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Newtonian mechanics and capstan

  1. Aug 5, 2006 #1
    Consider a capstan.A circular body around which a strong rope is wound.The free ends of the rope are pulled with tension Ta and Tb. Ta>>Tb.Co--eff. of friction is mu.theta is the total angle subtended by the attached portion of the rope on the centre of the drum.Prove that Ta=Tb[exp(-mu theta)]
     
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  3. Aug 5, 2006 #2

    Chi Meson

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  4. Aug 5, 2006 #3
    re newtonian mechanics

    I cannot give the picture here.Pleaase refer to Kleppner and Kolenkow 2.24 for this problem.My calclation gives Ta= Tb+(mu)N, where N has the same value as the centripetal force.according to the answer, N should be equal to (Ta-Ta exp(-mu theta)). I could not get it
     
  5. Aug 6, 2006 #4
    You need to derive the following equations:

    (T + dT) cos dtheta - T - mu N ds = 0
    (T + dT) sin dtheta - N ds = 0 where N is the normal force / unit length
    Use the fact that dtheta is small and eliminate N
    This is called Tension on a Cord Wrapped around a Rough Post
     
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