Energy is one of the central concepts of physics, and
one of the most difficult to define. One of the reasons we have
such a hard time defining it is because it appears in so many different
forms. There is the kinetic and potential energy of
kinematic motion, the thermal energy of heat reactions,
the chemical energy of your discman batteries, the mechanical energy of
a machine, the elastic energy that helps you launch rubber bands,
the electrical energy that keeps most appliances on this planet
running, and even mass energy, the strange phenomenon that Einstein
discovered and that has been put to such devastating effect in the
atomic bomb. This is only a cursory list: energy takes on an even
wider variety of forms.
How is it that an electric jolt, a loud noise, and a brick
falling to the ground can all be treated using the same concept?
Well, one way of defining energy is as a capacity to do work: any
object or phenomenon that is capable of doing work contains and
expends a certain amount of energy. Because anything that can exert
a force or have a force exerted on it can do work, we find energy
popping up wherever there are forces.
Energy, like work, is measured in joules (J). In fact,
work is a measure of the transfer of energy. However, there are
forms of energy that do not involve work. For instance, a box suspended
from a string is doing no work, but it has gravitational potential
energy that will turn into work as soon as the string is
cut. We will look at some of the many forms of energy shortly. First,
let’s examine the important law of conservation of energy.
Conservation of Energy
As the name suggests, the law of conservation of energy
tells us that the energy in the universe is constant. Energy cannot
be made or destroyed, only changed from one form to another form.
Energy can also be transferred via a force, or as heat. For instance,
let’s return to the example mentioned earlier of the box hanging
by a string. As it hangs motionless, it has gravitational potential
energy, a kind of latent energy. When we cut the string, that energy
is converted into kinetic energy, or work, as the force
of gravity acts to pull the box downward. When the box hits the
ground, that kinetic energy does not simply disappear. Rather, it
is converted into sound and heat energy: the box makes a loud thud
and the impact between the ground and the box generates a bit of
This law applies to any closed system. A closed system
is a system where no energy leaves the system and goes into the
outside world, and no energy from the outside world enters the system.
It is virtually impossible to create a truly closed system on Earth,
since energy is almost always dissipated through friction, heat,
or sound, but we can create close approximations. Objects sliding
over ice or air hockey tables move with a minimal amount of friction,
so the energy in these systems remains nearly constant. Problems
on SAT II Physics that quiz you on the conservation of energy will
almost always deal with frictionless surfaces, since the law of
conservation of energy applies only to closed systems.
The law of conservation of energy is important for a number
of reasons, one of the most fundamental being that it is so general:
it applies to the whole universe and extends across all time. For
the purposes of SAT II Physics, it helps you solve a number of problems
that would be very difficult otherwise. For example, you can often
determine an object’s velocity quite easily by using this law, while
it might have been very difficult or even impossible using only
kinematic equations. We will see this law at work later in this
chapter, and again when we discuss elastic and inelastic collisions
in the chapter on linear momentum.