What Is the Minimum Coefficient of Static Friction for a Ball Against a Wall?

[philnow]

Homework Statement

Here is a horrible diagram representing the problem:

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

Homework Equations

torque = r*F

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.

 

[Doc Al]

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.)