The sum of all external forces acting on all the particles is equal to the total external force applied to the system of particles. Why? – physics.stackexchange.com

As per the book: $\sum_{j=1}^N f_{j}^{ext}$+$\sum_{j=1}^N f_{j}^{int}$=$\sum_{j=1}^N dp_{j}/dt$ The first term, $\sum_{j=1}^N f_{j}^{int}$, is the sum of all internal forces acting on all the ...

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