A car races around a circular track. Friction on the tires is the _____that acts toward the center of the circle and keeps the car on the circular path.

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electreto05's profile pic

electreto05 | College Teacher | (Level 1) Assistant Educator

Posted on

The word in the blank is "force"

When a race car, it moves along a curve, receives the action of a centrifugal force in the radius direction, and towards the outside of the curve. This force depends on the mass and speed of the car and the radius of the curve, according to the following expression:

Fc = (mv^2)/r

Where:

m, is the mass of the car.

v,  is the velocity.

r, is the radius of curvature.

To compensate this force, in the case where the track is horizontal, the track and the tires must provide a friction force (Fr), at least equal to the centrifugal force. For a given friction coefficient of the track (μ), the friction force is proportional to the mass of the vehicle; so, we can find the speed limit that can reach the vehicle on a horizontal track:

Equating the centrifugal force and the friction force, we have:

Fc = Ff

(mv^2)/r = μ(m*g)

v = sqrt (μ*r*g)

 

 

 

shumbm's profile pic

Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

The answer is force. A force is always the cause of velocity change of a body.

Without force(s), or if several forces applied to a body balance each other, a body will remain motionless, or its motion will have a constant velocity (of course if an inertial frame of reference is used). This is Newton's First Law.

Also note that for a circular motion the friction force "acts toward the center of the circle" only if the speed (the magnitude of the velocity) is constant.

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