Game Development Reference
In-Depth Information
force, the object will accelerate, because net force and acceleration always
go together. There are no exceptions to this rule. The acceleration of an
object is always proportional to the net force acting on it at that moment.
Now this does not mean that when there are any forces on an object,
it will necessarily accelerate. Nor does it mean that if an object is not
accelerating, then there are no forces acting on it. The
f
in
f
= m
a
is
the net force. Consider the tremendous forces exerted on the beams at the
bottom of a skyscraper. Clearly there is a force that wants to accelerate
the beam downward. However, since the beams do not in fact accelerate
downward, we know by Newton's second law that this downward force must
be exactly opposed by some other force acting in the opposite direction.
What sort of quantity is force? First of all, force has magnitude and
direction, and so it is a vector quantity, just like acceleration (although at
times it is easier to study force in a one-dimensional setting, just like we did
with acceleration). And force must have the same dimensions (1D, 2D, or
3D, depending on the “world” in which we are working) as the acceleration
a
for Equation (12.1) to make sense, because m is a scalar quantity.
Let's use dimensional analysis to determine the physical units that we
should use to measure force. Mass is one of our fundamental quantities,
denoted M, and from the previous chapter we know that acceleration has
units L/T
2
. Therefore (dropping the bold to indicate vector quantities),
force must have units
Dimensional analysis of
force
f = ma = (M)(L/T
2
).
When measuring with the SI units—mass in kilograms, length in meters,
and time in seconds—force has the units of “kilogram meter per second
squared.” This is quite a mouthful, so it goes by a special name, the
Newton, denoted N:
1 N = 1 kg
m
The Newton is an SI
unit of force
s
2
.
If you're having trouble grasping just what a “kilogram meter per second
squared” is, just remember that a Newton is the amount of force required
to accelerate a mass of 1 kg at a rate of 1 m/s
2
.
There's a common misunderstanding that we'd like to cut off as early as
possible. Force creates an acceleration on a body, and it acts over time. For
example, the question, “How much force does it take to get a 100 lb object
to go 100 mi/hr?” does not make sense. Force doesn't produce velocity
directly, it causes the velocity to change over time. This can be especially
confusing when you consider collisions, such as a ball bouncing on the floor
or being struck by a bat. Although the velocity appears to have changed
instantaneously, what is really happening is that a very large force is acting
for a very short (but finite) duration. We study collisions in more detail in
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