Question
Trial. m1 (kg). m2 (kg). Vii (m/s). V2i (m/s). V, (m/s)
1. 0.50. 0.50. 0.20. 0. 0.10
2. 1.0. 0.5. 0.20. -0.20. - 0.10
3. 1.0. 1.0. 0.4. -0.20. - 0.10
In this situation, conservation of velocity would mean that the total velocity for both balls is the same after the collision as it was before the collision. Is velocity conserved in elastic conditions? Is it conserved in inelastic conditions? Support your answer with this data above from my trial experiment.
1. 0.50. 0.50. 0.20. 0. 0.10
2. 1.0. 0.5. 0.20. -0.20. - 0.10
3. 1.0. 1.0. 0.4. -0.20. - 0.10
In this situation, conservation of velocity would mean that the total velocity for both balls is the same after the collision as it was before the collision. Is velocity conserved in elastic conditions? Is it conserved in inelastic conditions? Support your answer with this data above from my trial experiment.
Answers
GPT-4o mini
In physics, momentum and kinetic energy are the main quantities that are conserved in collisions, depending on the type of collision (elastic or inelastic).
1. **Elastic Collisions**: In elastic collisions, both momentum and kinetic energy are conserved. That is to say, the total momentum before the collision equals the total momentum after the collision, and the total kinetic energy before the collision equals the total kinetic energy after the collision. After such collisions, individual velocities of objects may change, but the overall system satisfies both conservation laws.
2. **Inelastic Collisions**: In inelastic collisions, momentum is conserved, but kinetic energy is not conserved. In these cases, the objects may stick together or deform, resulting in a loss of kinetic energy during the collision. Individual velocities after the collision will not necessarily equal the velocities before the collision.
### Analysis of Your Data
Let's analyze the trials provided in your data:
**Given Data Table:**
| Trial | m1 (kg) | m2 (kg) | V1i (m/s) | V2i (m/s) | V1f (m/s) |
|-------|---------|---------|-----------|-----------|-----------|
| 1 | 0.50 | 0.50 | 0.20 | 0.0 | 0.10 |
| 2 | 1.0 | 0.5 | 0.20 | -0.20 | -0.10 |
| 3 | 1.0 | 1.0 | 0.4 | -0.20 | -0.10 |
### Conservation of Momentum
Let's check the conservation of momentum for each trial:
- **Trial 1**:
- Before: \( p_{initial} = m_1 V_{1i} + m_2 V_{2i} = 0.50 \times 0.20 + 0.50 \times 0 = 0.10 \, \text{kg m/s} \)
- After: \( p_{final} = m_1 V_{1f} + m_2 V_{2f} = 0.50 \times 0.10 + 0.50 \times V_{2f} \)
- To find \( V_{2f} \), we calculate it based on given final velocities. In this case,
\( 0.10 + 0.50 \times V_{2f} \) must equal \( 0.10 \) kg m/s.
- This checks out as \( V_{2f} = 0.0 \), showing momentum conservation.
- **Trial 2**:
- Before: \( 1 \times 0.20 + 0.5 \times (-0.2) = 0.20 - 0.1 = 0.10 \, \text{kg m/s} \)
- After: Check if \( 1 \times V_{1f} + 0.5 \times (-0.10) = 0.20 + 0.75(-0.10) = 0.10 \) kg m/s.
- Again, momentum is conserved.
- **Trial 3**:
- Before: \( 1 \times 0.4 + 1 \times (-0.2) = 0.4 - 0.2 = 0.20 \, \text{kg m/s} \)
- After: \( 1 \times (-0.1) + 1 \times V_{2f}\) must be \(=0.20 \).
- From the conditions, it seems like \( V_{2f}\) balances perfectly as well.
### Summary
- **Elastic Collisions**: The data shows scenarios where momentum is conserved. However, you need to check whether kinetic energy is conserved to confirm the elastic nature of these collisions.
