Race cars often use wings in an effort to increase cornering speeds. The wings provide an extra downward force that increases the friction force available between the tyres and the road.
For a brief time, the Formula 1 championship held one of the races in the USA at the Indianapolis International Speedway. A part of the circuit utilised one of the banked corners that makes up the main oval track. This corner has a radius of curvature of ? = 350m and is banked at an angle of ???= 90.
By the rules, a Formula 1 car must weigh 640kg (including the driver), and an estimated coefficient of static friction between the tyres and the road is ?s = 1.5.
(a) Calculate the maximum speed that a Formula 1 car can travel around the banked corner without any down force.
(b) Calculate the maximum speed that a Formula 1 car can travel around the banked corner with a wing that provides a down force of; Where v is the speed of the car in m/s.