Question

At the same rotational speed and coefficient of static friction between sock and the drum, would a sock of twice the mass slide down the wall? Explain your answer

Answer 1

A wet socks clinging to the inside of a washing machine drum which is spinning at a speed of 4.7 m/s. The radius of the drum is 30 cm.

At the same rotational speed (V) and coefficient of static friction ($\mu_s$ ) sock will not up down the wall if mass is increase to 2 m. Because $\mu_s$ does not depend on mass it only depend on rotational speed as ($\mu_s = \frac{gR}{V^2}$ )

If we write new equation for mass 2 m sock.

$N’ = \frac{2mV^2}{R} \\ \mu_s’ N’ ≥ 2mg \\ \mu_s’ \times \frac{2mV^2}{R} ≥ 2mg \\ \mu_s’ ≥ \frac{gR}{V^2} \\ \mu_s’ = \mu_s$

If rotational speed decrease then sock need more $\mu_s$ to stick to wall.