Circular turns of radius r in a race track are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present, and use the coordinate system specified. Part (a) Find the y-component of the normal force FN on a car going around the turn in terms of the angle θ and the magnitude of the normal vector FN. Part (b) Find the x-component of the normal force FN on a car going around the turn in terms of the angle θ and the magnitude of the normal vector FN. Part (c) Now write the magnitude of the normal force in terms of the force of gravity Fg and the angle θ. Part (d) Now write the magnitude of the normal force again, this time in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling at v. Part (e) Now assume that the car is moving at 15 m/s and the radius of the track is 410 m. What is the angle θ in degrees?

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