1. Refer to figure 1. Two carts collide and merge together. Calculate the final velocity of the merged carts, determine whether it was an elastic or inelastic collision, and whether energy was conserved or not. m₁ m₁ = 10.0 kg V1 = 8.00 m/s Figure 1 m₂ m₂ = 30.0 kg V₂ = 0.00 m/s m3 = 40.0 kg V = ?

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**Educational Content: Collision of Carts**

**Problem Statement:**
Refer to Figure 1. Two carts collide and merge together. Calculate the final velocity of the merged carts, determine whether it was an elastic or inelastic collision, and whether energy was conserved or not.

**Illustration:**

1. **Cart 1:**
   - Mass (\(m_1\)) = 10.0 kg
   - Velocity (\(v_1\)) = 8.00 m/s
   - Color: Green

2. **Cart 2:**
   - Mass (\(m_2\)) = 30.0 kg
   - Velocity (\(v_2\)) = 0.00 m/s
   - Color: Yellow

3. **Combined Cart:**
   - Total Mass (\(m_3\)) = 40.0 kg
   - Final Velocity (\(v\)) = ?

**Analysis:**

- **Type of Collision:**
  - This scenario describes two carts that combine after colliding, indicating an inelastic collision where kinetic energy may not be conserved.
  
- **Conservation of Momentum:**
  - Since momentum is always conserved, we calculate the final velocity using the formula: 
    \[
    (m_1 \cdot v_1) + (m_2 \cdot v_2) = m_3 \cdot v
    \]
  
- **Energy Considerations:**
  - To determine if energy is conserved, compare kinetic energy before and after the collision. If they are not equal, energy is not conserved, confirming an inelastic collision.

The objective is to apply the conservation principles to solve for the final velocity and characterize the collision.
Transcribed Image Text:**Educational Content: Collision of Carts** **Problem Statement:** Refer to Figure 1. Two carts collide and merge together. Calculate the final velocity of the merged carts, determine whether it was an elastic or inelastic collision, and whether energy was conserved or not. **Illustration:** 1. **Cart 1:** - Mass (\(m_1\)) = 10.0 kg - Velocity (\(v_1\)) = 8.00 m/s - Color: Green 2. **Cart 2:** - Mass (\(m_2\)) = 30.0 kg - Velocity (\(v_2\)) = 0.00 m/s - Color: Yellow 3. **Combined Cart:** - Total Mass (\(m_3\)) = 40.0 kg - Final Velocity (\(v\)) = ? **Analysis:** - **Type of Collision:** - This scenario describes two carts that combine after colliding, indicating an inelastic collision where kinetic energy may not be conserved. - **Conservation of Momentum:** - Since momentum is always conserved, we calculate the final velocity using the formula: \[ (m_1 \cdot v_1) + (m_2 \cdot v_2) = m_3 \cdot v \] - **Energy Considerations:** - To determine if energy is conserved, compare kinetic energy before and after the collision. If they are not equal, energy is not conserved, confirming an inelastic collision. The objective is to apply the conservation principles to solve for the final velocity and characterize the collision.
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