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Homework Help: Torque Equilibrium question

  1. Dec 6, 2013 #1
    1. The problem statement, all variables and given/known data

    A uniform sphere of weight mg and radius r0 is tethered to a wall by a rope of length ℓ. The rope is tied to the wall a distance h above the contact point of the sphere, as shown in the figure.(Figure 1) The rope makes an angle θ with respect to the wall and is not in line with the ball's center. The coefficient of static friction between the wall and sphere is μ.

    To find: a) Frictional force in terms of r0, m, h, theta
    b) Suppose the sphere is on the verge of slipping. Derive an expression for coefficient of friction in terms of h and theta.

    2. Relevant equations
    Sum(Forces) = 0
    Sum(Torques) = 0

    3. The attempt at a solution
    From Sum(Forces) = 0:
    Ff = mg - TCosθ
    For torques:
    This is where I am confused:
    Considering torques with respect to the point of junction between the string and the wall:
    In counterclockwise: torque due to tension TLCosθ
    In clockwise: torque due to friction?

    I'm at a conceptual misunderstanding here!
  2. jcsd
  3. Dec 6, 2013 #2
    Where is Figure 1?
  4. Dec 6, 2013 #3
    Here it is:

    Attached Files:

  5. Dec 6, 2013 #4
    Because friction is applied at the junction, it cannot have any torque with respect to the junction. But there is another force at a distance from the junction, it is even shown in the figure.
  6. Dec 6, 2013 #5
    Alright, so that would be the torque due to the force of gravity. What I don't get is how I determine the reference point for calculating the torques. Right now I am using the rope-wall junction.
  7. Dec 6, 2013 #6
    It does not matter. Any point will do. Choose one that makes the calculations easiest.
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