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10

Introduction to Energy Methods

10.1 Introduction
In this chapter, we consider energy methods with a focus on the work–energy principle.
Energy methods are very convenient for a broad class of systems — particularly those
with relatively simple geometrics and those for which limited information is desired.
Energy methods, like impulse–momentum principles, are formulated in terms of veloc-
ities, thus avoiding the computation of accelerations as is required with Newton’s laws
and d’Alembert’s principle. But, unlike the impulse–momentum principles, energy
methods are formulated in terms of scalars. By thus avoiding vector operations, energy
methods generally involve simpler analyses. The information gained, however, may
be somewhat limited because often only one equation is obtained with the work–energy
method.
We begin our study with a brief discussion of “work” and its computation. We then
discuss power and kinetic energy and their relation to work. The balance of the chapter
is then devoted to examples illustrating applications and combined use with
impulse–momentum principles. In the next chapter we will discuss more advanced energy
methods and the concepts of generalized mechanics.

10.2 Work
Intuitively, work is related to expended effort or expenditure of energy. In elementary
physics, work is defined as the product of a force (effort) and the displacement (movement)
of an object to which the force is applied. To develop these concepts, let P be a particle
and let F be a force applied to P as represented in Figure 10.2.1. Let P move through a
distance d in the direction of F as shown. Then, the work W done by F is defined as:

W = F d (10.2.1)
D

Generally when a force is applied on a particle (or object) the force does not remain
constant during the movement of the particle (or object). Both the magnitude and the
direction of the force may change. Also, the particle (or object) will in general not move
on a straight line.

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