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Coefficient of static friction of uniform rod

  1. Dec 10, 2011 #1
    1. The problem statement, all variables and given/known data
    A uniform rod AB has a length l and a weight W0. End A is in contact with a rough wall, but it is not fixed. A massless cord connects end B and is fixed to the wall at point C. The rod AB is now horizontal and the angle formed between the cord and rod is θ as shown in the figure. (a) In order to achieve static equilibrium, what is the minimum value of the coefficient of static friction between the rod and the wall? (b) If a block of weight W=W0/2 is hang on the rod with the hanging point a distance d from the end point A, what is then the minimum value of the coefficient of static friction between the rod and the wall? Express all your results in terms of l, d, W0, and θ. (ANS: μ≥tanθ ; μ≥(2l-d)tanθ/(l+d) )


    2. Relevant equations
    Which point should we regard as the pivot?


    3. The attempt at a solution
    Set A as the pivot, then
    Tsinθ+μN=W0
    Tcosθ=N
    Tsinθ*l+W0*l/2=0
    Then I get μ=-3tanθ. What's wrong?
     
  2. jcsd
  3. Dec 10, 2011 #2
    All correct except the + in the torque equation.
    Try replacing the + by -.
     
  4. Dec 10, 2011 #3
    Thank you! I'd try again
     
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