Peoples Physics Book Version-2

http://www.ck12.org Chapter 3. Energy Conservation Appendix

FIGURE 3.1

Illustration for the Equivalence Derivation

Since equation [3] always holds exactly (as far as we’re concerned), we can certainly use it. Before it was raised, the
object was at the surface, so its potential energy from Earth’s gravity was given by:

EGi=

Gm 1 m 2

Rearth

[4]

This held because therin [3] is the distance between the two objects’ centers of mass. The center of mass of the
earth is, predictably, at its center, so we can replacerabove withRearthfor objects on its surface. After the object is