Question

A 600-kg car is going around a curve with a radius of 120 m that is banked at an angle of 20° with a speed of 24.5 m/s. What is the minimum coefficient of static friction required for the car not to skid?

Answer 1

$F_n \to$ normal reaction Force

$F_F \to$ frictional Force

$Mg \to$ weight

$F_c \to$ centrifugal Force

$\begin{cases} F_N -Mgcos20^o - F_Csin20^o = 0 \to F_N = Mgcos20^o + F_Csin20^o \\ F_Ccos20^o - F_F-Mgsin20^o=0 \end{cases}$

$F_Ccos20^o - F_F-Mgsin20^o=0$

$F_F=F_Ccos20^o -Mgsin20^o$

$\mu F_N=$ $F_Ccos20^o -Mgsin20^o$

$\mu F_N=\frac{MV^2}{R}cos20^o-Mgsin20^o$

$\mu = \frac{1}{F_N}\lbrack\frac{MV^2}{R}cos20^o-Mgsin20^o\rbrack$

$\mu = \frac{1}{Mgcos20^o + F_Csin20^o}\lbrack\frac{MV^2}{R}cos20^o-Mgsin20^o\rbrack$

$\mu = 0.1235$