To find the total momentum of the system after the collision, we first need to calculate the total momentum before the collision.
The formula for momentum (p) is:
\[ p = m \cdot v \]
where \(m\) is mass and \(v\) is velocity.
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Calculate the momentum of the left train car (car 1):
- Mass \(m_1 = 600 , \text{kg}\)
- Velocity \(v_1 = 4 , \text{m/s}\) \[ p_1 = m_1 \cdot v_1 = 600 , \text{kg} \cdot 4 , \text{m/s} = 2400 , \text{kg} \cdot \text{m/s} \]
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Calculate the momentum of the right train car (car 2):
- Mass \(m_2 = 400 , \text{kg}\)
- Velocity \(v_2 = 0 , \text{m/s}\) (since it's at rest) \[ p_2 = m_2 \cdot v_2 = 400 , \text{kg} \cdot 0 , \text{m/s} = 0 , \text{kg} \cdot \text{m/s} \]
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Calculate the total momentum before the collision: \[ p_{\text{total before}} = p_1 + p_2 = 2400 , \text{kg} \cdot \text{m/s} + 0 , \text{kg} \cdot \text{m/s} = 2400 , \text{kg} \cdot \text{m/s} \]
After the collision, the two cars stick together and move as one mass.
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Total mass after the collision: \[ m_{\text{total}} = m_1 + m_2 = 600 , \text{kg} + 400 , \text{kg} = 1000 , \text{kg} \]
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The total momentum after the collision must equal the total momentum before the collision (conservation of momentum): \[ p_{\text{total after}} = p_{\text{total before}} = 2400 , \text{kg} \cdot \text{m/s} \]
So the total momentum of the system after the collision is:
\[ \boxed{2400 , \text{kg} \cdot \text{m/s}} \]
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