3.4 Conservation of Energy

Single-Object Systems For a single object, energy changes arise only from external work.

${W_{net} = \Delta K}$

Multi-Object Systems For systems with multiple objects, both kinetic and potential energies exist. The total mechanical energy is:

${E_{mech} = K + U}$

In a closed system (no external work or non-conservative forces), mechanical energy is conserved:

${E_{mech,initial} = E_{mech,final}}$

If work is done by an external force, the change in total energy equals that work: ${W = \Delta E}$

Law of Conservation of Energy: Energy cannot be created or destroyed. It can change form—between kinetic, potential, thermal, or other types—but the total energy of an isolated system remains constant.

In systems with friction or drag, mechanical energy decreases, but total energy (including thermal) still remains conserved.