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Law of Sines for Tension?

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data
    A large chandelier is supported by two ropes. Rope 1 makes a 40 degree angle with the ceiling and has a tension of 150N. Rope two forms a 50 degree angle with the ceiling. What is the tension in rope 2 and what is the mass of the chandelier given the chandelier.


    2. Relevant equations
    F = ma
    T-mg = ma
    Law of sines?
    3. The attempt at a solution
    So i solved it through the law of sines and got an answer significantly different than what my professor said it should be. I would be interested in knowing why.
    Here is the work:
    150/sin(50) = T2/sin40
    T2 = 150*sin(40)/sin(50)
    T2 = 125.86N whereas the correct answer is 179N.

    Then for the mass:
    150*sin(40)+125.86*sin(50) = mg
    m = 19.66kg whereas the correct answer is 23.8kg.

    I was wondering why the law of sines did not provide a correct answer in this case, and what different steps I should take to get at the right answer. Thanks in advance!
     
  2. jcsd
  3. Sep 15, 2009 #2
    Is there any particular reason you are using the law of sines? Draw a picture, how can you divide the triangle into two right triangles? Once you do this it is simple right angle trigonometry .
     
  4. Sep 15, 2009 #3
    My apologies, I overcomplicated this problem. Upon drawing a diagram it is obvious Fx = T2cos(50) - 150cos(40). Fy = T2sin50 + 150sin40. Apply second law to Fx and force comes out nicely to 178.8N, plug that into Fy and it is in fact 23.8kg. Thanks for the help :).
     
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