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Free Body Diagrams/Equilibrium

  1. Sep 7, 2008 #1
    1. The problem statement, all variables and given/known data
    The movable bracket shown may be placed at any height on the 50-mm-diameter pipe. If the coefficient of static friction between the pipe and bracket is 0.30, determine the minimum distance x at which the load P can be supported. Assume that the bracket is weightless.
    [​IMG]

    2. Relevant equations
    Sum of Forces and Moments = 0 for equilibrium
    F_f = uN

    3. The attempt at a solution
    I got stuck after getting the equilibrium equations. Too many variables and not enough equations.
    [​IMG]
     
  2. jcsd
  3. Sep 7, 2008 #2
    Your FBD is oversimplified. The friction force acts at points A and B. The 50 mm diameter of the pipe must be accounted for. The friction force at A is acting on the left side of the pipe, and at B on the right side of the pipe. Also, the normal force N is related to the horizontal force components.
     
  4. Sep 7, 2008 #3
    Is this what you are talking about?
    With these equations I still have 4 unknowns and 3 equations
    [​IMG]
     
  5. Sep 7, 2008 #4
    A numnerical answer is not possible since the loading P is not known. Write your answer in terms of P.
     
  6. Sep 7, 2008 #5
    There are 5 choices for the answer and they are all numerical answers
    A. 0.025 m
    B. 0.1667 m
    C. 0.1920 m
    D. 0.200 m
    E. 0.217 m

    According to the key, the answer is B
     
  7. Sep 8, 2008 #6
    I hate it when that happens...

    The answer key is correct. You have the equations that you need, except that x is measured from the centerline of the pipe, and so in eqn 3, the term on the left in parenthesis should be (x + 0.025).

    Sub for NA in eqn 2 from eqn 1. Sub from that result for P into eqn 3. NB will cancel out; solve for x and you should get answer B.
     
  8. Sep 8, 2008 #7
    Thank you very much.
    I think the FBD part was the hardest part of the question. But once that is in place, everything falls together really well. I tend to have trouble with the FBD part and trying to think about how each force goes.
     
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