As shown in the figure below, two blocks (m1 and m2) are each released from rest at a height of h = 4.03m on a frictionless track and when they meet on the horizontal section of the track they undergo an elastic collision. If m1 = 2.50 kg and m2 = 4.55kg, determine the maximum heights ( in m) to which they rise after the collision. Use the coordinate system shown in the figure. Answer y1f= M y2f= M
As shown in the figure below, two blocks (m1 and m2) are each released from rest at a height of h = 4.03m on a frictionless track and when they meet on the horizontal section of the track they undergo an elastic collision. If m1 = 2.50 kg and m2 = 4.55kg, determine the maximum heights ( in m) to which they rise after the collision. Use the coordinate system shown in the figure. Answer y1f= M y2f= M
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As shown in the figure below, two blocks (m1 and m2) are each released from rest at a height of h = 4.03m on a frictionless track and when they meet on the horizontal section of the track they undergo an elastic collision.
If m1 = 2.50 kg and m2 = 4.55kg, determine the maximum heights ( in m) to which they rise after the collision. Use the coordinate system shown in the figure. Answer
y1f= M
y2f= M
![### Potential and Kinetic Energy in Classical Mechanics
#### Diagram Explanation:
The diagram illustrates two masses, \( m_1 \) and \( m_2 \), placed on a curved, frictionless track. The positions of the masses can be described as follows:
1. **Masses:**
- \( m_1 \) is positioned on the left incline of the track.
- \( m_2 \) is positioned on the right incline of the track.
2. **Heights:**
- The height at which \( m_1 \) is located above the reference point (lowest point on the track) is denoted as \( h_1 \).
- The height at which \( m_2 \) is located above the reference point is denoted as \( h_2 \).
3. **Horizontal Distance:**
- The horizontal distance between the bases of the inclines where \( m_1 \) and \( m_2 \) rest is denoted as \( l \).
4. **Arrows and Directions:**
- Vertical arrows extending from \( m_1 \) and \( m_2 \) to the ground level indicate the heights (\( h_1 \) and \( h_2 \)).
- Horizontal arrows represent the path of motion the masses will take if released.
#### Concept Explanation:
This setup typically demonstrates the principles of conservation of energy in a frictionless system:
- **Potential Energy (PE):** At their initial positions, both masses possess gravitational potential energy which depends on their heights (\( h_1 \) and \( h_2 \)) and is given by \( PE = mgh \), where \( g \) is the acceleration due to gravity.
- **Kinetic Energy (KE):** When the masses are released, they convert potential energy into kinetic energy as they move towards the lowest point of the track.
The energy conservation principle states that the total mechanical energy of the system (potential + kinetic) remains constant in the absence of non-conservative forces, such as friction. This means:
\[ PE_{\text{initial}} (m_1) + PE_{\text{initial}} (m_2) = KE_{\text{final}} (m_1) + KE_{\text{final}} (m_2) \]
This illustration helps in understanding how potential energy gets converted into kinetic energy and vice versa in an ideal system. The eventual velocities of the masses](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81610fbc-71d4-4f51-a970-c974c7e9c894%2Fa1ac9b49-1214-4fdb-af1f-2a7ef511fd39%2Frl2ujl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Potential and Kinetic Energy in Classical Mechanics
#### Diagram Explanation:
The diagram illustrates two masses, \( m_1 \) and \( m_2 \), placed on a curved, frictionless track. The positions of the masses can be described as follows:
1. **Masses:**
- \( m_1 \) is positioned on the left incline of the track.
- \( m_2 \) is positioned on the right incline of the track.
2. **Heights:**
- The height at which \( m_1 \) is located above the reference point (lowest point on the track) is denoted as \( h_1 \).
- The height at which \( m_2 \) is located above the reference point is denoted as \( h_2 \).
3. **Horizontal Distance:**
- The horizontal distance between the bases of the inclines where \( m_1 \) and \( m_2 \) rest is denoted as \( l \).
4. **Arrows and Directions:**
- Vertical arrows extending from \( m_1 \) and \( m_2 \) to the ground level indicate the heights (\( h_1 \) and \( h_2 \)).
- Horizontal arrows represent the path of motion the masses will take if released.
#### Concept Explanation:
This setup typically demonstrates the principles of conservation of energy in a frictionless system:
- **Potential Energy (PE):** At their initial positions, both masses possess gravitational potential energy which depends on their heights (\( h_1 \) and \( h_2 \)) and is given by \( PE = mgh \), where \( g \) is the acceleration due to gravity.
- **Kinetic Energy (KE):** When the masses are released, they convert potential energy into kinetic energy as they move towards the lowest point of the track.
The energy conservation principle states that the total mechanical energy of the system (potential + kinetic) remains constant in the absence of non-conservative forces, such as friction. This means:
\[ PE_{\text{initial}} (m_1) + PE_{\text{initial}} (m_2) = KE_{\text{final}} (m_1) + KE_{\text{final}} (m_2) \]
This illustration helps in understanding how potential energy gets converted into kinetic energy and vice versa in an ideal system. The eventual velocities of the masses
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