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Tension Problem using Trig

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Two cables are attached to a sign at point A to steady the sign as it is being lowered. Using Trigonometry, determine a) the magnitude and direction of the smallest force P for which the resultant R of the two forces applied at A is vertical, b) the corresponding magnitude of R


    2. Relevant equations
    Use Law of cosines (R^2 = Q^2 + P^2 - 2QPcos(theta))
    and Law of sines P/sin(opp. angle) = Q/sin(opp. angle)

    3. The attempt at a solution
    diagram is shown in attachment. I only have one magnitude and one angle and I'm supposed to get an angle alpha so that P is the min.
     

    Attached Files:

    • p1.bmp
      p1.bmp
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  2. jcsd
  3. Jan 14, 2009 #2
    I have no idea where ure stuck at but ill drop a small hint:

    The horizontal component of force Q must cancel for the resultant to be vertical.
     
  4. Jan 14, 2009 #3
    Right, thanks. it's the small things that get me. taking the horz component of Q (80sin(35) = P = 45.9) gives the magnitude of p. Then, using law of sines to get alpha, I can get the third angle and then use law of cosines to get mag of R
     
  5. Jan 15, 2009 #4
    if you have already noticed if you went ahead with the above, alpha should be a right angle since the smallest force you need with p is a horizontal force to cancel out with the horizontal component of Q.
     
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