Circular Motion

We know that, static friction force, $f_{s}=\mu_{s} N$ where, $\mu_{s}$ is the coefficient of static friction and $N$ is the normal force acting on the body. As the car is travelling on a circular track, so centripetal force is also acting on it. $\Rightarrow \;\; f_{C}=\;\frac{m v^{2}}{R}$ In limiting condition, $f_{s}=f_{C} \Rightarrow \mu_{s} N=\;\frac{m v^{2}}{R}$ $\Rightarrow \;\; N=\;\frac{m v^{2}}{\mu_{s} R}$....(i) The magnitude of negative lift $f_{L}$ acting downwards on the car is given by $f_{L}=m g-N$ $=m g-\;\frac{m v^{2}}{\mu_{s} R}$ $\Rightarrow \;\; |f_{L}|=m\left(\;\frac{v^{2}}{\mu_{s} R}-g\right)$