A curve in a speed track has a radius of 1000 ft and a rated speed of 120 mi/h. (From Sample Prob. 12.7 is the definition of rated speed: The rated speed of a banked highway curve is the speed at which a car should travel to have no lateral friction force exerted on its wheels.) Knowing that a racing car starts skidding on the curve when traveling at a speed of 160 mi/h, determine

Explanation:

If the question is: Determine the banking angle θ

We have the forces involved on the figure attached.

For this case we know that the weight is given by:

And for this case the centripetal acceleration would be given by:

If we analyze the sum of forces on x and y we have:

And if we solve for the force we got:

If we solve for the normal force we got:

In order to find the banking angle we use the fact that F =0

The velocity on this case is 120 mi/h if we convert this into ft/ s we got:

And then we have this:

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explanation: