Energy - Dynamics and Relativity - page 55

Unlike momentum, we will see that energy can appear in many different forms.
Kinetic energy is associated with the motion of things. In a macroscopic body
made of very many atoms it is usual to distinguish between the kinetic energy
of the body as a whole, which arises as a result of the coherent motion of all of
the atoms, and the kinetic energy possessed by the atoms as they jiggle randomly
around within the body. The latter is commonly called the thermal energy of the
body: hotter bodies have more thermal energy than colder ones. Potential energy
is the energy that is stored up within a system. It might be the energy stored up as
a result of the specific chemical arrangements of molecules in a mouthful of food
or a drop of petrol. Or it could be the energy stored up by gravity at the start of a
roller-coaster ride, or in a collapsing star. What is important is that energy can be
converted from one type to another and yet, provided we account for all forms of
energy, the total is a conserved quantity. This is hugely significant. Provided we
do the book keeping correctly, and add up the numerical values of all the forms
of energy of an isolated system, the total will always be the same, irrespective
of the details. A roller coaster starting its decent can be described in terms of a
transformation of gravitational potential energy into kinetic energy; a tennis player
may use the chemical energy stored in a banana to help her complete a match;
a rocket converts chemical energy into gravitational potential energy and kinetic
energy following its launch.
Just as the conservation of momentum can be derived using Newton's laws so
we will see that energy conservation is also already encoded within them. We shall
see this soon when we encounter the Work-Energy Theorem. But to pave the way
we first need to introduce the idea of work.

3.1 WORK, POWER AND KINETIC ENERGY
The work done d W by a force F acting on a particle as it moves through an
infinitesimal displacement d r is defined to be

d W = F · d r . (3.1)

The SI unit of work is the joule 2

1 . 0Nm).
The utility of this definition will become apparent very soon, for now we shall
explore some of its properties. Consider the situation depicted in Figure 3.1. A
force F is pushing a block against a wall. We can resolve F into components
parallel and perpendicular to the wall but the displacement is constrained always
to be parallel to the wall. Notice that it is only the component of force parallel to
the displacement that contributes to the work; the perpendicular component of the
force does not contribute to the scalar product in Eq. (3.1) and hence does no work.
So how do we calculate the work done when a particle travels between two points
along an arbitrary path? It may not be immediately obvious how the definition
Eq. (3.1) for the infinitesimal work d W is to be turned into an expression for
the work done along a path of finite length. Some insight can be obtained by

(1 . 0J ≡

2 After James Prescott Joule (1818 - 89).