Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Certainly! To find the final velocity of the two model cars after a perfectly inelastic collision, we can use the principle of conservation of momentum. Here's the step-by-step solution:
1. Define the variables and given data:
- Mass of Car 1, [tex]\( m_1 = 2.0 \text{ kg} \)[/tex]
- Initial velocity of Car 1, [tex]\( v_{1i} = 2 \, \text{m/s} \)[/tex]
- Mass of Car 2, [tex]\( m_2 = 1.0 \text{ kg} \)[/tex]
- Initial velocity of Car 2, [tex]\( v_{2i} = -3 \, \text{m/s} \)[/tex]
2. Understand that after a perfectly inelastic collision, the two cars stick together and move with the same final velocity, [tex]\( v_f \)[/tex].
3. Apply the conservation of momentum:
- The total initial momentum of the system is given by the sum of the momenta of both cars before the collision.
[tex]\[ p_{\text{initial}} = (m_1 \cdot v_{1i}) + (m_2 \cdot v_{2i}) \][/tex]
4. Plug in the given values:
[tex]\[ p_{\text{initial}} = (2.0 \, \text{kg} \cdot 2 \, \frac{\text{m}}{\text{s}}) + (1.0 \, \text{kg} \cdot (-3) \, \frac{\text{m}}{\text{s}}) \][/tex]
5. Calculate the total initial momentum:
[tex]\[ p_{\text{initial}} = (4 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}) + (-3 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}) = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \][/tex]
6. Combine the masses after the collision since they stick together:
[tex]\[ m_{\text{combined}} = m_1 + m_2 = 2.0 \, \text{kg} + 1.0 \, \text{kg} = 3.0 \, \text{kg} \][/tex]
7. Set up the momentum conservation equation:
[tex]\[ p_{\text{initial}} = p_{\text{final}} \][/tex]
[tex]\[ 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} = (m_{\text{combined}} \cdot v_f) \][/tex]
[tex]\[ 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} = (3.0 \, \text{kg} \cdot v_f) \][/tex]
8. Solve for the final velocity [tex]\( v_f \)[/tex]:
[tex]\[ v_f = \frac{1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{3.0 \, \text{kg}} = 0.3333333333333333 \, \frac{\text{m}}{\text{s}} \][/tex]
9. Conclusion:
The final velocity immediately after the collision is [tex]\( 0.333 \, \frac{\text{m}}{\text{s}} \)[/tex].
So, the two cars, after colliding and sticking together, will move with a final velocity of approximately [tex]\( 0.333 \, \frac{\text{m}}{\text{s}} \)[/tex].
1. Define the variables and given data:
- Mass of Car 1, [tex]\( m_1 = 2.0 \text{ kg} \)[/tex]
- Initial velocity of Car 1, [tex]\( v_{1i} = 2 \, \text{m/s} \)[/tex]
- Mass of Car 2, [tex]\( m_2 = 1.0 \text{ kg} \)[/tex]
- Initial velocity of Car 2, [tex]\( v_{2i} = -3 \, \text{m/s} \)[/tex]
2. Understand that after a perfectly inelastic collision, the two cars stick together and move with the same final velocity, [tex]\( v_f \)[/tex].
3. Apply the conservation of momentum:
- The total initial momentum of the system is given by the sum of the momenta of both cars before the collision.
[tex]\[ p_{\text{initial}} = (m_1 \cdot v_{1i}) + (m_2 \cdot v_{2i}) \][/tex]
4. Plug in the given values:
[tex]\[ p_{\text{initial}} = (2.0 \, \text{kg} \cdot 2 \, \frac{\text{m}}{\text{s}}) + (1.0 \, \text{kg} \cdot (-3) \, \frac{\text{m}}{\text{s}}) \][/tex]
5. Calculate the total initial momentum:
[tex]\[ p_{\text{initial}} = (4 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}) + (-3 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}) = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \][/tex]
6. Combine the masses after the collision since they stick together:
[tex]\[ m_{\text{combined}} = m_1 + m_2 = 2.0 \, \text{kg} + 1.0 \, \text{kg} = 3.0 \, \text{kg} \][/tex]
7. Set up the momentum conservation equation:
[tex]\[ p_{\text{initial}} = p_{\text{final}} \][/tex]
[tex]\[ 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} = (m_{\text{combined}} \cdot v_f) \][/tex]
[tex]\[ 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} = (3.0 \, \text{kg} \cdot v_f) \][/tex]
8. Solve for the final velocity [tex]\( v_f \)[/tex]:
[tex]\[ v_f = \frac{1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}}}{3.0 \, \text{kg}} = 0.3333333333333333 \, \frac{\text{m}}{\text{s}} \][/tex]
9. Conclusion:
The final velocity immediately after the collision is [tex]\( 0.333 \, \frac{\text{m}}{\text{s}} \)[/tex].
So, the two cars, after colliding and sticking together, will move with a final velocity of approximately [tex]\( 0.333 \, \frac{\text{m}}{\text{s}} \)[/tex].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
