Free Body Diagrams/Equilibrium

  • #1

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 [Broken]

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 [Broken]
 
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Answers and Replies

  • #2
116
0
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.
 
  • #3
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 [Broken]
 
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  • #4
116
0
A numnerical answer is not possible since the loading P is not known. Write your answer in terms of P.
 
  • #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
 
  • #6
116
0
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.
 
  • #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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