Flat Curves Practice Problems

An automobile of mass 1200 kg travels at 14 m/s around a flat curve with a radius of 50 m. What is the bare minimum coefficient of friction that the tires must have with the ground in order for the car to turn?

A truck with a mass of 2600 kg is driving on a horizontal unbanked curve with a radius of 38 meters at a constant speed of 18 m/s. What is the magnitude of the force of friction acting on the truck that is required to keep it moving in a circular path?

A race car driver is able to take a sharp turn on a dry, unbanked road at a maximum speed of 75 km/h. However, due to unexpected rainfall, the coefficient of static friction is reduced by 70%. What is the maximum speed at which the race car can take the same turn on a rainy day without skidding off the road? Assume that the conditions of the road are identical except for the change in the coefficient of static friction.

The enhanced braking system of a bus allows it to stop at a minimum distance of 67 m on a slick and level road while traveling at a speed of 96 km/h. On a frost-covered surface, what is the smallest radius value of the sharpest curve that the bus can navigate without sliding off of the road?

A motorcycle spirals inward on a large open track, maintaining a constant speed of 12.0 m/s from an initial position of 52.0 m from the center. Given the friction coefficient between the tire and track is 0.90, at what distance from the center will the motorcycle begin to slide?