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Equilibrium and Statics involving a mass attached to three strings

  1. Jan 19, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the forces of the three strings of this image.

    http://www.flickr.com/photos/79276401@N05/8395815988/in/photostream

    2. Relevant equations

    Using gravitational constant to find force of the mass.
    Using algebra to find the forces of the three strings.

    3. The attempt at a solution
    I tried to create two equations, one for the x-axis and another for the y-axis. However, in the x-axis, the two strings of 25° cancel themselves. Do you think there is a missing data? This blocks me from using substitution to find the other forces. How would you proceed?
     
  2. jcsd
  3. Jan 19, 2013 #2

    SteamKing

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    You have three supports but only two equations of statics. Therefore, the problem is statically indeterminate. In order to solve this system, additional equations must be introduced.
     
  4. Jan 19, 2013 #3

    haruspex

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    If the strings are completely inextensible then there is no way to solve this. You can obtain consistent solutions by setting e.g. the tension in the centre string to 0, or by setting the other two to 0.
    In the real world, all strings are at least a little extensible. If you consider a small extension to the centre string, you can calculate the extensions to the other two. Taking the tensions to be in proportion to these, a solution can be found.
     
  5. Jan 20, 2013 #4
    Actually, I have never seen string extensibility in grade 11. Your reply interests me. Could you explain how we could proceed to find the three forces? How do we find how much they extend? Very bizarrely, the teacher said this question was in last year's exam...
     
  6. Jan 20, 2013 #5

    haruspex

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    It requires a little differential calculus, so I'm guessing that also puts it beyond your syllabus.
    Let the two angled strings be attached w from the centre. If the centre string has length x, the other two have length √(x2+w2). If the centre string is stretched by amount δx the other two are each stretched √((x+δx)2+w2) - √(x2+w2) ≈ xδx/√(x2+w2) = δx sec(θ). So the tension in the side strings is sec(θ) times that in the centre string. That's enough extra info to solve it.
     
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