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 107 m, while the largest has a radius of172 m, as the drawing illustrates. The height of the outer wall is14.9 m. Find (a) the smallest and(b) the largest speed at which cars can move onthis track without relying on friction.

(a)

Number

Units

(b)

Number

Units

Answer a1: the number of significant digitsis set to 3; the tolerance is +/-2%
Answer b1: the number of significant digits isset to 3; the tolerance is +/-2%

Chapter 5, Problem 22

Explanation / Answer

The speed of the cars on this track without relying onfriction          v =(rgtan) Height of the outer wall is h = 14.9 m From fig we can write tan = 14.9m / 172m -107 m          = 0.23   therefore vmin = (107*9.8*0.23)                         = 15.52 m/s   and                vmax = (172*9.8*0.23)                          =19.68m/s            

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