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Kinetics in Nromal and Tangential coordinates - SPINING ROD W/ SPOOL

  1. Jun 18, 2006 #1
    Kinetics in Nromal and Tangential coordinates - SPINNING ROD W/ SPOOL

    The 2-kg spool fits loosely on the inclined rod for which the coefficient of static friction is [itex]\mu_s\,=\,0.2[/itex]. If the spool is located 0.25 m from A, determine the maximum speed the spool can have so that it does not slip up the rod.

    [​IMG]

    Here is what I have for this problem, but it is wrong according to the answer in the text:

    [tex]sin\,\theta\,=\,\frac{3}{5}[/tex]

    [tex]\theta\,=\,36.9[/tex]

    [tex]\sum\,F_x\,=\,N\,cos\,53.1\,-\,f_s\,cos\,36.9\,=\,m\,a_n[/tex]

    [tex]\sum\,F_y\,=\,N\,sin\,53.1\,+\,f_s\,sin\,36.9\,-\,m\,g\,=\,m\,a_y[/tex]

    [tex]N\,=\,\frac{m\,g}{sin\,53.1\,+\,\mu_s\,sin\,36.9}[/tex]

    [tex]N\,=\,21.31\,N[/tex]

    Then I use another version of the [itex]F_x[/itex] equation to solve for [itex]v_{max}[/itex]:

    [tex]N\,cos53.1\,-\,N\,\mu_s\,cos\,36.9\,=\,m\,\frac{v_{max}^2}{\rho}[/tex]

    [tex]v_{max}^2\,=\,\frac{9.39}{10}[/tex]

    [tex]v_{max}\,=\,0.969\,\frac{m}{s}[/tex]

    The answer is 1.48 in the text though! Any suggestions?
     
    Last edited: Jun 18, 2006
  2. jcsd
  3. Jun 18, 2006 #2

    Doc Al

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    Staff: Mentor

    What's the direction of the friction force on the spool?
     
  4. Jun 18, 2006 #3
    Down the rod towards point A, right?
     
  5. Jun 19, 2006 #4

    Doc Al

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    Staff: Mentor

    Exactly. Now revise your equations accordingly.
     
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