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-Circular turns of radius r in a race track are often banked at an angle of 0 to allow the cars to achieve higher speeds around the turns. Assume friction is not present, and use the coordinate system specified. a) Write an expression for the sum of the forces in the x- direction, F b) Write an expression for the sum of the forces in the y- direction, ΣF, . (7) c) Now assume that the car is moving with speed of 15 m/s and the radius of the track is 60 m. What is the angle in degrees? (6) (7) 8

-Circular turns of radius r in a race track are often banked at an angle of 0 to allow the cars to achieve higher speeds around the turns. Assume friction is not present, and use the coordinate system specified. a) Write an expression for the sum of the forces in the x- direction, F b) Write an expression for the sum of the forces in the y- direction, ΣF, . (7) c) Now assume that the car is moving with speed of 15 m/s and the radius of the track is 60 m. What is the angle in degrees? (6) (7) 8

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Banked Circular Turns in Racetracks** Circular turns of radius \( r \) in a racetrack are often banked at an angle \( \theta \) to allow cars to achieve higher speeds around the turns. Assume friction is not present, and use the specified coordinate system. a) Write an expression for the sum of the forces in the x-direction, \( \Sigma F_x \). b) Write an expression for the sum of the forces in the y-direction, \( \Sigma F_y \). c) Now assume that the car is moving with a speed of 15 m/s and that the radius of the track is 60 m. What is the angle \( \theta \) in degrees? **Diagram Description:** The diagram shows a car on a banked curve. The car is tilted towards the center of the circular path, which is horizontal along the ground. The angle of the incline with the horizontal surface is labeled as \( \theta \). A blue arrow pointing downwards represents the force due to gravity, while another blue arrow is perpendicular to the surface of the track, indicating the normal force.
Transcribed Image Text:**Banked Circular Turns in Racetracks** Circular turns of radius \( r \) in a racetrack are often banked at an angle \( \theta \) to allow cars to achieve higher speeds around the turns. Assume friction is not present, and use the specified coordinate system. a) Write an expression for the sum of the forces in the x-direction, \( \Sigma F_x \). b) Write an expression for the sum of the forces in the y-direction, \( \Sigma F_y \). c) Now assume that the car is moving with a speed of 15 m/s and that the radius of the track is 60 m. What is the angle \( \theta \) in degrees? **Diagram Description:** The diagram shows a car on a banked curve. The car is tilted towards the center of the circular path, which is horizontal along the ground. The angle of the incline with the horizontal surface is labeled as \( \theta \). A blue arrow pointing downwards represents the force due to gravity, while another blue arrow is perpendicular to the surface of the track, indicating the normal force.
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