Cracking the SAT Physics Subject Test

CONSERVATION OF MECHANICAL ENERGY

We have seen energy in its two basic forms: kinetic energy (K) and potential energy
(U). The sum of an object’s kinetic and potential energies is called its mechanical
energy, E.

E = K + U

(Notice that because U is relative, so is E.) Assuming that no nonconservative
forces (friction, for example) act on an object or a system as it undergoes some
change, mechanical energy is conserved. That is, the initial mechanical energy, Ei,

is equal to the final mechanical energy, Ef, or

Ki + Ui = Kf + Uf

This is the simplest form of the law of conservation of total energy, which we
mentioned at the beginning of this section.

Let’s evaluate three stages of an object falling from rest at the top of a building and
calculate the total mechanical energy at each stage.