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Free-hanging string with 4 attached masses!

  1. Sep 16, 2013 #1
    1. The problem statement, all variables and given/known data
    http://home.phys.ntnu.no/brukdef/undervisning/tfy4145/ovinger/Ov03.pdf
    look at "oppgave 5".

    In the problem, you have a massless string with 4 uniform masses attached symmetrically, and you are supposed to show that the implicit equation for x (and x = cos(alpha)) is correct. Each of the masses are L/5 apart and the distance between the two ends of the string is D.

    3. The attempt at a solution

    I should be getting 5 equations for the 5 unkowns, but I am only getting 4 (the last 4 equations written on the paper)..

    https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/1234158_10201385459335100_1607600845_n.jpg
     
    Last edited: Sep 16, 2013
  2. jcsd
  3. Sep 16, 2013 #2

    SteamKing

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    This problem would make a lot more sense if I read Norwegian.
     
  4. Sep 16, 2013 #3
    Look at the picture in the pdf: You see a massless string weighed down by 4 attached point-masses. Each of the mass is a distance L/5 apart from each-other, where L = total length of the string. D= distance between the two ends of the string.

    Next you can see two angles: alpha and beta. The point with this problem is to show that the implicit equation for cosine of alpha written in the assignment,where x = cos(a), is correct.

    Please tell me if there is something more you do not understand! I really need help with this
     
  5. Sep 16, 2013 #4
    It is more convenient to simplify your notation by calling the tensions T and S.
     
  6. Sep 16, 2013 #5
    Then use your D equation to get cosβ in terms of x where x = cosα.
     
  7. Sep 16, 2013 #6
    I think that you do not need to use S[itex]_{3}[/itex].
     
  8. Sep 16, 2013 #7
    You are probably right, but if I removed [tex]S_3[/tex] I would have 4 unkowns and 3 equations.. I don't understand how I can get my last equation?

    Also sorry about the notation, but I took it from the assignment.
     
  9. Sep 16, 2013 #8
    You have FOUR equations.

    Two from vertical equilibrium and one from horizontal equilibirum if you do not use the third tension. But you have also your D equation from which to get cosβ in terms of x where x = cosα.
     
  10. Sep 16, 2013 #9
    You mean those involving G? But G is also an unknown, because I don't know the mass. Do you think G would disappear if I inserted the equations into the one for D?

    thanks for all help :)
     
  11. Sep 16, 2013 #10
    OK after a fresh look at the problem I see you were completely right. thanks !!
     
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