Game Development Reference
In-Depth Information
So far in this topic, I've been using the acceleration due to gravity, g , as a constant 9.8
m/s 2 (32.174 ft/s 2 ). This is true when you are near the earth's surface—for example, at
sea level. In reality, g varies with altitude—maybe not by much for our purposes, but it
does. Consider Newton's second law along with the law of gravitation for a body near
the earth. Equating these two laws, in equation form, yields:
m a = (G M e m) / (R e + h) 2
where m is the mass of the body, a is the acceleration of the body due to the gravitational
attraction between it and the earth, M e is the earth's mass, R e is the radius of the earth,
and h is the altitude of the body. If you solve this equation for a , you'll have a formula
for the acceleration due to gravity as a function of altitude:
a = g' = (G M e ) / (R e + h) 2
The radius of the earth is approximately 6.38×10 6 m, and its mass is about 5.98×10 24
kgs. Substituting these values in the preceding equation and assuming 0 altitude (sea
level) yields the constant g that we've been using so far—that is, g at sea level equals 9.8
m/s 2 .
Friction
Frictional forces (friction) always resist motion and are due to the interaction between
contacting surfaces. Thus, friction is a contact force. Friction is always parallel to the
contacting surfaces at the point of contact—that is, friction is tangential to the contacting
surfaces. The magnitude of the frictional force is a function of the normal force between
the contacting surfaces and the surface roughness.
This is easiest to visualize by looking at a simple block on a horizontal surface, as shown
in Figure 3-1 .
Figure 3-1. Friction: block in contact with horizontal surface