Banked Curves (finding smallest & largest speed)

[helen3743]

Hello, thank you for helping.

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!

 

[Fermat]

tan(@) = 18/56 = 0.34143

But you used tan(18/56)!

which = 5.61x10^-3

That's why your answers are so low.

If you use tan@ = 0.34143, you will get the correct answers.

 

[helen3743]

oooo.. makes sense. Thank you!