### Roller-Coaster ProblemA roller-coaster car has a mass of **505 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.#### Diagram ExplanationThe diagram shows a section of the roller-coaster with two labeled points, **A** and **B**, which are horizontally aligned on the roller-coaster track. Both points are at the top of circular sections of the track, with **A** having a smaller radius of curvature than **B**.#### Questions**(a)** If the vehicle has a speed of **19.1 m/s** at point **A**, what is the force exerted by the track on the car at this point?- **Answer:****(b)** What is the maximum speed the vehicle can have at **B** and still remain on the track?- **Answer:**These questions involve concepts such as centripetal force and gravitational force acting on the roller-coaster car as it moves over the hills of the roller-coaster track.

Answered: Image /qna-images/answer/1269dd25-2659-45d5-b789-15a661dddf2c.jpg

A roller-coaster car has a mass of 505 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 ₁ = 10.0 m and r₂ = 15.0 m, respectively. (a) If the vehicle has a speed of 19.1 m/s at point, what is the force exerted by the track on the car at this point? (b) What is the maximum speed the vehicle can have at B and still remain on the track?

A roller-coaster car has a mass of 505 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 ₁ = 10.0 m and r₂ = 15.0 m, respectively. (a) If the vehicle has a speed of 19.1 m/s at point, what is the force exerted by the track on the car at this point? (b) What is the maximum speed the vehicle can have at B and still remain on the track?

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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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

### Roller-Coaster Problem

A roller-coaster car has a mass of **505 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.

#### Diagram Explanation
The diagram shows a section of the roller-coaster with two labeled points, **A** and **B**, which are horizontally aligned on the roller-coaster track. Both points are at the top of circular sections of the track, with **A** having a smaller radius of curvature than **B**.

#### Questions

**(a)** If the vehicle has a speed of **19.1 m/s** at point **A**, what is the force exerted by the track on the car at this point?

- **Answer:**

**(b)** What is the maximum speed the vehicle can have at **B** and still remain on the track?

- **Answer:**

These questions involve concepts such as centripetal force and gravitational force acting on the roller-coaster car as it moves over the hills of the roller-coaster track.

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