In Chapter 7 we dealt with forces on a particle that depend on the speed of the particle. In Chapter 8 we dealt with forces that depend on the time. In this chapter, we deal with forces that depend only on the position of a particle. Such forces are called conservative forces. While only conservative forces act, the sum of potential and kinetic energies is conserved.
In the principle of virtual work, we imagine that we act upon the system in such a manner as to increase one of the coordinates. We ask ourselves how much work we have to do on the system in order to increase this coordinate by a small amount. If the system starts from equilibrium, this work will be very small, and, in the limit of an infinitesimally small displacement, this “virtual work” will be zero.
Thumbnail: A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. (Public Domain; CompuChip).