When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy conservation, we study more than one body at the same time. Second, identify all forces acting on the object and determine whether each force doing work is conservative. If a non-conservative force (e.g., friction) is doing work, then mechanical energy is not conserved. The system must then be analyzed with non-conservative work. Third, for every force that does work, choose a reference point and determine the potential energy function for that force. The reference points for the various potential energies do not have to be at the same location. Finally, apply the principle of mechanical energy conservation by setting the sum of the kinetic energies and potential energies equal at every point of interest.
Note that systems generally consist of more than one particle or object. However, the conservation of mechanical energy is a fundamental law of physics and applies to any system. In such a case, include the kinetic and potential energies of all the particles and the work done by all the non-conservative forces acting on them.
This text is adapted from Openstax, University Physics Volume 1, Section 8.3: Conservation of Energy.
