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 117 m, while the largest has a radius of 153 m, as the drawing illustrates. The height of the outer wall is 11.0 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 117 m, while the largest has a radius of 153 m, as the drawing illustrates. The height of the outer wall is 11.0 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.

Explanation / Answer

The formula is tan theta = V^2/rg ? V = sqrt(rgtan theta)
tan theta seems to be 11/(153-117) = .3055, so

a) V = sqrt(117*9.8*.3055) = 18.71 and

b) V = sqrt(153*9.8*.3055) = 21.40

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