A roller-coaster car has a mass of 499 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) If the vehicle has a speed of 20.9 m/s at point, what is the force exerted by the track on the car at this point? 24851.2 X Draw a free-body diagram of the cart at the point. Include only 'real' forces (i.e. do not include anything labeled centripetal or centrifugal). In what direction should the net force point? N (b) What is the maximum speed the vehicle can have at Band still remain on the track? m/s

A roller-coaster car has a mass of 499 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) If the vehicle has a speed of 20.9 m/s at point, what is the force exerted by the track on the car at this point? 24851.2 X Draw a free-body diagram of the cart at the point. Include only 'real' forces (i.e. do not include anything labeled centripetal or centrifugal). In what direction should the net force point? N (b) What is the maximum speed the vehicle can have at Band still remain on the track? m/s

Name: **Roller Coaster Physics Problem**A roller-coaster car has a mass of
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Description: **Roller Coaster Physics Problem**A roller-coaster car has a mass of **499 kg** when fully loaded with passengers. The path of the coaster, from its initial point shown in the diagram to point **B**, involves only up-and-down motion (as seen by the

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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Question

**Roller Coaster Physics Problem**

A roller-coaster car has a mass of **499 kg** when fully loaded with passengers. The path of the coaster, from its initial point shown in the diagram 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.

### Questions

**(a)** If the vehicle has a speed of **20.9 m/s** at point **A**, what is the force exerted by the track on the car at this point?

*24851.2 N*

*Draw a free-body diagram of the cart at the point **A**. Include only 'real' forces (i.e., do not include anything labeled centripetal or centrifugal). In what direction should the net force point?*

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

*m/s*

### Diagram Explanation

The image shows a roller coaster with labeled points **A** and **B** at the bottom and top of two circular arcs, respectively. Point **A** is at the dip of the first hill, while point **B** is at the top of the second hill. The radii of these circular sections are \( r_1 = 10.0 \, \text{m} \) at **A** and \( r_2 = 15.0 \, \text{m} \) at **B**.

This setup helps analyze the forces and speeds involved as the roller coaster moves along the track, focusing specifically on the effects of centripetal force and gravitational force at these points.

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