Energy of motion, $KE = \frac{1}{2}mv^2$

Energy due to an object's height, $PE_g = mgh$

Energy stored in a spring, $PE_e = \frac{1}{2}kx^2$

The sum of kinetic and potential energies: $ME = KE + PE$

A force where energy can be converted between KE and PE without loss (e.g., gravity, spring force).

The transfer of energy to or from a system.

The total mechanical energy of the system changes; energy is often lost as heat or sound.

The total mechanical energy of the system is conserved.

Friction does negative work, reducing the kinetic energy of the object and converting it to thermal energy.

Friction converts mechanical energy into thermal energy, reducing the total mechanical energy of the system.

The total energy of the system increases.

The total energy of the system decreases.

Increasing the height increases the gravitational potential energy: $$PE_g = mgh$$

Increasing the spring constant increases the potential energy stored in the spring: $$PE_s = \frac{1}{2}kx^2$$

The total mechanical energy of the system stays constant.