Corners on public roads, race tracks and test tracks, are banked so that less larteral friction force is required when taking the corners at speed. Spectacular banking is seen in this velodrome (cycle track).
1 A road has a curve with a radius of 100 meters. A car is to be driven around the curve at 40 m/s.
a Find and draw the inertial force (the virtual gravity) on the car as a consequence of its centripetal acceleration.
b Find the angle at which the road must be banked for the most comfortable ride.
2 The Ferrari F50 shown is driven at speed on a test track which is banked at 45° in a corner with a radius of 400 meters.
a Find the speed of the car if there is no lateral friction force under the tyres.
b Find the apparent weight of an eighty kilogram driver in magnitude and direction.