We consider an automobile of mass m traveling along a curved but level road. To avoid skidding, the road must supply a frictional force F = ma, where a is the car’s acceleration vector. The maximum magnitude of the frictional force is μmg, where μ is the coefficient of friction and g = 9.8 m/s². Let v be the car’s speed in meters per second.

What is the smallest radius R about which an automobile can turn without skidding at 100 km/h if μ = 0.75 (a typical value)?