For a particle within the System, the Work on it would be:
Which, using the Work-Energy Theorem:
Change in Potential Energy within the system can also be determined by the internal work, the work on a particle from forces within the system:
We can substitute these equations to create a representation for the change in total Mechanical Energy of a system by forces outside the system:
Where the work external creates a change in Kinetic Energy and Potential Energy.