Work is a scalar quantity. It is the product of a force and the corresponding
displacement. Potential energy is the capacity of a system to do work on
another system. These concepts are advantageous in the analysis of equilibrium
of complex systems, in dynamics, and in mechanics of materials.

Work of a Force

The work U of a constant force F is

U = Fs

where s = displacement of a body in the direction of the vector F.
For a displacement along an arbitrary path from point 1 to 2, with dr tangent
to the path,

In theory, there is no work when:
1. A force is acting on a ?xed, rigid body (dr = 0, dU = 0).
2. A force acts perpendicular to the displacement (F ? dr = 0).

Work of a Couple

A couple of magnitude M does work

U = M?

where ? = angular displacement (radians) in the same plane in which the
couple is acting. In a rotation from angular position ? to ?,

Virtual Work

The concept of virtual work (through imaginary, in?nitesimal displacements
within the constraints of a system) is useful to analyze the equilibrium of
complex systems. The virtual work of a force F or moment M is
expressed as

?U = F. ?r
?U = M. ??

There is equilibrium if

Read more…