Answer to Question #266330 in Mechanics | Relativity for sadman2222

Question

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. What is the minimum coefficient of static friction

between sock and the drum so that the sock will not slip down?

Answer 1

The Newton’s second law equation

$F_N =ma_c \\ a_c = ω^2γ \\ f_s = mg \\ \mu_sF_N = mg \\ \mu_sm ω^2γ = mg \\ r= 0.3 \;m \\ ω = \frac{V}{r} = \frac{4.7}{0.3} = 15.667 \; rad/s \\ \mu_s = \frac{g}{ω^2γ} = \frac{9.8}{(15.667)^2 \times 0.3} = 0.133$

The minimum coefficient of static friction is 0.133