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The total momentum of a system of particles is the vector sum of the momenta of all the particles in the system. It is calculated as \( \mathbf{P} = \sum m_i \mathbf{v}_i \), where \(m_i\) and \(v_i\) represent the mass and velocity of each particle. The acceleration of the system depends only on external forces, as internal forces cancel due to Newton's third law. This relationship is expressed as \( \mathbf{F}_{ext} = \frac{d\mathbf{P}}{dt} \).

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Here are 5 related questions:
1. How is momentum conserved in a closed system?
2. What are examples of external forces in physical systems?
3. Can momentum be transferred between particles in a system?
4. How does Newton’s third law affect the system's momentum?
5. What is the relationship between momentum and kinetic energy?

**Tip:** Always analyze both internal and external forces when considering momentum in a system.

Define total momentum of a system of particles. Show how acceleration of the system of particles depends on external forces.

Understand the concept of total momentum in a system of particles and how acceleration depends on external forces. This problem explores key physics concepts like Newton’s third law, momentum conservation, and their application in a system of particles. Suitable for advanced high school students and first-year college physics.

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