How Can the Minimum Distance x for Load P on a Movable Bracket Be Determined?

[hp-p00nst3r]

Homework Statement

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.
http://img396.imageshack.us/img396/18/220selftest27vo7.gif

Homework Equations

Sum of Forces and Moments = 0 for equilibrium
F_f = uN

The Attempt at a Solution

I got stuck after getting the equilibrium equations. Too many variables and not enough equations.
http://img254.imageshack.us/img254/7721/mech220fbd7mj4.jpg

 

[edziura]

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.

 

[hp-p00nst3r]

Is this what you are talking about?
With these equations I still have 4 unknowns and 3 equations
http://img381.imageshack.us/img381/9784/mech220fbd7xu5.jpg

 

[edziura]

A numnerical answer is not possible since the loading P is not known. Write your answer in terms of P.

 

[hp-p00nst3r]

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

 

[edziura]

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.

 

[hp-p00nst3r]

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.