Initial O v = 0 Final Y = 0 A 14 kg ball initially at rest rolls down a 142 m tall hill. When the ball reaches the bottom it is travelin 31.1 m/s. How much energy is dissipated by friction on the ball?

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Chapter1: Units, Trigonometry. And Vectors
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## Energy Dissipation in Rolling Motion

### Diagram Explanation:

The diagram shows the motion of a ball rolling down a hill. There are two main points depicted:

1. **Initial Position:**
   - Located at the top of the hill.
   - The ball is at rest (`V = 0`).

2. **Final Position:**
   - Located at the bottom of the hill (`Y = 0`).
   - The ball is moving with a certain velocity.

### Problem Statement:

A 14 kg ball initially at rest rolls down a 142 m tall hill. When the ball reaches the bottom, it is traveling at 31.1 m/s. How much energy is dissipated by friction on the ball?

### Solution:

To determine the energy dissipated by friction, compare the initial potential energy with the final kinetic energy and calculate the difference:

1. **Initial Potential Energy (PE):**
   - \( PE = m \times g \times h \)
   - \( m = 14 \text{ kg} \)
   - \( g = 9.81 \text{ m/s}^2 \) (acceleration due to gravity)
   - \( h = 142 \text{ m} \)

2. **Final Kinetic Energy (KE):**
   - \( KE = \frac{1}{2} \times m \times v^2 \)
   - \( v = 31.1 \text{ m/s} \)

3. **Energy Dissipated by Friction:**
   - \( \text{Energy dissipated} = PE - KE \)

Use these equations to calculate the difference and determine the energy lost due to friction.
Transcribed Image Text:## Energy Dissipation in Rolling Motion ### Diagram Explanation: The diagram shows the motion of a ball rolling down a hill. There are two main points depicted: 1. **Initial Position:** - Located at the top of the hill. - The ball is at rest (`V = 0`). 2. **Final Position:** - Located at the bottom of the hill (`Y = 0`). - The ball is moving with a certain velocity. ### Problem Statement: A 14 kg ball initially at rest rolls down a 142 m tall hill. When the ball reaches the bottom, it is traveling at 31.1 m/s. How much energy is dissipated by friction on the ball? ### Solution: To determine the energy dissipated by friction, compare the initial potential energy with the final kinetic energy and calculate the difference: 1. **Initial Potential Energy (PE):** - \( PE = m \times g \times h \) - \( m = 14 \text{ kg} \) - \( g = 9.81 \text{ m/s}^2 \) (acceleration due to gravity) - \( h = 142 \text{ m} \) 2. **Final Kinetic Energy (KE):** - \( KE = \frac{1}{2} \times m \times v^2 \) - \( v = 31.1 \text{ m/s} \) 3. **Energy Dissipated by Friction:** - \( \text{Energy dissipated} = PE - KE \) Use these equations to calculate the difference and determine the energy lost due to friction.
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