**Two disks A and B, having a mass of 2 kg and 4 kg respectively, collide with initial velocities shown. If v_A = 6 m/s and v_B = 2 m/s, and e = 0.75, determine the velocities of the disks after the collision.****Notes:**- \( v_A = 6 \) m/s: The initial velocity of disk A.- \( v_B = 2 \) m/s: The initial velocity of disk B.- \( e = 0.75 \): The coefficient of restitution between the two disks.**Solution Approach:**1. **Use conservation of momentum:** \[ m_A v_{A} + m_B v_{B} = m_A v_{A}' + m_B v_{B}' \] Where \( v_{A}' \) and \( v_{B}' \) are the velocities of disks A and B after collision.2. **Use the coefficient of restitution formula:** \[ e = \frac{v_{B}' - v_{A}'}{v_A - v_B} \]By solving these two equations, we can determine the final velocities \( v_{A}' \) and \( v_{B}' \).**Detailed Explanation of Solution:**1. Using the conservation of momentum equation:\[ (2 \text{ kg})(6 \text{ m/s}) + (4 \text{ kg})(2 \text{ m/s}) = 2v_{A}' + 4v_{B}' \]\[ 12 \text{ kg}\cdot\text{m/s} + 8 \text{ kg}\cdot\text{m/s} = 2v_{A}' + 4v_{B}' \]\[ 20 \text{ kg}\cdot\text{m/s} = 2v_{A}' + 4v_{B}' \quad \text{(Equation 1)} \]2. Using the coefficient of restitution formula:\[ 0.75 = \frac{v_{B}' - v_{A}'}{6 \text{ m/s} - 2 \text{ m/s}} \]\[ 0.75 = \frac{v_{B}' - v_{A}'}{4 \text{ m/s}} \]\[ 3 = v_{B}' - v

A partially elastic head-on collision refers to a type of collision between two objects where there…

Answered: Two disks A and B, having a mass of 2…

Two disks A and B, having a mass of 2 kg and 4 kg respectively, collide with initial velocities shown. If VÀ = 6 m/s and VB = 2 m/s, and e = 0.75, determine the velocities of the disks after

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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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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

**Two disks A and B, having a mass of 2 kg and 4 kg respectively, collide with initial velocities shown. If v_A = 6 m/s and v_B = 2 m/s, and e = 0.75, determine the velocities of the disks after the collision.**

**Notes:**
- \( v_A = 6 \) m/s: The initial velocity of disk A.
- \( v_B = 2 \) m/s: The initial velocity of disk B.
- \( e = 0.75 \): The coefficient of restitution between the two disks.

**Solution Approach:**
1. **Use conservation of momentum:**
\[ m_A v_{A} + m_B v_{B} = m_A v_{A}' + m_B v_{B}' \]
Where \( v_{A}' \) and \( v_{B}' \) are the velocities of disks A and B after collision.

2. **Use the coefficient of restitution formula:**
\[ e = \frac{v_{B}' - v_{A}'}{v_A - v_B} \]

By solving these two equations, we can determine the final velocities \( v_{A}' \) and \( v_{B}' \).

**Detailed Explanation of Solution:**
1. Using the conservation of momentum equation:
\[ (2 \text{ kg})(6 \text{ m/s}) + (4 \text{ kg})(2 \text{ m/s}) = 2v_{A}' + 4v_{B}' \]
\[ 12 \text{ kg}\cdot\text{m/s} + 8 \text{ kg}\cdot\text{m/s} = 2v_{A}' + 4v_{B}' \]
\[ 20 \text{ kg}\cdot\text{m/s} = 2v_{A}' + 4v_{B}' \quad \text{(Equation 1)} \]

2. Using the coefficient of restitution formula:
\[ 0.75 = \frac{v_{B}' - v_{A}'}{6 \text{ m/s} - 2 \text{ m/s}} \]
\[ 0.75 = \frac{v_{B}' - v_{A}'}{4 \text{ m/s}} \]
\[ 3 = v_{B}' - v

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