Question

A NASCAR racecar rounds one end of the Martinsville Speedway. This end of the track is a turn with radius approximately 57.0 m. If we approximate the track to be completely flat and the racecar is traveling at a constant 26.5 m / s (about 59 mph) around the turn, what is the racecar\'s centripetal (radial) acceleration?

What is the force responsible for the centripetal acceleration in this case?

friction, normal, gravity, or weight?

To keep from skidding into the wall on the outside of the turn what is the minimum coefficient of static friction between the racecar\'s tires and track?

Answer 1

Concepts and reason

The required concepts to solve the given question are the centripetal force, centripetal acceleration and the frictional force acting on the race car.

First, calculate the centripetal acceleration using the relation between the speed, radius of the curve and the centripetal acceleration. Then, find the force responsible for the centripetal acceleration. Compare the centripetal force and the frictional force and then calculate the minimum coefficient of static friction between the tires of the race car and the track.

Fundamentals

Newton’s second law states that the acceleration of an object produced by a net force is directly proportional to the magnitude of net force and inversely proportional to the mass of an object.

The mathematical expression is given as,

$F=ma $

Here, F is the force acting on an object, m is the mass, and a is its acceleration.

Centripetal force may be defined as “the force acting on a body moving in a circular path and directed towards the center around which the body is moving”.

The mathematical expression for centripetal force is given as,

Here, is the centripetal force, m is the mass of the particle, v is the velocity, and R is the radius of the circular orbit.

The direction of the acceleration is towards the center of the circle. It depends upon the speed of the particle and the radius of the circular path it moves.

Weight of an object is “the force of gravity”. It is defined as the mass times, the acceleration due to gravity.

Express the relation for weight of an object.

Here, W is the weight of an object, m is the mass of an object, and g is the acceleration due to gravity.

The normal force acting on an object is equal and opposite to the gravitational force applied on an object.

Friction is the resistance to move. The frictional force is the resistive force which opposes the relative motion between the surfaces that are in contact with each other. It acts in the opposite direction of motion. There are mainly two types of frictional forces: static friction and dynamic friction.

Static frictional force can be calculated by “taking the coefficient of friction between the two surfaces and multiplying it by the normal force that the surface applies on an object”. The normal force is equal to the force of gravity acting on an object, if it is on a flat surface.

Express the relation for static frictional force.

Here, is the static friction force, is the coefficient of static friction, and N is the normal force acting on an object.

(1)

Express the relation for the Newton’s law of motion,

Here, is the centripetal acceleration.

Express the relation for the centripetal force.

For an object in a circular motion, the force acting is centripetal force. Hence, compare the expressions for centripetal force and Newton’s law of motion.

The centripetal acceleration of the race car is,

Substitute for v, and 57 m for R.

(2)

When the car makes a turn, frictional force begins to act upon the wheels of the car. This force provides the necessary centripetal force required for the circular motion. Hence the force responsible for the centripetal acceleration is friction force.

(3)

Express the relation for force acting on the car.

$F=ma $ ……(1)

Express the relation for friction force acting between the race car wheel and the track.

…….(2)

Compare the forces acting on the race car and static friction.

Substituting for , and for .

Ans: Part 1

The centripetal acceleration of the race car is .

Part 2

The force responsible for the centripetal acceleration is friction.

Part 3

The minimum coefficient of static friction is .