# Friction, you make my head right round!

**Classical Mechanics**Level 5

The friction coefficient between the plank and the incline is \(\displaystyle\mu_1\), and that between sphere and plank is \(\displaystyle \mu_2\).

Find the **maximum** value of \(\displaystyle \frac{\mu_1}{\mu_2}\), such that the sphere is always pure rolling on the plank.

**Details and Assumptions:**

\(\bullet\) \(\displaystyle m = 2kg\)

\(\bullet\) \(\displaystyle \theta = 30^o\)

\(\bullet\) \(\displaystyle R = 15cm\)

\(\bullet\) \(\displaystyle g = 9.8m/s^2\)