In classical mechanics, the law of conservation of energy states that the total energy of an isolated system remains constant over time. It states that energy cannot be created or destroyed but can only be transferred or transformed from one form to another.
The conservation of mechanical energy specifically refers to the conservation of the sum of kinetic energy and potential energy in a system. In a closed, isolated system where only conservative forces (such as gravity or elastic forces) are acting, the total mechanical energy remains constant.
The mechanical energy of a system is the sum of its kinetic energy (KE) and potential energy (PE):
Mechanical Energy (ME) = KE + PE
The conservation of mechanical energy implies that as long as no external forces do work on the system and no non-conservative forces (such as friction) are present, the total mechanical energy of the system will remain constant. This means that the energy can change from kinetic to potential or vice versa, but the total amount will stay the same.
It's important to note that while mechanical energy may be conserved in certain situations, other forms of energy, such as thermal energy or sound energy, may be generated or lost due to non-conservative forces. The law of conservation of energy, on the other hand, applies to all forms of energy, not just mechanical energy.