A car traveling on a flat (unbanked), circular track accelerates uniformly from

Question

A car traveling on a flat (unbanked), circular track accelerates uniformly from rest with a tangential acceleration ofa. The car makes it one quarter of the way around the circle before it skids off the track. From these data, determine the coefficient of static friction between the car and the track. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)
?s=

Explanation / Answer

In order for the car to stay within the circular track, the static friction between the tires of the car and the road must provide the centripetal acceleration. Just when the car begins to skid: F(friction,static) = F(centripetal) ==> u(s)mg = mv^2/r ==> v^2 = u(s)rg. The car skids once it travels a distance of (1/4)(2?r) = ?r/2, where r is the radius of the circle. At a constant acceleration a, we see that the speed of the car after it has traveled a distance of (1/2)?r is: v^2 = 2ad = 2a(?r/2) = ?ar. Equating the values of v^2 gives: ?ar = u(s)rg ==> u(s) = ?a/g = (3.14)(2.05 m/s^2)/(9.8 m/s^2) = 0.657.

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