In the figure, block A (mass 1.8 kg) slides into block B (mass 2.6 kg), along a frictionless surface. The directions of velocities before and after the collision are indicated; the corresponding speeds are vAi = 5.5 m/s, vBi = 2.9 m/s, and vBf = 4.5 m/s. What is velocity vAf (including sign, where positive denotes motion to the right)?
In the figure, block A (mass 1.8 kg) slides into block B (mass 2.6 kg), along a frictionless surface. The directions of velocities before and after the collision are indicated; the corresponding speeds are vAi = 5.5 m/s, vBi = 2.9 m/s, and vBf = 4.5 m/s. What is velocity vAf (including sign, where positive denotes motion to the right)?
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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In the figure, block A (mass 1.8 kg) slides into block B (mass 2.6 kg), along a frictionless surface. The directions of velocities before and after the collision are indicated; the corresponding speeds are vAi = 5.5 m/s, vBi = 2.9 m/s, and vBf = 4.5 m/s. What is velocity vAf (including sign, where positive denotes motion to the right)?
![### Understanding Momentum and Collisions: An Example
This diagram illustrates two blocks involved in a collision, helping us understand how momentum is conserved. Let's break down the information:
#### Description of the Diagram:
1. **Initial State (Top Image):**
- Block A, represented by the blue block on the left, is moving to the right with an initial velocity \( \vec{V}_{Ai} \).
- Block B, represented by the purple block on the right, is also moving to the right but with a different initial velocity \( \vec{V}_{Bi} \).
2. **Final State (Bottom Image):**
- After the interaction, Block B continues to move to the right and has a final velocity \( \vec{V}_{Bf} \).
- The final velocity of Block A, \( \vec{V}_{Af} \), is the unknown quantity we need to determine in this scenario.
### Explanation:
- **Conservation of Momentum** is an essential principle here. The total momentum of the system (both blocks) before the collision will be equal to the total momentum after the collision, provided no external forces act on the system.
#### Conservation of Momentum Equation:
\[ m_A \vec{V}_{Ai} + m_B \vec{V}_{Bi} = m_A \vec{V}_{Af} + m_B \vec{V}_{Bf} \]
Where:
- \( m_A \) and \( m_B \) are the masses of blocks A and B, respectively.
- \( \vec{V}_{Ai} \) and \( \vec{V}_{Bi} \) are the initial velocities of blocks A and B.
- \( \vec{V}_{Af} \) and \( \vec{V}_{Bf} \) are the final velocities of blocks A and B.
#### Use in Education:
This diagram serves as a graphical representation to study the concepts of momentum, conservation laws, and collisions. By analyzing and applying the conservation of momentum, students can solve for the unknown final velocity of block A, thereby reinforcing their understanding of these fundamental physics principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ad094f-0957-46f5-bf21-6173c0426f44%2F3cab15fd-f4af-4f8c-937f-bfbdff89066b%2Fl5eam5k.gif&w=3840&q=75)
Transcribed Image Text:### Understanding Momentum and Collisions: An Example
This diagram illustrates two blocks involved in a collision, helping us understand how momentum is conserved. Let's break down the information:
#### Description of the Diagram:
1. **Initial State (Top Image):**
- Block A, represented by the blue block on the left, is moving to the right with an initial velocity \( \vec{V}_{Ai} \).
- Block B, represented by the purple block on the right, is also moving to the right but with a different initial velocity \( \vec{V}_{Bi} \).
2. **Final State (Bottom Image):**
- After the interaction, Block B continues to move to the right and has a final velocity \( \vec{V}_{Bf} \).
- The final velocity of Block A, \( \vec{V}_{Af} \), is the unknown quantity we need to determine in this scenario.
### Explanation:
- **Conservation of Momentum** is an essential principle here. The total momentum of the system (both blocks) before the collision will be equal to the total momentum after the collision, provided no external forces act on the system.
#### Conservation of Momentum Equation:
\[ m_A \vec{V}_{Ai} + m_B \vec{V}_{Bi} = m_A \vec{V}_{Af} + m_B \vec{V}_{Bf} \]
Where:
- \( m_A \) and \( m_B \) are the masses of blocks A and B, respectively.
- \( \vec{V}_{Ai} \) and \( \vec{V}_{Bi} \) are the initial velocities of blocks A and B.
- \( \vec{V}_{Af} \) and \( \vec{V}_{Bf} \) are the final velocities of blocks A and B.
#### Use in Education:
This diagram serves as a graphical representation to study the concepts of momentum, conservation laws, and collisions. By analyzing and applying the conservation of momentum, students can solve for the unknown final velocity of block A, thereby reinforcing their understanding of these fundamental physics principles.
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