Answer to Question #267241 in Mechanics | Relativity for Ahanaf

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.

(a) (Marks: 2) What is the minimum coefficient of static friction

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

(b) (Marks: 1) 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.

(c) (Marks: 2) As the drum slows down after the washing is done

at an angular retardation of 3.25 rad/sec2

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