A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively.
A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively.
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively.
![### Educational Resource: Physics of Roller Coasters
**Problem Statement:**
A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points A and B are parts of vertical circles of radius \( r_1 = 10.0 \, \text{m} \) and \( r_2 = 15.0 \, \text{m} \), respectively.
**Figure Description:**
- **Roller-Coaster Path:** The diagram shows a section of a roller-coaster track with two key points, A and B, marked on it.
- **Point A:** Located at the bottom of a vertical circular path with radius \( r_1 = 10.0 \, \text{m} \).
- **Point B:** Situated at the top of another vertical circle with radius \( r_2 = 15.0 \, \text{m} \).
**Questions:**
(a) If the vehicle has a speed of \( 19.0 \, \text{m/s} \) at point A, what is the force exerted by the track on the car at this point?
\[ \text{Force} \, = \, \_\_\_\_\_ \, \text{N} \]
(b) What is the maximum speed the vehicle can have at point B and still remain on the track?
\[ \text{Speed} \, = \, \_\_\_\_\_ \, \text{m/s} \]
This problem helps in understanding concepts of circular motion and the forces acting on a roller-coaster car as it travels through vertical loops. The force exerted by the track and the maximum permissible speed are important in ensuring the safety and structural integrity of roller coasters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdabb8348-a989-41f3-81da-50fefdf00912%2Fac491c41-2818-4057-bde2-f71d054558de%2Fuby35o3_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Physics of Roller Coasters
**Problem Statement:**
A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points A and B are parts of vertical circles of radius \( r_1 = 10.0 \, \text{m} \) and \( r_2 = 15.0 \, \text{m} \), respectively.
**Figure Description:**
- **Roller-Coaster Path:** The diagram shows a section of a roller-coaster track with two key points, A and B, marked on it.
- **Point A:** Located at the bottom of a vertical circular path with radius \( r_1 = 10.0 \, \text{m} \).
- **Point B:** Situated at the top of another vertical circle with radius \( r_2 = 15.0 \, \text{m} \).
**Questions:**
(a) If the vehicle has a speed of \( 19.0 \, \text{m/s} \) at point A, what is the force exerted by the track on the car at this point?
\[ \text{Force} \, = \, \_\_\_\_\_ \, \text{N} \]
(b) What is the maximum speed the vehicle can have at point B and still remain on the track?
\[ \text{Speed} \, = \, \_\_\_\_\_ \, \text{m/s} \]
This problem helps in understanding concepts of circular motion and the forces acting on a roller-coaster car as it travels through vertical loops. The force exerted by the track and the maximum permissible speed are important in ensuring the safety and structural integrity of roller coasters.
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