Kinetic and potential energy can transform into one another. When only conservative forces do work, their sum remains constant.

The mechanical energy is

$$E=K+U.$$

For two states of an isolated conservative system,

$$K_i+U_i=K_f+U_f.$$

Falling object

As an object falls under gravity, gravitational potential energy decreases while kinetic energy increases. Ignoring air resistance,

$$\Delta K=-\Delta U_g.$$

The speed can therefore be related directly to the change in height without solving for the time of fall.

Nonconservative work

If nonconservative external forces transfer energy into or out of the mechanical system, then

$$\Delta(K+U)=W_{\mathrm{noncons}}$$

for the chosen system under the usual bookkeeping convention.

Friction may reduce mechanical energy while increasing internal thermal energy; total energy is not destroyed.

Choosing the system

Whether a force is represented through work or potential energy depends on which interacting objects are included in the system. Energy methods therefore require a clearly chosen system boundary just as force methods require a clear free-body diagram.

Mechanical-energy conservation is a special case of energy accounting, not a statement that kinetic or potential energy remains individually constant.