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My Question:

On a banked race track, the smallest circular path on which cars can move has a radius r1 = 107 m, while the largest has a radius r2 = 163. The height of the outer wall is 18 m.

Find the smallest speed and largest speed at which cars can move on this track without relying on friction.

I already solved the problem but I was wondering if it was correct.

r2-r1 = 163m-107m= 56m.

tan(theta) = 18/56

tan(theta) = v^2 / (rg)

v = sqrt(tan(theta)rg)

for smallest speed:

v = sqrt(tan(18/56)107*9.8) = 2.45 m/s

for largest speed:

v = sqrt (tan(18/56)163*9.8) = 2.99 m/s

Thanks again!

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# Banked Curves (finding smallest & largest speed)

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