Final answer:
The law of conservation of energy is represented by the formula KEi + PEi = KEf + PEf for conservative forces, or the more general form KEi + PEi + Wnc + OEi = KEf + PEf + OEf when nonconservative forces or other forms of energy are involved.
Step-by-step explanation:
The formula that represents the law of conservation of energy depends on the context of the problem being solved. In cases where all forces are conservative and can be described in terms of potential and kinetic energy, the formula is:
KEi + PEi = KEf + PEf,
where KEi is the initial kinetic energy, PEi is the initial potential energy, KEf is the final kinetic energy, and PEf is the final potential energy. If nonconservative forces are involved, or if other forms of energy need to be considered, the general form of the energy conservation equation is used:
KEi + PEi + Wnc + OEi = KEf + PEf + OEf,
where Wnc represents the work done by nonconservative forces, and OE represents other forms of energy that may be present.