You have done quite a bit of problem solving using energy concepts. Back in chapter 2 we
defined energy as a transferable physical quantity that an object can be said to have and we said
that if one transfers energy to a material particle that is initially at rest, that particle acquires a
speed which is an indicator of how much energy was transferred. We said that an object can
have energy because it is moving (kinetic energy), or due to its position relative to some other
object (potential energy)1. We said that energy has units of joules. You have dealt with
translational kinetic energy
1
2
K =
v
m
, rotational kinetic energy
1
2
K = Iw , spring potential
2
2
energy
1
2
U = k x , near-earth’s-surface gravitational potential energy U =
gy
m
, and the
2
G m m
universal gravitational potential energy U = −
r1 2 corresponding to the Universal Law of
Gravitation. The principle of the conservation of energy is, in the opinion of this author, the
central most important concept in physics. Indeed, at least one dictionary defines physics as the
study of energy. It is important because it is conserved and the principle of conservation of
energy allows us to use simple accounting procedures to make predictions about the outcomes of
physical processes that have yet to occur and to understand processes that have already occurred.
According to the principle of conservation of energy, any change in the total amount of energy of
a system can be accounted for in terms of energy transferred from the immediate surroundings to
the system or to the immediate surroundings from the system. Physicists recognize two
categories of energy transfer processes. One is called work and the other is called heat flow. In
this chapter we focus our attention on work.
Conceptually, positive work is what you are doing on an object when you push or pull on it in
the same direction in which the object is moving. You do negative work on an object when you
push or pull on it in the direction opposite the direction in which the object is going. The
mnemonic for remembering the definition of work that helps you remember how to calculate it is
“Work is Force times Distance.” The mnemonic does not tell the whole story. It is good for the
case of a constant force acting on an object that moves on a straight line path when the force is in
the same exact direction as the direction of motion.
A more general, but still not completely general, “how-to-calculate-it” definition of work applies
to the case of a constant force acting on an object that moves along a straight line path (when the
force is not necessarily directed along the path). In such a case, the work W done on the object,
when it travels a certain distance along the path, is: the along-the-path component of the force F|
times the length of the path segment ∆r.
W = F| ∆r
(24-1)
Even this case still needs some additional clarification: If the force component vector along the
path is in the same direction as the object’s displacement vector, then F| is positive, so the work
is positive; but if the force component vector along the path is in the opposite direction to that of
1 As mentioned before, the potential energy is actually the energy of the system of the objects and their fields as a
whole, but it is common to assign it to part of the system for “bookkeeping” purposes as I do in this book.
1
62