A sphere and a ring exists. They both have a mass of M, and has a radius of r. They roll, with no slipping, down a track as depicted in the image. The two objects are at rest initially, and will shoot vertically upwards once they reach the end of the path. 1. Please explain which object, ring or sphere, will reach greater heights and why? 2. For the max height that the ring will reach, please determine and algebraic expression.

College Physics
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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A sphere and a ring exists. They both have a mass of M, and has a radius of r. They roll, with no slipping, down a track as depicted in the image. The two objects are at rest initially, and will shoot vertically upwards once they reach the end of the path.

1. Please explain which object, ring or sphere, will reach greater heights and why?

2. For the max height that the ring will reach, please determine and algebraic expression.

 

The image shows a diagram representing a scenario in physics involving a small object on a track. Here's a description suitable for an educational website:

**Diagram Description:**

The diagram illustrates a track with a small object positioned at the top. Key features of the diagram include:

- **Initial Height (H):** The object starts at a height "H" from the ground, indicated by a vertical measurement on the left side of the diagram.
- **Inclined Ramp:** The track slopes downward from the initial height, allowing the object to gain speed as it descends.
- **Circular Loop Segment:** At the bottom right, the track features a circular section with radius "R" before leveling out. This part of the track is essential for analyzing motion through the loop.

This diagram can be used to explore concepts such as potential and kinetic energy, acceleration, and the forces involved as the object moves along the track.
Transcribed Image Text:The image shows a diagram representing a scenario in physics involving a small object on a track. Here's a description suitable for an educational website: **Diagram Description:** The diagram illustrates a track with a small object positioned at the top. Key features of the diagram include: - **Initial Height (H):** The object starts at a height "H" from the ground, indicated by a vertical measurement on the left side of the diagram. - **Inclined Ramp:** The track slopes downward from the initial height, allowing the object to gain speed as it descends. - **Circular Loop Segment:** At the bottom right, the track features a circular section with radius "R" before leveling out. This part of the track is essential for analyzing motion through the loop. This diagram can be used to explore concepts such as potential and kinetic energy, acceleration, and the forces involved as the object moves along the track.
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