Game Development Reference
In-Depth Information
FVg
=
r
(9.1)
B
w
w
The buoyancy force acts through the geometrical center of an object, which is not always
the same as the center of mass of an object. If the geometrical center and center of mass are in
different locations, the buoyancy force and gravitational force will create a torque that will
cause the object to rotate. This fact has potentially serious consequences for boats. For example,
if all of the people on a crowded boat move to one side of a boat, the center of mass of the boat
may shift enough to create a torque large enough to capsize the boat.
If you recall from Chapter 3, the density of an object is equal to the mass of the object
divided by its volume. Equation (9.1) isn't just for objects floating in water. It is applicable to
any fluid, including air. The densities of fresh water, salt water, and air at sea-level conditions
are shown in Table 9-1. It probably comes as no surprise that water is significantly more dense
than air, which means that objects will have a much easier time floating in water than they
would floating in air.
Table 9-1. Density of Water and Air
Density ( kg/m 3 )
Substance
Fresh water
1000
Seawater
1025-1030
Air (sea level)
1.2
When a boat floats, the buoyancy force due to the water displaced by the boat balances the
gravitational force acting on the boat. If the weight of the boat increases, if more people get on
the boat, for example, the boat will sink a little lower in the water as shown in Figure 9-4. By
doing so, more water is displaced, which increases the buoyancy forces acting on the boat,
which balances out the additional weight of the boat.
Figure 9-4. If weight is added to a boat, it will float lower in the water.
Equation (9.1) can be used to compute the maximum loading that can be placed on a boat
(or any other object) and have it still float. The maximum buoyancy force the boat can generate
is equal to the volume of the boat hull multiplied by the density of the fluid in which the boat is
floating and the gravitational constant. The weight of the boat and whatever is inside the boat
must be less than this value.
mg
<
r
V g
(9.2)
b
w
w
The gravitational constant appears on both sides of Equation (9.2) and can be cancelled out.
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