Final answer:
To find the minimum coefficient of static friction between the pavement and the tires of a car navigating a banked curve, we need to consider the centripetal force and the maximum static friction force. By setting up a system of equations and solving for the unknown coefficient of static friction, we can determine the value needed for the car to navigate the curve without skidding.
Step-by-step explanation:
To determine the minimum coefficient of static friction, we need to consider the forces acting on the car while it navigates the curve. The centripetal force required to keep the car moving in a circular path is given by FC = mv²/r, where m is the mass of the car, v is its velocity, and r is the radius of the curve.
Next, we need to consider the forces that provide the necessary friction to prevent the car from skidding. In this case, the friction force is provided by the static friction between the tires and the pavement. The maximum static friction force is given by f_max = μsN, where μs is the coefficient of static friction and N is the normal force.
With these equations, we can set up a system of equations to solve for the unknown coefficient of static friction. The normal force can be determined by considering the forces in the vertical direction, N = mg cos(theta), where g is the acceleration due to gravity and theta is the angle of the banked curve.
By substituting the given values and solving the equations, we can find the minimum coefficient of static friction required for the car to navigate the curve without skidding.