Question

An isolated system consists of three particles of mass m_1, m₂, and m₃ that are initially at rest. They interact with pairwise forces, F_ij(r_i, r_j).

what is the net force on the system?

Answer 1

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Answer 2

 Explanation:

1. Isolated System: An isolated system has no external forces acting on it. All forces are internal, arising from interactions between the particles within the system.

2. 
   

3. Newton's Third Law: The pairwise forces between particles satisfy ${\vec{F}}_{ij}=-{\vec{F}}_{ji}$. For example, the force exerted by particle 1 on particle 2 (${\vec{F}}_{12}$) is equal in magnitude and opposite in direction to the force exerted by particle 2 on particle 1 (${\vec{F}}_{21}$).

4. 
   

5. Sum of Internal Forces: When you sum all the internal forces in the system, they cancel out in pairs due to Newton's Third Law.

   $${\vec{F}}_{\text{net}}={\vec{F}}_{12}+{\vec{F}}_{21}+{\vec{F}}_{13}+{\vec{F}}_{31}+{\vec{F}}_{23}+{\vec{F}}_{32}=\vec{0}$$

6. $$\stackrel{⃗}{}$$

7. Initial Rest Condition: Since the particles are initially at rest and the net force is zero, the system's center of mass remains at rest (consistent with Newton's First Law).

Thus, the net force on the system is always zero,