On a banked race track, the smallest circular path on which carscan move has a r

Question

On a banked race track, the smallest circular path on which carscan move has a radius of 101 m, while thelargest has a radius 155 m, as the drawingillustrates. The height of the outer wall is 18 m.
(a) Find the smallest speed at which cars canmove on this track without relying on friction.
1 m/s

(b) Find the largest speed at which cars can move on this trackwithout relying on friction.
2 m/s
(a) Find the smallest speed at which cars canmove on this track without relying on friction.
1 m/s

(b) Find the largest speed at which cars can move on this trackwithout relying on friction.
2 m/s

Explanation / Answer

we have : Ptan = mv^2/r => v=(g*r*tan) tan = 18/(155-101) = 1/3
1) The smallest speed when the radius is smallest => Vmin =(9.8*101*1/3) = 18.164 m/s 2)the largeast speed :
Vmax =(9.8*155*1/3) = 22.5m/s

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