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Maximum angular velocity and free body diagram

  1. Mar 3, 2013 #1
    1. The problem statement, all variables and given/known data
    I have found the question I am having trouble with here:

    http://www.chegg.com/homework-help/...se-height-incline-ish-50cm--coefficie-q218123

    2. Relevant equations
    See below

    3. The attempt at a solution
    After doing my free body diagram, I picked the vertical axis to be y and the horizontal axis to be r.
    Force total in the r direction= Fnsinθ-Ffrcosθ= m((v^2)/r)
    In the y direction, = Ffrsinθ + FnCosθ-mg=0, b/c a=0

    If this box is not to be in motion, then the sum of these forces should be zero. I set the two equations = to zero, while solving for v, but it did not come out to the 1.8 that is given as a solution. Are my components at least correct? If so, where am I going wrong?
     
    Last edited: Mar 3, 2013
  2. jcsd
  3. Mar 3, 2013 #2

    haruspex

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    In which direction does each of those forces act? What is the direction of acceleration?
     
  4. Mar 3, 2013 #3
    Don't the negative and positive signs indicate the direction? This is knowing that r is positive to the right and y is positive upwards.
     
  5. Mar 3, 2013 #4

    haruspex

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    I was hinting that you have some signs wrong.
     
  6. Mar 3, 2013 #5
    I see a is negative, but I don't see anything wrong with the other signs. My rough free body diagram is attached
     

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    • mg.doc
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  7. Mar 3, 2013 #6

    haruspex

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    You diagram is fine as far as I can tell (you don't show where the axis is). I ask again, which way is the centripetal acceleration? Which of the forces you have in the equation act in that direction?
     
  8. Mar 3, 2013 #7
    Pointing towards the center, thus, technically it is -v^2/r. However, does that have any bearing on the sign of the components of the normal force and friction? I thought that had to do with which way the coordinate axes point
     
  9. Mar 3, 2013 #8

    haruspex

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    The correct equation is certainly Ffrcosθ - Fnsinθ = m((v^2)/r). But maybe you fixed it up later in your calculation somehow.
    I get 1.99 rad/sec, not 1.8. What do you get? If not 1.99, please post the details of your whole calculation.
     
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