A car is driving on a flat curve with a radius of 50 m . If the coefficient of friction between

step 1 In order for a car to make a curve without slipping, the road should provide a force of centipit

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 $\mathrm{m}$ . 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 $\mathrm{m}$ . 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

Newton's Second Law

Newton’s Second Law states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This law is used to relate the frictional force acting on a car to the centripetal acceleration needed for it to navigate a curve.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. It acts towards the center of the circle and is given by the expression F = mv²/r, where m is mass, v is speed, and r is the radius of the circle. This concept is crucial when analyzing any scenario involving objects in circular motion.

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. In the context of a vehicle making a turn, static friction between the tires and the road supplies the necessary centripetal force to keep the car on a curved path instead of sliding outward.

Coefficient of Friction

The coefficient of friction is a dimensionless value that quantifies the amount of friction between two surfaces. It is used to determine the maximum frictional force that can be exerted before sliding occurs, which in turn limits the maximum speed or acceleration available for circular motion.

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