Kinetics: Energy of System of Particles

Similarly to work and energy of an particle, energy is also a physical approach to study the kinetic motion of a systme of particles.

Equipollent System of Overall Force

For a system with n particles, let individual particle pi of mass mi, with position ri, and acceleration ai, where 1≤i≤n, be particles of the system with reference to a newtonian frame of reference. The overall force acting on the system of particles is the initial cause for the motion of the system of particles.

Overall Force of A System of Particles

Since there are more than one particle object in the system, forces acting upon an object pi can be an internal force fij, exerted by another particle pj of the system and an resultant external force Fi of all the external forces acting on the particle pi. Internal force fij, is the force acting on the ith particle due to the iteraction with the jth particle, where 1≤i≤n and 1≤j≤n. By Newton's third law, an internal force fij is equal to the negative sense of the corresponding internal force fji. And internal force acting on itself must be equal to zero because there is no interaction, fij=fii=0 when j=i. By Newton's second law, the dynamic equilibrium equation in terms of forces for the ith particle is

The overall force of a system of particles can therefore be obtained by adding all the n force equations of the particles in the system.