: I have the following:

    1. The problem statement, all variables and given/known data

    A wire of unstretched length l is extended by a distance (1/1000)l when a mass M is hung from its bottom end. If this same wire is connected between points A and B that are at a distance l from each other on the same horizontal level, and the mass M is hung from the midpoint of the wire, find the depression y of the midpoint.


    2. Relevant equations
    2Tsin(theta) = mg
    sin(theta) = y/(the stretched length of l/2).

    3. The attempt at a solution

    Not sure where to go from there. Would it be safe to say that each half of the wire is stretched by l/2000? Thanks.
     
  2. jcsd
  3. Mar 15, 2010 #2

    tiny-tim

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    Hello bodensee9! :smile:

    (have a theta: θ :wink:)
    How did you get that?

    Use Pythagoras, and an approximation.
     
  4. Apr 11, 2010 #3
    I need help with this problem too. 2Tsintheta=mg, and tantheta=2y/l, for small angles tan theta=sin theta, so if we could use that approximation then sin theta=2y/l,...I can also use Pythagoras to find the hypotenuse and then find the real sin theta and equate them to find y, I don't think that's a proper answer though...I'm not sure where the L/1000 comes in...

    This isn't homework, I know the answer already is L/20, just don't know how to get that..
     
  5. Apr 11, 2010 #4

    tiny-tim

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    L/2 = adjacent, (1 + 1/1000)L/2 = hypotenuse.
     
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