A car is driving on a flat curve with a radius of 50 m. If...

A car is driving on a flat curve with a radius of 50 m. If the coefficient of friction between the ground the car’s tires is 0.8, what is the maximum speed of the car in order to make the curve without sliding? (A) 8 $\mathrm{m} / \mathrm{s}^{2}$ (B) 12 $\mathrm{m} / \mathrm{s}^{2}$ (C) 16 $\mathrm{m} / \mathrm{s}^{2}$ (D) 20 $\mathrm{m} / \mathrm{s}^{2}$

A car is driving on a flat curve with a radius of 50 m. If the coefficient of friction between the ground the car’s tires is 0.8, what is the maximum speed of the car in order to make the curve without sliding?
(A) 8 $\mathrm{m} / \mathrm{s}^{2}$
(B) 12 $\mathrm{m} / \mathrm{s}^{2}$
(C) 16 $\mathrm{m} / \mathrm{s}^{2}$
(D) 20 $\mathrm{m} / \mathrm{s}^{2}$

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Key Concepts

Uniform Circular Motion

Uniform circular motion describes the motion of an object traveling at a constant speed along a circular path. It is characterized by a constant change in direction, which implies the presence of an inward acceleration known as centripetal acceleration. In real-world applications, such as vehicles taking a curve, the force responsible for this acceleration keeps the object moving in a circular path.

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. On flat curves, static friction is key because it provides the necessary force to propel a vehicle inward, towards the center of the circle, counteracting the car's tendency to move in a straight line due to inertia.

Centripetal Force and Its Calculation

Centripetal force is the net force required to keep an object moving in a circular path and is directed toward the center of the circle. In many practical applications, the maximum speed of an object around a curve without slipping is determined by setting the maximum static frictional force equal to the required centripetal force, leading to the formula v = sqrt(mu * g * r), where mu is the coefficient of friction, g is the acceleration due to gravity, and r is the radius of the curvature.

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