Question

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?

Answer 1

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 \(g\).
\[F_f = F_c \Rightarrow \mu mg = \frac{mv^2}{r} \Rightarrow \boxed{\displaystyle r=\frac{v^2}{\mu g}}\]