College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Title: Energy Analysis of a Block on a Frictionless Track**

**Introduction:**
A block with a mass of 8.3 kg is released from rest at point A and slides down a frictionless track as shown in the diagram.

**Diagram Explanation:**
The diagram shows a frictionless track with three key points: A, B, and C. The heights of these points above the ground are indicated as follows:
- Point A: 5.00 meters
- Point B: 3.20 meters
- Point C: 2.00 meters

Arrows indicate the vertical distances from each point to the ground, signifying the potential energy each position holds.

**Objective:**
Calculate and list the potential energy, kinetic energy, and total mechanical energy at points A, B, and C.

**Energy Calculations:**

1. **At Point A:**
   - **Potential Energy:**
     - Formula: \( PE = mgh \)
     - \( m = 8.3 \text{ kg}, \, g = 9.81 \text{ m/s}^2, \, h = 5.00 \text{ m} \)

   - **Kinetic Energy:**
     - Formula: \( KE = \frac{1}{2}mv^2 \)
     - Since the block starts from rest, \( v = 0 \text{ m/s} \)

   - **Total Mechanical Energy:**

2. **At Point B:**
   - **Potential Energy:**
     - \( h = 3.20 \text{ m} \)

   - **Kinetic Energy:**

   - **Total Mechanical Energy:**
     - Note: Total mechanical energy remains constant throughout the motion.

3. **At Point C:**
   - **Potential Energy:**
     - \( h = 2.00 \text{ m} \)

   - **Kinetic Energy:**

   - **Total Mechanical Energy:**

**Conclusion:**
By understanding the conservation of mechanical energy in a frictionless system, we can determine the potential and kinetic energy at different points without needing further details about velocity or time.
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Transcribed Image Text:**Title: Energy Analysis of a Block on a Frictionless Track** **Introduction:** A block with a mass of 8.3 kg is released from rest at point A and slides down a frictionless track as shown in the diagram. **Diagram Explanation:** The diagram shows a frictionless track with three key points: A, B, and C. The heights of these points above the ground are indicated as follows: - Point A: 5.00 meters - Point B: 3.20 meters - Point C: 2.00 meters Arrows indicate the vertical distances from each point to the ground, signifying the potential energy each position holds. **Objective:** Calculate and list the potential energy, kinetic energy, and total mechanical energy at points A, B, and C. **Energy Calculations:** 1. **At Point A:** - **Potential Energy:** - Formula: \( PE = mgh \) - \( m = 8.3 \text{ kg}, \, g = 9.81 \text{ m/s}^2, \, h = 5.00 \text{ m} \) - **Kinetic Energy:** - Formula: \( KE = \frac{1}{2}mv^2 \) - Since the block starts from rest, \( v = 0 \text{ m/s} \) - **Total Mechanical Energy:** 2. **At Point B:** - **Potential Energy:** - \( h = 3.20 \text{ m} \) - **Kinetic Energy:** - **Total Mechanical Energy:** - Note: Total mechanical energy remains constant throughout the motion. 3. **At Point C:** - **Potential Energy:** - \( h = 2.00 \text{ m} \) - **Kinetic Energy:** - **Total Mechanical Energy:** **Conclusion:** By understanding the conservation of mechanical energy in a frictionless system, we can determine the potential and kinetic energy at different points without needing further details about velocity or time.
A block with a mass of 8.3 kg is released from rest at point A and slides down the frictionless track as shown above.

**List the following energies at point A:**

- Potential Energy: [ ] J
- Kinetic Energy: [ ] J
- Total Mechanical Energy: [ ] J

**List the following energies at point B:**

- Potential Energy: [ ] J
- Kinetic Energy: [ ] J
- Total Mechanical Energy: 0 J

**List the following energies at point C:**

- Potential Energy: [ ] J
- Kinetic Energy: [ ] J
- Total Mechanical Energy: [ ] J

(Note: J is the unit for energy, joules.)
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Transcribed Image Text:A block with a mass of 8.3 kg is released from rest at point A and slides down the frictionless track as shown above. **List the following energies at point A:** - Potential Energy: [ ] J - Kinetic Energy: [ ] J - Total Mechanical Energy: [ ] J **List the following energies at point B:** - Potential Energy: [ ] J - Kinetic Energy: [ ] J - Total Mechanical Energy: 0 J **List the following energies at point C:** - Potential Energy: [ ] J - Kinetic Energy: [ ] J - Total Mechanical Energy: [ ] J (Note: J is the unit for energy, joules.)
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