1. The FedEx car that is leading the pack is traveling at 188 mph (84.0 m/s). Th

Question

1. The FedEx car that is leading the pack is traveling at 188 mph (84.0 m/s). They are racing in the Daytona 500 on the famous tri-oval track and are in the middle of turns one and two. At that location, the track is banked at 31.0 degrees.

Find the radius of curvature such that the Fed Ex car can travel through the corner without turning the steering wheel.

I'm having trouble with the concepts in this problem, could someone help me please? Detailed information about which equations were used and why would be extremely helpful! Thanks!

Explanation / Answer

In the case of banked curves, The weight of the body balanced with the horizontal component of normal reaction.                N cos = mg And the vertical component of normal reaction is balanced with centripetal force                N sin = mv^2/r By using the above two equations we have that                mv^2/r = mg tan By simplifying the above we have                       r = v^2 / (g tan)                                        ...... (1) Given that                      v = 84.0 m/s                      = 31.0 degree By substituting all these values in the above equation (1) we get                       r = (84.0 m/s)^2 / (9.8 tan31)                       r = 1198.3 m SO the radius of curvature is given by r = 1198.3 m                       r = v^2 / (g tan)                                        ...... (1) Given that                      v = 84.0 m/s                      = 31.0 degree By substituting all these values in the above equation (1) we get                       r = (84.0 m/s)^2 / (9.8 tan31)                       r = 1198.3 m SO the radius of curvature is given by r = 1198.3 m

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