Centripetal acceleration automobile problem

[Haniszmi]

Homework Statement

6. A car of mass 1750 kg rounds a circular turn of radius of 21 m. The road is flat and the coefficient of kinetic friction between the tires and the road is 0.3, while the coefficient of static friction is 0.76. How fast can the car go without skidding?

Homework Equations

Mu(static)mg = mv^2/r

The Attempt at a Solution

I understand how to do the problem, I just don't understand why the coefficient of static friction would be used and not the coefficient of kinetic friction since the car is moving and not stationary(static friction)

 

[thepanda]

The friction force is not the one that opposes the forward motion but rather the force towards the center that provides the centripetal acceleration (thus, stops the motion of the car from going outward).

 

[thomate1]

in the circular turn.

I can provide an explanation for the use of the coefficient of static friction in this problem. When a car is moving in a circular turn, it experiences a centripetal force that keeps it moving in a circular path. This force is provided by the friction between the tires and the road. In order for the car to maintain its circular motion without skidding, the force of friction must be equal to the centripetal force.

Now, there are two types of friction - static and kinetic. Static friction is the force that prevents two surfaces from sliding against each other when they are stationary. Kinetic friction, on the other hand, is the force that opposes the motion of two surfaces that are sliding against each other.

In this problem, the car is moving in a circular turn, which means that the tires are constantly sliding against the road. However, the car is not slipping or skidding, which means that the force of friction acting between the tires and the road is static friction. This is because the car is moving fast enough that the tires do not lose contact with the road and start sliding, but not too fast that the force of static friction is exceeded.

Therefore, in order to determine the maximum speed at which the car can go without skidding, we need to use the coefficient of static friction in the equation for centripetal force. This represents the maximum amount of friction that can be provided by the tires before they start sliding.

I hope this helps to clarify the use of the coefficient of static friction in this problem. It is important to understand the difference between static and kinetic friction and when each one is applicable in a given situation.