**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: Green2. **Cart 2:** - Mass (\(m_2\)) = 30.0 kg - Velocity (\(v_2\)) = 0.00 m/s - Color: Yellow3. **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.

Here, we can apply the conservation of momentum to find the final velocity (V) of the merged…

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 = ?

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 = ?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**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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Step 1: Conservation of momentum

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Step 2: To find the total momentum of the carts before the collision

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Step 3: To find the total momentum of the merged carts after the collision

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Step 4: To find the final velocity of the merged carts

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Step 5: To find the kinetic energy of the system before collision

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Step 6: To find the kinetic energy of the system after collision

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Step 7: Type of collision

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