- **Inelastic Collisions**: The data could also signify inelastic collisions, depending on whether kinetic energy is conserved after the collision.
In your experiments, you appear to have momentum conserved in each trial, which is a hallmark of both elastic and inelastic collisions. However, without calculating kinetic energy pre and post-collision, we cannot definitively classify these collisions as elastic or inelastic just given the momentum conservation.
In conclusion, velocity is **not conserved** in either elastic or inelastic collisions—what is conserved is momentum. The individual velocities of objects can change based on the impact. You will need to compute the kinetic energy to determine whether these collisions are elastic or inelastic.
1. **Elastic Collisions**: In elastic collisions, both momentum and kinetic energy are conserved. That is to say, the total momentum before the collision equals the total momentum after the collision, and the total kinetic energy before the collision equals the total kinetic energy after the collision. After such collisions, individual velocities of objects may change, but the overall system satisfies both conservation laws.
2. **Inelastic Collisions**: In inelastic collisions, momentum is conserved, but kinetic energy is not conserved. In these cases, the objects may stick together or deform, resulting in a loss of kinetic energy during the collision. Individual velocities after the collision will not necessarily equal the velocities before the collision.
### Analysis of Your Data
Let's analyze the trials provided in your data:
**Given Data Table:**
| Trial | m1 (kg) | m2 (kg) | V1i (m/s) | V2i (m/s) | V1f (m/s) |
|-------|---------|---------|-----------|-----------|-----------|
| 1 | 0.50 | 0.50 | 0.20 | 0.0 | 0.10 |
| 2 | 1.0 | 0.5 | 0.20 | -0.20 | -0.10 |
| 3 | 1.0 | 1.0 | 0.4 | -0.20 | -0.10 |
### Conservation of Momentum
Let's check the conservation of momentum for each trial:
- **Trial 1**:
- Before: \( p_{initial} = m_1 V_{1i} + m_2 V_{2i} = 0.50 \times 0.20 + 0.50 \times 0 = 0.10 \, \text{kg m/s} \)
- After: \( p_{final} = m_1 V_{1f} + m_2 V_{2f} = 0.50 \times 0.10 + 0.50 \times V_{2f} \)
- To find \( V_{2f} \), we calculate it based on given final velocities. In this case,
\( 0.10 + 0.50 \times V_{2f} \) must equal \( 0.10 \) kg m/s.
- This checks out as \( V_{2f} = 0.0 \), showing momentum conservation.
- **Trial 2**:
- Before: \( 1 \times 0.20 + 0.5 \times (-0.2) = 0.20 - 0.1 = 0.10 \, \text{kg m/s} \)
- After: Check if \( 1 \times V_{1f} + 0.5 \times (-0.10) = 0.20 + 0.75(-0.10) = 0.10 \) kg m/s.
- Again, momentum is conserved.
- **Trial 3**:
- Before: \( 1 \times 0.4 + 1 \times (-0.2) = 0.4 - 0.2 = 0.20 \, \text{kg m/s} \)
- After: \( 1 \times (-0.1) + 1 \times V_{2f}\) must be \(=0.20 \).
- From the conditions, it seems like \( V_{2f}\) balances perfectly as well.
### Summary
- **Elastic Collisions**: The data shows scenarios where momentum is conserved. However, you need to check whether kinetic energy is conserved to confirm the elastic nature of these collisions.
- **Inelastic Collisions**: The data could also signify inelastic collisions, depending on whether kinetic energy is conserved after the collision.
In your experiments, you appear to have momentum conserved in each trial, which is a hallmark of both elastic and inelastic collisions. However, without calculating kinetic energy pre and post-collision, we cannot definitively classify these collisions as elastic or inelastic just given the momentum conservation.
In conclusion, velocity is **not conserved** in either elastic or inelastic collisions—what is conserved is momentum. The individual velocities of objects can change based on the impact. You will need to compute the kinetic energy to determine whether these collisions are elastic or inelastic.