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Unwounding spool of wire

  1. Feb 2, 2008 #1
    1. The problem statement, all variables and given/known data
    A spool of wire mass M and radius R is unwound under a constant force F. Assuming the spool is a uniform solid cylinder that doesnt slip, show that the acceleration of center of mass is 4F/3M


    2. Relevant equations
    [tex]\tau[/tex] = I[tex]\alpha[/tex] = F*R


    3. The attempt at a solution

    Here's what I got, not sure if this is right.
    [tex]\tau_{}net[/tex] = [tex]\tau[/tex]F - [tex]\tau[/tex]Ffric
    I[tex]\alpha = F*R - Ffric*R[/tex]
    [tex].5MR^2(a_{cm}/R) = F*R - Ffric*R[/tex]

    [tex]a_{cm} = (F-Ffric)/.5M[/tex]

    The problem is that I don't know Ffric (Friction force).

    Thank you in advance for help
     
  2. jcsd
  3. Feb 2, 2008 #2
    Use F = ma on the spool to get another equation, this should allow you to eliminate F_fric.
     
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