Rank the following items in order of INCREASING (low to high) kinetic energy. Provide an explanation for the ranking. v=2m/s v=0m/s v=4m/s v=3m/s m=20kg m=5kg m=8kg Object B Object C Object D m=10 kg Object A

Principles of Physics: A Calculus-Based Text
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Chapter6: Energy Of A System
Section: Chapter Questions
Problem 38P
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**Title: Ranking Objects by Kinetic Energy**

**Objective:**
Rank the following items in order of increasing (low to high) kinetic energy. Provide an explanation for the ranking.

**Data for Each Object:**
- **Object A**: 
  - Velocity (\(v\)) = 2 m/s
  - Mass (\(m\)) = 10 kg

- **Object B**: 
  - Velocity (\(v\)) = 0 m/s
  - Mass (\(m\)) = 20 kg

- **Object C**: 
  - Velocity (\(v\)) = 4 m/s
  - Mass (\(m\)) = 5 kg

- **Object D**: 
  - Velocity (\(v\)) = 3 m/s
  - Mass (\(m\)) = 8 kg

**Explanation:**
The kinetic energy (\(KE\)) of an object is calculated using the formula:

\[ KE = \frac{1}{2} mv^2 \]

**Calculation:**

1. **Object A:**
   \[ KE = \frac{1}{2} \times 10 \, kg \times (2 \, m/s)^2 = 20 \, J \]

2. **Object B:**
   \[ KE = \frac{1}{2} \times 20 \, kg \times (0 \, m/s)^2 = 0 \, J \]

3. **Object C:**
   \[ KE = \frac{1}{2} \times 5 \, kg \times (4 \, m/s)^2 = 40 \, J \]

4. **Object D:**
   \[ KE = \frac{1}{2} \times 8 \, kg \times (3 \, m/s)^2 = 36 \, J \]

**Ranking by Increasing Kinetic Energy:**

1. Object B: 0 J
2. Object A: 20 J
3. Object D: 36 J
4. Object C: 40 J

**Conclusion:**
By comparing the calculated kinetic energies, the order from lowest to highest is Object B, Object A, Object D, and Object C.
Transcribed Image Text:**Title: Ranking Objects by Kinetic Energy** **Objective:** Rank the following items in order of increasing (low to high) kinetic energy. Provide an explanation for the ranking. **Data for Each Object:** - **Object A**: - Velocity (\(v\)) = 2 m/s - Mass (\(m\)) = 10 kg - **Object B**: - Velocity (\(v\)) = 0 m/s - Mass (\(m\)) = 20 kg - **Object C**: - Velocity (\(v\)) = 4 m/s - Mass (\(m\)) = 5 kg - **Object D**: - Velocity (\(v\)) = 3 m/s - Mass (\(m\)) = 8 kg **Explanation:** The kinetic energy (\(KE\)) of an object is calculated using the formula: \[ KE = \frac{1}{2} mv^2 \] **Calculation:** 1. **Object A:** \[ KE = \frac{1}{2} \times 10 \, kg \times (2 \, m/s)^2 = 20 \, J \] 2. **Object B:** \[ KE = \frac{1}{2} \times 20 \, kg \times (0 \, m/s)^2 = 0 \, J \] 3. **Object C:** \[ KE = \frac{1}{2} \times 5 \, kg \times (4 \, m/s)^2 = 40 \, J \] 4. **Object D:** \[ KE = \frac{1}{2} \times 8 \, kg \times (3 \, m/s)^2 = 36 \, J \] **Ranking by Increasing Kinetic Energy:** 1. Object B: 0 J 2. Object A: 20 J 3. Object D: 36 J 4. Object C: 40 J **Conclusion:** By comparing the calculated kinetic energies, the order from lowest to highest is Object B, Object A, Object D, and Object C.
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Four objects with different masses and velocities

Required:

The increasing order of the kinetic energy 

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