Question

A highway curve with a radius of 450 m is banked properly for a car traveling 80 km/h. If a 1560- kg Porshe 928S rounds the curve at 250 km/h, how much sideways force must the tires exert against the road if the car does not skid?

Answer 1

if the highway curve was made properly for a car traveling 80km/h, then we can say that the car is traveling too fast (3 times the top allowed speed). However, the speed the car describes (seeing from outside the road) is a speed tangential to the curve, which means that the car will experience a centrifugal force (so it will experience a centripetal force). This force (aplying the Second Law of Newton) is given by the following:

Using the fact that the top allowed speed is equals 80km/h (22.22m/s), the mass of the car is equals 1560Kg and the radius of the curve is equals 450m, we can find the centrifugal force that WILL NOT make the car skid on the road. This is:

However, this car is traveling at a lineal speed equals 250km/h (69.44m/s). The centripetal force will be equals:

if the car at this speed does not skid, then the tires have to exert a sideways force against the road equals 15Nw approximately