Objective: To examine the relative ability of a van or car
to float.
An object floats when the weight of it is less than the
maximum amount of water that the object can displace (its
total volume). If the van floats, it is a small boat. Since
boats can support a rather large weight without displacing
very much water, one might guess that the van might float
if it runs off the road and into a lake. This assumes the
windows are closed and no water enters from holes in the floor
One person in van:
To check this let us assume that we have a 4,000 pound van
with outside dimensions 12 feet long by 6 feet wide and five
feet high. We will look at it as a brick shape and not worry
about the tires. We will also assume the bottom is water tight
and water will not come in too fast in any holes in the floorboard,
at least for a little time. The area of the van is
If the van floats then the buoyancy force equals the weight
of the van.
Buoyancy force = Weight of the van
Buoyancy force = 4,000 pounds
The volume of water that needs to be displaced to equal
the weight of the van is given by rearranging
Buoyancy force = (Density) (Volume) to give
and in our case the volume of displaced water is
Now since
Volume of water displaced = (area of van)
(depth in water)
64 cubic feet = (72 square feet) (depth in water)
The depth the van is in the water is then about 64/72 foot
or about 11 inches. Since the side of the van is five feet
high that makes it floating.
Four people in van:
If we assume there are 4 people in the van, and the average
weight of each is 150 pounds then the van will displace 4,450
pounds of water.
Volume of water displaced = (area of van)(depth
of water)
The following calculator allows you to input the volume of
material that is displaced, its density, and the calculator
provides the buoyancy force. This works for water with a density
of 62.4 pounds per cubic foot as well as other liquids and
even gases such as cool air.
