Chapter 12, Problem 93GP

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 Fig. 12–99. 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. (a) Determine the value of the frictional force on the sphere due to the wall. [Hint: A wise choice of axis will make this calculation easy.] (b) Suppose the sphere is just on the verge of slipping. Derive an expression the μ in terms of h and θ.

FIGURE 12–99

Problem 93.