# Homework Help: Torque Equilibrium question

1. Dec 6, 2013

### accioquote

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. Dec 6, 2013

### voko

Where is Figure 1?

3. Dec 6, 2013

Here it is:

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4. Dec 6, 2013

### voko

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.

5. Dec 6, 2013

### accioquote

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.

6. Dec 6, 2013

### voko

It does not matter. Any point will do. Choose one that makes the calculations easiest.