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Surface tension, Fluid mechanics

  1. Mar 24, 2015 #1
    1. The problem statement, all variables and given/known data
    A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A
    loop of 6.28 cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The
    thread loop takes the shape of a circle. Find the tension in the thread. Surface tension of soap solution
    = 0.030 N/m

    2. Relevant equations


    3. The attempt at a solution

    First i found the the radius of the loop which is 1cm.
    I drew below diagram. I wrote eqn 2Tsin(dϑ)=2*(S*2Rdϑ) where T is tension and S is surface tension. I multiplied the RHS by 2 because soap solution has two layers. But by solving this i am getting answer 6×10-4 but my book says answer is 3×10-4. Please tell me where i am wrong ??
    5otkbb.jpg
     
  2. jcsd
  3. Mar 24, 2015 #2
    Your equation looks correct. So you got T = 2SR. Are you confident of your subsequent arithmetic?

    Chet
     
  4. Mar 24, 2015 #3
    yes i am confident. I am getting answer 6×10-4 but my book says answer is 3×10-4. Please tell me where i am wrong
     
  5. Mar 24, 2015 #4
    Who says you're wrong? If you have confidence in what you did, then maybe the book is wrong. There is no question that you were correct in saying that the soap has two layers.

    Chet
     
  6. Mar 24, 2015 #5
    Ok thanks, i think the book might be wrong.
     
  7. Jun 4, 2016 #6
    http://file:///C:/Users/Compaq/Desktop/soluing.png [Broken]
     
    Last edited by a moderator: May 7, 2017
  8. Jun 4, 2016 #7
    soluing.png
     

    Attached Files:

  9. Jun 20, 2017 #8
    Yeah, you're right if you're thinking that the tension is due to the whole half part but that's not the case.
    The one quarter of the string will be the cause of tension in the string and the other quarter will cause the opposite side of the string in creating a tension.
     
  10. Jun 20, 2017 #9
    This is a little hard to follow. Can you please explain in more detail, perhaps using diagrams.
     
  11. Jun 29, 2017 #10
    Yes, I can explain that. DSC_0014.jpeg
    As you can see tension at point A and B will addup to balance the force due to surface tension on the right side. Since 2T is the force to be balanced due to whole half part so we can say that one quarter part will cause the tension at a single point.
     
  12. Jun 30, 2017 #11

    haruspex

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    No, you are missing the point under discussion. Lavankosa got the same equation you have, by a different method, for a single surface. But lavankosa correctly realised there are two surfaces. The soap film is a thin sheet with air on both sides. Each surface is subject to surface tension.
     
  13. Jun 30, 2017 #12
    Oh, I completely forgot about that. I thought that there is difficulty in handling the tension problem but it's not. Sorry about that!
    Yes, the OP has right solution. His book probably has the wrong answer.
     
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