Game Development Reference
In-Depth Information
Conservation of Energy
We have already talked about how energy can be converted from one form into another. This
concept can be expanded into one of the fundamental concepts of physics—
conservation of
energy
, which states that energy can neither be created nor destroyed, only converted from
one form into another.
There are times when you can use the conservation of energy principle to model the motion
of an object. For example, let's say that a ball of mass
m
is held motionless at a height
h
0
above
the earth. If the ball is released, it will fall to the earth. As the ball falls, some of its initial potential
energy is converted into kinetic energy. If only kinetic and potential energy is being considered,
the velocity of the ball,
v
, at any height,
h
, during its fall could be obtained from the conservation
of energy equation.
1
2
2
mv
+=
mgh mgh
(3.24)
0
A common mistake that is made is to assume that conservation of energy applies only to
kinetic and potential energy—that the sum of kinetic and potential energy for a given system is
constant. This statement is only true if there are no other energy modes (thermal, chemical,
etc.) that are available. If there is some other way that energy can be stored, into thermal energy
for instance, then the sum of kinetic and potential energy may not be constant.
For example, let's say that there is a box resting on top of a ramp at an initial height,
h
0
, as
shown in Figure 3-13. At some point the box is released and slides to the bottom of the ramp. If
only kinetic and potential energy were being considered, you might think to compute the velocity
of the box when it reaches the bottom of the ramp by Equation (3.24). However, the actual
velocity of the box will be less than the value predicted by Equation (3.24). The reason is that
there will be friction between the box and the ramp and some of the initial potential energy of
the box will be converted to thermal energy. The bottom of the box and the surface of the ramp
will heat up by a small amount. The overall energy of the system is still conserved, but the sum
of the potential and kinetic energy is not.
h
0
Figure 3-13.
A box sliding down a ramp will generate some heat.
Power
You have learned that work is performed when a force is applied to an object over a certain
distance. But nowhere in the definition of work is the concept of how long it took to perform
the work. The concept of
power
is used to characterize the rate at which work is being performed.
Power is defined as the amount of work performed per unit time. It has units of
J/s
, which is also
