Kevin S. Huang

2008: Problem 8

Topic: Dynamics
Concepts: Circular motion, Forces in mechanics

Solution:

The normal force provides the centripetal acceleration so we have

N=m\omega^2R=\frac{m\omega^2d}{2}

The friction force must balance gravity and is bounded by the threshold for static friction,

f=mg \leq \mu N

Substituting in the normal force,

mg \leq \frac{\mu m\omega^2d}{2}

\mu \geq \frac{2g}{\omega^2d}=\frac{2(10\,\mathrm{m/s^2})}{(45\,\mathrm{\frac{rev}{min}} \cdot \frac{1}{60}\,\mathrm{\frac{min}{s}} \cdot 2\pi\,\mathrm{\frac{rad}{rev}})^2(8.0\,\mathrm{m})}=0.11

so the answer is C.