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Need help in Unit Vectors

  1. Dec 25, 2006 #1
    1. The problem statement, all variables and given/known data

    The cable AB keeps the 8-kg collar A in place on the smooth bar CD. The y axis points upward. Determine the distance s from C to the collar A for which the tension in the cable is 150N.
    location of:
    B: (0m, 0.5m, 0.15m)
    C: (0.4m, 0.3m, 0m)
    D: (0.2m, 0m, 0.25m)

    collar A's location is unknown. The required is the distance between C and collar A. The answer is 0.305m, but I need the solution for it.
    For an easier look, go here

    Someone answered this in yahoo answers. Can someone verify it?
    link

    2. Relevant equations

    e dc= dc/|dc|
    W=mg
    edc=eac
    s=distance between A and C

    3. The attempt at a solution

    DC=0.2i+0.3j-0.25k
    e dc=0.4558i-0.6838j+0.5698k
    I'm not sure about this part...
    eab= -Axi+(0.5-Ay)j+(0.15-Az)k
    sqrt(Ax^2+Ay^2+Az^2-Ay-0.3Az+0.2725)
    eac= (0.4-Ax)i+(0.3-Ay)j-Azk
    sqrt(Ax^2+Ay^2+Az^2-0.8Ax-0.6Ay+0.25)

    sedci=-150eabi
    sedcj=-150eabj
    sedck=-150eabk

    eabi=-Axi/|AB|
    eabj=(0.5-Ay)j/|AB|
    eabk=(0.15-Az)k/|AB|

    I equated the "s" in the previous part and got...
    Ay=0.5-1.5Ax
    Az=1.25Ax+0.15
    After that, my solutions just go in circles. I couldn't get what Ax is.
    Also, Is my use of Ax, Ay, Az correct? I'm doubting about it.
     
    Last edited: Dec 25, 2006
  2. jcsd
  3. Dec 26, 2006 #2

    Astronuc

    User Avatar

    Staff: Mentor

    The weight of the collar acts downward, but the movement of the collar is contrained by the rod between C&D, so one must find the force component along C&D, which acts toward D.

    The tension in AB has a component which acts upward toward C.

    For a static situation, the corresponding x, y, and z components of the forces must = 0.
     
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