A car is travelling at 60 km/h on a road such that the coefficient of friction between its tires and the road is 0.50. What is the minimum turning radius of the car?

Question

anonymous · Answer

In the minimal case, the maximum value of the friction force will equal the centripetal force.  Let the mass of the car be $m$, the velocity be $v$, the coefficient of static friction be $\mu$, turning radius be $r$, and gravitational acceleration be $g$.
$$F_f = F_c \Rightarrow \mu mg = \frac{mv^2}{r} \Rightarrow \boxed{\displaystyle r=\frac{v^2}{\mu g}}$$