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Coplanar forces equilibrium- a rod in a sphere

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data
    A rod whose CG divides it into two portions of length a and b rests inside a smooth sphere in a position inclined to the angle θ to the horizontal. If 2α is the angle it subtends at the centre of the sphere, prove that

    tanθ= (b-a)/(b+a) tanα

    Picture is attached.

    2. Relevant equations



    3. The attempt at a solution

    Well I drew the force triangle with the weight of the rod, and the two normal forces. I know the normal force on the left side will be greater than the one on the right... now the thing is I am not quite sure what to do to get tan θ, if you do that with the weight of the rod, what is the adjacent component of that triangle? hmm sorry I am really confused haha..
     

    Attached Files:

  2. jcsd
  3. Apr 1, 2012 #2

    tiny-tim

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    hi enadiz! :smile:

    (where have you been for the last five years? :biggrin:)

    this is just a geometry question, all you need is a proper diagram :wink:

    draw the three forces onto the diagram, and the distances a and b …

    what does that give you? :smile:
     
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