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Ball against a wall, statics.

  1. Sep 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Here is a horrible diagram representing the problem:

    Picture1.png

    The problem is to find the minimum coefficient of static friction between the ball and the wall so that the ball remains motionless.

    2. Relevant equations

    torque = r*F

    3. The attempt at a solution

    I've divided the tension force into x and y components, Tsinθ and Tcosθ respectively. Therefore the normal force (the wall pushing against the ball) is N = Tsinθ. The friction force is = uN = u(Tsinθ).

    So now, because the ball is motionless, the two torques must cancel each other out. So Torque from the tension T(t) = (radius)*T and torque from the friction force T(f) = radius*Friction force = radius* uTsinθ. This gives u = (1/sinθ)... but I'm really not sure... also, how do I minimize this u?

    Thanks in advance for any help.
     
  2. jcsd
  3. Sep 9, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good to me. Setting the static friction force to equal to its maximum value μN (as you did) will give you the smallest μ. (Generally static friction ≤ μN.)
     
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