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Helix (spool and wire) geometry

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data
    (From Stewart's Calculus Early Transcendentals (4th ed), Ch. 13 Problems Plus #8)

    A cable has radius r and length L and is wound around a spool with radius R without overlapping. What is the shortest length along the spool that is covered by the cable?

    2. Relevant equations

    See image link below.

    3. The attempt at a solution
    I've read the solution from the solutions guide and it makes sense, aside from this geometric representation:
    (h=vertical distance between coils)

    http://img242.imagevenue.com/img.php?loc=loc164&image=th_34593_spool2_122_164lo.jpg"

    I'm trying to understand the rationale for this geometric image. Specifically, where is the 2Pi(R+r) coming from? This is clearly the circumference of the spool/cable, but I don't understand its presence in the image. Could someone describe what the image is showing (where the spool is, how it's oriented, what the two parallel line are, etc)? Thanks!

    http://img107.imagevenue.com/img.php?image=35205_spool_122_371lo.jpg"
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. May 4, 2009 #2
    I thought I would repost the image, as the link above has too many ads.
    Any ideas?

    20tqngh.jpg
     
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