Friction provides the force needed for a car to travel around a flat, circular race track. What is the maximum speed at which a car can safely travel if the radius of the track is 84.0 m and the coefficient of friction is 0.42?

The maximum speed at which the car can safety travel around the track is 18.6m/s.

Explanation:

Since the car is in circular motion, there has to be a centripetal force . In this case, the only force that applies for that is the static frictional force between the tires and the track. Then, we can write that:

And since and , we have:

Now, if we write the vertical equation of motion of the car (in which there are only the weight and the normal force), we obtain:

Substituting this expression for and solving for , we get:

Finally, plugging in the given values for the coefficient of friction and the radius of the track, we have:

It means that in its maximum value, the speed of the car is equal to 18.6m/s.

Explanation:

We need to equal the friction force and the centripetal force:

I hope it helps you!

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explanation: