On a banked race track, the smallest circular path on which cars can move has a

Question

On a banked race track, the smallest circular path on which cars can move has a radius of 114 m, while the largest has a radius of 151 m, as the drawing illustrates. The height of the outer wall is 12.5 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction. On a banked race track, the smallest circular path on which cars can move has a radius of 114 m, while the largest has a radius of 151 m, as the drawing illustrates. The height of the outer wall is 12.5 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction. On a banked race track, the smallest circular path on which cars can move has a radius of 114 m, while the largest has a radius of 151 m, as the drawing illustrates. The height of the outer wall is 12.5 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.

Explanation / Answer

A) angle of banking, tan theta = (12.5)/(151-114) =0.3378

Smallest speed v = sqrt(rg tan theta)

                 = sqrt(114*9.8*0.3378)

              = 19.4 m/s

B) Largest speed = sqrt (Rg tan theta)

      = sqrt (151*9.8*0.3378)

     = 22.36 m/s

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