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Homework Help: Surface Tension Problem

  1. May 20, 2006 #1
    Sir,
    The material of a wire has a density of 1.4 gm/cc. If it is not wetted by a liquid of surface tension of 44 dyne/cm, then what is the maximum radius of the wire that can float on the surface of the liquid?
    Can you give a hint to solve this problem?
     
  2. jcsd
  3. May 20, 2006 #2

    Andrew Mason

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    What is the force of gravity (per cm) on the wire as a function of its radius? What is the force (per cm) required to overcome the surface tension?

    AM
     
  4. May 21, 2006 #3
    I solved it in the following way:
    Let the radius, density and length of the wire be r, d and l respectively. Let T be surface tension.
    Mass per unit length of the wire = volume x density
    = (pi) x (r^2) x d
    Force per unit length of the wire = (pi)(r^2)d x g (g ~ 1000 cm/sec^2)
    By definition of surface tension,
    Force per unit length of the wire = surface tension
    (pi)(r^2)d x g = T
    r^2 = T/[(pi) x d x g]
    By solving I get,
    r =1/10 cm
    But the book answer is 10/7 cm. Is there any mistake in my solution?
     
  5. May 21, 2006 #4

    Andrew Mason

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    Your answer appears to be correct. A metal wire 1.4 cm thick will not float on water. Again, your book is wrong.

    AM
     
    Last edited: May 21, 2006
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