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Required information A roller-coaster car of mass 331 kg (including passengers) travels around a horizontal curve of radius 40.2 m. Its speed is 11.8 m/s. What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. 88.29

Required information A roller-coaster car of mass 331 kg (including passengers) travels around a horizontal curve of radius 40.2 m. Its speed is 11.8 m/s. What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. 88.29

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter6: Applications Of Newton’s Laws Of Motion
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**Required Information** A roller-coaster car of mass 331 kg (including passengers) travels around a horizontal curve of radius 40.2 m. Its speed is 11.8 m/s. **Question:** What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. **Answer:** 88.29° **Explanation for Students:** When solving for the direction of the total force exerted on a roller-coaster car by the track, it is important to consider both the horizontal and vertical components of the force. The car is subject to centripetal force, which acts horizontally towards the center of the curve, and gravitational force, which acts vertically downward. To find the total force and its direction, you use vector addition of these two forces and then determine the angle relative to the horizontal. If the resultant force vector is above the horizontal axis, the angle is positive; if it's below, the angle is negative. In this example calculation, the direction of the force is found to be 88.29° above the horizontal. This suggests that the resultant force vector is almost vertical, slightly leaning upward from the horizontal plane.
Transcribed Image Text:**Required Information** A roller-coaster car of mass 331 kg (including passengers) travels around a horizontal curve of radius 40.2 m. Its speed is 11.8 m/s. **Question:** What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. **Answer:** 88.29° **Explanation for Students:** When solving for the direction of the total force exerted on a roller-coaster car by the track, it is important to consider both the horizontal and vertical components of the force. The car is subject to centripetal force, which acts horizontally towards the center of the curve, and gravitational force, which acts vertically downward. To find the total force and its direction, you use vector addition of these two forces and then determine the angle relative to the horizontal. If the resultant force vector is above the horizontal axis, the angle is positive; if it's below, the angle is negative. In this example calculation, the direction of the force is found to be 88.29° above the horizontal. This suggests that the resultant force vector is almost vertical, slightly leaning upward from the horizontal plane.
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