Game Development Reference

In-Depth Information

Figure 1-8. Example body consisting of car, driver, and fuel

The properties of each component in this example are given in
Table 1-2
. Note that

length is measured along the x-axis, width along the y-axis, and height would be coming

out of the screen. Also note that the coordinates—in the form (
x
,
y
)—to the centroid of

each component are referenced to the global origin.

Table 1-2. Example properties

Car

Driver (seated)

Fuel

Length = 4.70 m

Length = 0.90 m

Length = 0.50 m

Width = 1.80 m

Width = 0.50 m

Width = 0.90 m

Height = 1.25 m

Height = 1.10 m

Height = 0.30 m

Weight = 17,500 N

Weight = 850 N

Density of fuel = 750 kg/m
3

Centroid = (30.5, 30.5) m

Centroid = (31.50, 31.00) m

Centroid = (28.00, 30.50) m

The first mass property we want to calculate is the mass of the body. This is a simple

calculation since we are already given the weight of the car and the driver. The only

other component of weight we need is that of the fuel. Since we are given the mass

density of the fuel and the geometry of the tank, we can calculate the volume of the tank

and multiply by the density and the acceleration due to gravity to get the weight of the

fuel in the tank. This yields 920.6 N of fuel, as shown here:

W
fuel
= ρvg = (750 kg/m
3
) (0.50 m) (0.90 m) (0.30 m) (9.81 m/s
2
)

= 993 N

Acceleration due to gravity is the acceleration of a falling object as it

falls toward the earth. The weight of an object is equal to its mass times

the acceleration due to gravity. The symbol
g
is used to represent the

acceleration due to gravity, and on Earth the value of
g
is approximately

9.8 m/s
2
at sea level. Units for weight in the metric system are Newtons,

N
.