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Tension on ropes

  1. Apr 20, 2007 #1
    1. The problem statement, all variables and given/known data
    A 1100 kg steel beam is supported by two ropes. Each rope has a maximum sustained tension of 6200 N.

    Then it shows a diagram of two ropes holding a steal beam at the center, both are angled out. The rope on the left is angled away at 20 deg from y axis. The rope on the right is angled 30 deg from y axis.


    2. Relevant equations
    Fnet = ma


    3. The attempt at a solution
    So basically I used substitution...
    R1 = rope 1 (left)
    R2 = rope 2 (right)
    E = summation
    F = Force

    E(Fx) = MAx = 0

    R2*sin(30) - R1*sin(20) = 0
    R2*sin(30) = R1*sin(20)
    R2 = R1*[sin(20)/sin(30)]

    Plug that into sum of forces in y direction...

    E(Fy) = MAy = 0

    R1*cos(20) + R2*cos(30) - Mg = 0
    R1*cos(20) + R2*cos(30) = Mg = 10791 N
    plug in R2...
    R1*[cos(20) + sin(20)/sin(30)] = 10791
    R1 = 6645.96 N

    Now I did it like this.. plugged that back into the original and got 4546.11 N for R2. However it was wrong. So I thought okay since the max tension is supposedly 6200 I'll use that as R1 and got 4241.05 for R2. Wrong again. Any ideas?
     
  2. jcsd
  3. Apr 20, 2007 #2

    Doc Al

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    Staff: Mentor

    Redo your plugging in of R2; looks like you dropped the cos(30).
     
  4. Apr 20, 2007 #3
    Not sure where you're getting the cos... both are sine since the x vector is opposite of the angle.. making it sine. Right?
     
  5. Apr 20, 2007 #4
    [​IMG]

    here is the problem
     
  6. Apr 20, 2007 #5

    Doc Al

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    Staff: Mentor

    The cosine you dropped is the one right here:
     
  7. Apr 20, 2007 #6
    oh wow what a stupid mistake, thanks! it works now
     
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