College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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### Rolling Motion and Energy Conservation

**Problem Statement:** A ball with an initial velocity of **5.17 m/s** rolls up a hill without slipping.

**(a)** **Treating the ball as a spherical shell, calculate the vertical height (in meters) it reaches.**
- Input provided: **3.64 m** 
  - The given answer is incorrect (marked with a red cross).

**(b)** **Repeat the calculation (in meters) for the same ball if it slides up the hill without rolling.**
- Input provided: **1.364 m**
  - The given answer is correct (marked with a green check mark).

### Explanation:

**(a)** When the ball is treated as a spherical shell, the calculation involves considering both the translational and rotational kinetic energy. The ball's energy is distributed between its movement up the hill and its rotational motion.

**(b)** If the ball slides up the hill without rolling, its energy is solely translational kinetic energy, which simplifies the calculation. The result is 1.364 meters, indicating that it requires less energy to gain height when not accounting for rotational motion. 

This exercise highlights the principles of energy conservation and the differences in energy distribution between rolling and sliding motions.

Note: Diagrams and further mathematical explanation would be beneficial for a comprehensive understanding of the physics involved.
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Transcribed Image Text:### Rolling Motion and Energy Conservation **Problem Statement:** A ball with an initial velocity of **5.17 m/s** rolls up a hill without slipping. **(a)** **Treating the ball as a spherical shell, calculate the vertical height (in meters) it reaches.** - Input provided: **3.64 m** - The given answer is incorrect (marked with a red cross). **(b)** **Repeat the calculation (in meters) for the same ball if it slides up the hill without rolling.** - Input provided: **1.364 m** - The given answer is correct (marked with a green check mark). ### Explanation: **(a)** When the ball is treated as a spherical shell, the calculation involves considering both the translational and rotational kinetic energy. The ball's energy is distributed between its movement up the hill and its rotational motion. **(b)** If the ball slides up the hill without rolling, its energy is solely translational kinetic energy, which simplifies the calculation. The result is 1.364 meters, indicating that it requires less energy to gain height when not accounting for rotational motion. This exercise highlights the principles of energy conservation and the differences in energy distribution between rolling and sliding motions. Note: Diagrams and further mathematical explanation would be beneficial for a comprehensive understanding of the physics involved.
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