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Find tension as a vector on point A and point B

  1. Feb 22, 2015 #1
    1174i7m.jpg
    1. The problem statement, all variables and given/known data

    The tension in the supporting cable AB is T = 425 N. Write this tension as a vector (a) as it acts on point A and (b) as it acts on point B. Assume θ = 30°. [***I've attached a picture of the exact problem]

    The answer in my text book says TA = <221, -212, 294>
    TB = <-221, 212, -294>

    2. Relevant equations
    T
    = (T)(n)

    n
    = (AB) / (||AB||)

    3. The attempt at a solution

    I started by finding the AB which I used A = (0, 5cos(30), 5sin(30)) and B = (2, 0, 6), which gave me AB = <2, -4.33, 3.5>.

    Next I used n = (AB) / (||AB||) to find n = <.338, -.732, .5916>

    Then I found T = (T)(n) = <143.65, -311.1, 251.43>


    I'm not sure what I'm doing wrong here. The only thing I can think of is if I'm using incorrect points for point A
     
  2. jcsd
  3. Feb 22, 2015 #2

    Astronuc

    User Avatar

    Staff: Mentor

    It looks like θ is in the x-y (azimuthal) plane, so it should not apply directly to the z-coordinate as one did for the coordinates of A, necessarily.

    One needs to think in terms of two angles, poloidal and azimuthal. Note point B is offset from the polar axis.
     
  4. Feb 22, 2015 #3
    Thank you! I'm pretty sure fixed my problem. I absolutely hate when the text book doesn't make it obvious which plane the angle is in.

    So that changed my A to A = (-2.5, 4.33, 0), which changed my tension to the correct answer.
     
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