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