Game Development Reference
In-Depth Information
Energy
Energy
is defined as the capacity for doing work. Energy is a
state variable
, meaning that it is
used to characterize the physical state of an object. Energy, work, and force are closely related.
We learned in the last section that it requires a force to perform work. Since energy is the capacity
for doing work, the source of a force that performs work must possess a certain level of energy.
Objects can store energy. When the object work is performed, part or all of the stored energy of
an object is converted to work. Work and energy are both scalar quantities.
There are several different forms that energy can take.
Kinetic energy
is related to the
motion of an object.
Potential energy
can be thought of as stored energy and is related to the
position of an object. If work is performed to move an object from one location to another, part
or all of that work might be stored in the object as potential energy. Taken together, the kinetic
and potential energies of an object are also referred to as the
mechanical energy
of the object.
In addition to the mechanical energy components, there are also what are called internal
energy types that relate to how individual molecules and atoms store energy. The internal energy
type you are probably most familiar with is
thermal energy
, which is related to the temperature
of an object. Objects can also store
chemical energy
. When chemical energy is released rapidly,
the result can be an explosion—a topic we will explore in Chapter 13.
One of the characteristics of energy is that it can be converted from one form into another.
For example, the kinetic energy of an object can be converted into work that in turn is converted
into potential or thermal energy. For example, when a meteorite hits the ground, the kinetic
energy of the meteorite is very rapidly converted to heat and and/or work that is performed,
pushing the ground away from the point of impact. The SI units of energy are the same as those
of work, namely
N-m
or
J
.
Kinetic Energy
Kinetic energy is the energy of motion. The kinetic energy of an object,
E
K
, is proportional to
the mass of the object,
m
, and the square of the velocity of the object,
v
.
1
2
2
K
E v
=
(3.18)
Because kinetic energy is a scalar quantity, the velocity term in Equation (3.18) is the
velocity magnitude, or speed, of the object.
We know from Newton's second law that a force is required to change the velocity of an
object. According to something known as the
work-energy theorem
, the work done by a net
force on an object is equal to the change in the kinetic energy of an object.
1
2
(
)
2
2
0
Wmv
=
−
v
(3.19)
f
In Equation (3.19),
v
0
is the initial velocity of the object and
v
f
is the final velocity. We can
use the work-energy theorem to determine the height that a projectile that is shot straight up
into the air will reach. The projectile will have an initial kinetic energy equal to one half its mass
