PhysicsBowl 2019 Q28

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PhysicsBowl 2019

28) For this question, there is a 45° banked curve on a race track of radius 80 meters. We also know that this is a frictionless curve. In order to find a safe speed to drive, we can start by looking at the force diagram.

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

Since we don't want the car to slip up or down the incline, the net force in the y-direction should be 0, while the net force in the x-direction should be the centripetal force.

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

Finally, solving these two equations we can come up with a simplified equation.

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

Finally, by plugging in our given values, we can solve for the optimal speed.

Where v is velocity, r is radius, g is acceleration due to gravity, and θ is the angle of banking

Answer: D