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Find tension in three ropes suspending same mass

  1. Apr 5, 2004 #1
    A bird feeder is hanging off of a branch by 3 ropes. Rope1 and Rope2 are tied to the branch and both conect to rope3. Rope3 is conected to the birdfeeder. Rope 1 is 60 degrees of the branch and rope2 is 30 degrees.
    Symbolicly find the tensions of all of the ropes.

    We know that the tension of rope 3 would equal mass times gravity. t3=mg

    :confused: BUT, i was wondering if this would be a true statement. t1=66.6% of t3 and t2 would be 33.3% of t3?
    I got these numbers just from doing a simple ratio assuming that the angle of rope 1 and 2 are proportional to the tension of rope3, but i do not know how to prove if that is right or wrong. Which is why I am posting this, my teacher had a different answer for what he was looking for, but i was curious just to see if that is a true statement about t1 and t2.
  2. jcsd
  3. Apr 5, 2004 #2

    Doc Al

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    Staff: Mentor

    You are correct that the tension in rope 3, T3 = mg. But your reasoning about the other tensions is not correct.

    The right way to do it is to apply the condition for equilibrium: Forces in the x-direction and y-direction must add to zero. Apply this condition at the point where the three ropes connect and see what you get.
  4. Apr 5, 2004 #3


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    Science Advisor

    Represent the forces relative to where the ropes meet each other.

    [tex]\Sigma F_x = 0 = R_2 \cos (30) - R_1 \cos (60)[/tex]

    [tex]\Sigma F_y = 0 = R_1 \sin (60) + R_2 \sin (30) - mg[/tex]

    2 equations, 2 variables.
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