Find ty, the magnitude of the final velocity of the two-block system. Express your answer numerically. View Available Hint(s) by Submit Part C 阿 | ΑΣΦ → ? m/s What is the change AK-Kal-Kiinial in the two-block system's kinetic energy due to the collision? Express your answer numerically in joules. View Available Hint(s)

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### Physics Problem: Two-Block Collision

#### Situation Description:
- Block 1, of mass \( m_1 = 4.30 \, \text{kg} \), moves along a frictionless air track with speed \( v_1 = 2.30 \, \text{m/s} \).
- It collides with Block 2, of mass \( m_2 = 5.10 \, \text{kg} \), which was initially at rest.
- The blocks stick together after the collision.

The problem is divided into two parts (Part B and Part C) for analysis and solving specific questions about the system's final velocity and kinetic energy change post-collision.

#### Part B:
**Question:**
Find \( v_f \) (the magnitude of the final velocity) of the two-block system.

**Instruction:**
Express your answer numerically in meters per second (m/s).

**Input Field:**
\[ v_f \, = \, \_\_\_\_\_ \text{  m/s} \]

**Submit Button:**
[Submit]

#### Part C:
**Question:**
What is the change (\( \Delta K \)) in the kinetic energy of the two-block system due to the collision?

**Instruction:**
Express your answer numerically in joules (J).

**Input Field:**
\[ \Delta K \, = \, \_\_\_\_\_ \text{  J} \]

**Submit Button:**
[Submit]

#### Figure:
- The figure shows Block 1 and Block 2 before and after the collision.
  - **Before collision:** Block 1 (labeled "1") is moving towards Block 2 (labeled "2"), which is stationary.
  - **After collision:** Both blocks are stuck together and move as a single unit.

#### Explanation of Diagrams:
- **Before collision:**
  - Block 1 is represented as a green rectangle moving to the right.
  - Block 2 is represented as a red rectangle, initially stationary.
- **After collision:**
  - Both blocks are represented as a combined unit moving to the right, implying they are stuck together and moving with the same final velocity \( v_f \).

---

**Note:** To solve the problem, apply the principles of conservation of momentum for Part B and kinetic energy conservation for practical understanding in Part C, considering the energy lost due to the inelastic nature of
Transcribed Image Text:### Physics Problem: Two-Block Collision #### Situation Description: - Block 1, of mass \( m_1 = 4.30 \, \text{kg} \), moves along a frictionless air track with speed \( v_1 = 2.30 \, \text{m/s} \). - It collides with Block 2, of mass \( m_2 = 5.10 \, \text{kg} \), which was initially at rest. - The blocks stick together after the collision. The problem is divided into two parts (Part B and Part C) for analysis and solving specific questions about the system's final velocity and kinetic energy change post-collision. #### Part B: **Question:** Find \( v_f \) (the magnitude of the final velocity) of the two-block system. **Instruction:** Express your answer numerically in meters per second (m/s). **Input Field:** \[ v_f \, = \, \_\_\_\_\_ \text{ m/s} \] **Submit Button:** [Submit] #### Part C: **Question:** What is the change (\( \Delta K \)) in the kinetic energy of the two-block system due to the collision? **Instruction:** Express your answer numerically in joules (J). **Input Field:** \[ \Delta K \, = \, \_\_\_\_\_ \text{ J} \] **Submit Button:** [Submit] #### Figure: - The figure shows Block 1 and Block 2 before and after the collision. - **Before collision:** Block 1 (labeled "1") is moving towards Block 2 (labeled "2"), which is stationary. - **After collision:** Both blocks are stuck together and move as a single unit. #### Explanation of Diagrams: - **Before collision:** - Block 1 is represented as a green rectangle moving to the right. - Block 2 is represented as a red rectangle, initially stationary. - **After collision:** - Both blocks are represented as a combined unit moving to the right, implying they are stuck together and moving with the same final velocity \( v_f \). --- **Note:** To solve the problem, apply the principles of conservation of momentum for Part B and kinetic energy conservation for practical understanding in Part C, considering the energy lost due to the inelastic nature of
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