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Complicated mechanics resolving forces and angles question!

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data
    An object has a weight of 20N. It is supported by three strings to keep it in equilibrium, all attached to a smooth ring on the object. String A has a tension of 15N to the right of the block. String B is (a)degrees away from string A and String C is 90degrees away from String B. String B and C have the same tension. Show that the angle is 82 degrees


    2. Relevant equations
    cos(theta)/sin(theta)=tan(theta)
    Forces in equilibrium cancel each other out.

    3. The attempt at a solution
    So far I've got this, but get stuck past this point:

    15+Bcos(a)=Acos(90-a) and 20=Bsin(a) + Asin(90-a)
    A and B then can be replaced by T and rearranged:

    Tcos(a)=-Tsin(90-a) + 20
    Tsin(a)= Tcos(90-a)-15

    tan(a)= -Tsin(90-a)+20/Tcos(90-a)-15

    But then I don't know how to resolve it. Any help at all would be greatly appreciated! Many Thanks!
     
  2. jcsd
  3. Apr 2, 2009 #2

    Redbelly98

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    Perhaps you have the benefit of a figure that we cannot see, but when I read the question I would say that rope C's angle is 90+a.

    The LHS should be T sin(a) here.

    The LHS here should be T cos(a)

    Try making the corrections I indicated, then we'll have another look at what you have. Also, think about whether it's 90-a or 90+a for rope C. Again, you may be right about 90-a, if you have a figure that shows the rope arrangement.
     
  4. Apr 3, 2009 #3
    Sorry I think I've got slightly confused with the letters. I think that it is 90-a because the angles are along a straight line and so will add up to 180 degrees. And so the angle between string B and C is 90 degrees so angle (a) plus the angle between A and the line has also got to add up to 90 degrees and the angle will be 90-a. Am I totally wrong? But that is where I was coming from to get the angle.

    If I change the equations I then get:
    Tsin(a)=-Tsin(90+a)+20
    Tcos(a)=Tcos(90-a)-15

    I've got to show that a=81.87 and t=17.68 and it only works if the second one is minus.

    From there do I divide them to get tan(a) or do simultaneous equations?
     
  5. Apr 3, 2009 #4

    Redbelly98

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    I'm continuing the discussion in your other thread on this same problem here: (where there is a figure)

    https://www.physicsforums.com/showthread.php?t=304164

    Please, in the future don't double-post questions. Things would become very cluttered in the forums if everybody did that.
     
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