A curve of radius 80 meters is properly banked for a car travelling at 60km/hr, what should the coefficient of friction be for a car travelling at 90km/hr?
OCW Scholar - Physics I: Classical Mechanics
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If the road is properly banked for a car traveling 60km/h, then the no friction is required for a car at that speed. Forces up = forces down, and net force acting on the car is Fcentripetal towards the center since it is going in a circle. Force down is the weight of the car = mg. Force up has to be supplied by a component of the normal force The centripetal force = mv^2/r must be supplied by another component of the normal force. Setting up these equations will give you the angle the road is banked at. Once you know that, you can find what frictional force would be needed to overcome the increase in centripetal force (v goes up from 70km/h to 90 km/h).