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A roller-coaster car has a mass of 511 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 O and O are parts of vertical circles of radius r, = 10.0 m andr, = 15.0 m, respectively. (a) If the vehicle has a speed of 20.3 m/s at point O, 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 ® and still remain on the track? m/s

A roller-coaster car has a mass of 511 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 O and O are parts of vertical circles of radius r, = 10.0 m andr, = 15.0 m, respectively. (a) If the vehicle has a speed of 20.3 m/s at point O, 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 ® and still remain on the track? m/s

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**Roller Coaster Physics Problem** A roller-coaster car has a mass of 511 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 perceived by the riders), with no lateral motion. Assume the roller-coaster tracks at points \( \mathbf{A} \) and \( \mathbf{B} \) are parts of vertical circles with radii \( r_1 = 10.0 \, \text{m} \) and \( r_2 = 15.0 \, \text{m} \), respectively. ### Diagram Explanation: The diagram shows a roller coaster track with two notable points labeled \( \mathbf{A} \) and \( \mathbf{B} \). At these points, the track is part of vertical circular sections, where measurements are indicated for the radius of these circles. ### Problem Statement: 1. **(a)** If the vehicle has a speed of \( 20.3 \, \text{m/s} \) at point \( \mathbf{A} \), what is the force exerted by the track on the car at this point? - **Answer:** \(\text{__________ N}\) 2. **(b)** What is the maximum speed the vehicle can have at \( \mathbf{B} \) and still remain on the track? - **Answer:** \(\text{__________ m/s}\) Use the given data and diagrams to solve for needed physical quantities using principles of circular motion and forces.
Transcribed Image Text:**Roller Coaster Physics Problem** A roller-coaster car has a mass of 511 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 perceived by the riders), with no lateral motion. Assume the roller-coaster tracks at points \( \mathbf{A} \) and \( \mathbf{B} \) are parts of vertical circles with radii \( r_1 = 10.0 \, \text{m} \) and \( r_2 = 15.0 \, \text{m} \), respectively. ### Diagram Explanation: The diagram shows a roller coaster track with two notable points labeled \( \mathbf{A} \) and \( \mathbf{B} \). At these points, the track is part of vertical circular sections, where measurements are indicated for the radius of these circles. ### Problem Statement: 1. **(a)** If the vehicle has a speed of \( 20.3 \, \text{m/s} \) at point \( \mathbf{A} \), what is the force exerted by the track on the car at this point? - **Answer:** \(\text{__________ N}\) 2. **(b)** What is the maximum speed the vehicle can have at \( \mathbf{B} \) and still remain on the track? - **Answer:** \(\text{__________ m/s}\) Use the given data and diagrams to solve for needed physical quantities using principles of circular motion and forces.
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