On a banked race track, the smallest circular path on which cars can move has a radius of 116 m, while the largest has a radius of 174 m, as the drawing illustrates. The height of the outer wall is 15.8 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.
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Θ = arctan(15.8/(174 - 116)) = 15.24°
a) Vs = √[r*g*tanΘ] = 17.60 m/s
b) VL= √[R*g*tanΘ] = 21.55 m/s
a) Vs = √[r*g*tanΘ] = 17.60 m/s
b) VL= √[R*g*tanΘ] = 21.55 m/s