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Writer's picturekeshprad

PhysicsBowl 2018 Q8

8) This question includes topics of banking and centripetal motion. We want to find the minimum banking angle necessary to make a 100 m radius turn at 35 m/s. Let's start this problem with a free body diagram.

Where F[g] is the gravitational force, m is mass, g is acceleration of gravity, N is normal force, and θ is the banking angle

The car doesn't move up or down the incline, so we can equate the vertical forces. Additionally, since the car moves in a circular path, the horizontal forces will be equal to the centripetal force. Now we can set up and solve this system of equations.

Where F is force, m is mass, v is velocity, r is radius, N is normal, g is acceleration of gravity, and θ is the banking angle

Now that we have come up with this equation, we can plug in our given values and solve for θ.

Where θ is the minimum banking angle

Answer: D

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