Page 329 - NS-2 Textbook

Buoyancy

Why does a metal ship float? How can a submarine As it fills, the combined weight of the boat plus the water
hover at a desired depth? To answer questions such as inside would be always be greater than the weight of the
these it is necessary to know something about a type of water being displaced, no matter how far down it sinks.
force called the buoyant force. Thus in this situation the boat would eventually fill com-
Over 2,000 years ago the Greek scientist Archimedes pletely and sink to the bottom, just as in the example of
(287-212 B.C.) found that an object immersed in a fluid is the stone above. So it really does not matter what mate-
pushed up with a force that equals the weight of the fluid rial is used to construct the boat. A hollow boat will al-
it displaces. This force has come to be called the buoyant ways float as long as there is still some part of it above
force, and the principle that describes it is named water when it has sunk to a depth at which its weight is
Archimedes' law in honor of its discoverer. For purposes of matched by the upward buoyant force provided by the
Archimedes' law, it does not matter whether the "fluid" water being displaced.
is a liquid or a gas. The law applies equally to both. Density is a scientific term used to describe how
much of a material is present per unit of its volume. It is
usually specified using the meh'ic system, in kilograms
WHY OBJECTS FLOAT per cubic meter or sometimes grams per cubic centime-
ter. Anything with a density less than that of water, such
Suppose that a stone with a volume of half a cubic meter as wood, will always float, since when it sinks into water
weighs 9,800 newtons in air. When it was submerged in it will always achieve equality of the upward buoyant
water, by Archimedes' law it would feel an upward force force with the downward weight before it is totally sub-
equal to the volume of water displaced, or 4,900 newtons merged. Solids having a greater density than water will
in this case, since the weight of a cubic meter of water is always have a greater downward weight than upward
9,800 newtons. TI,e apparent weight of the stone in the buoyant force, so they will always submerge completely.
water-its weight in air minus the buoyant force-- Gases as well as liquids exert upward buoyant forces.
would now be 4,900 newtons and it would sink. Instead of a boat model, suppose we experinlent with a
Now let us suppose that instead of a stone, we had a small rubber balloon. If we blow up the balloon with air
hollow iron boat also weighing 9,800 newtons. We place at the same or lower temperature than the air surround-
the boat in the water and it begins to sink. As it does so, ing it, by Archimedes' law an upward force will begin to
it begins to displace some of the water, so again by act on it equal to the weight of the outside air being dis-
Archimedes' law it begins to feel an upward force equal placed. But the weight of the balloon's skin plus the air
to the weight of the water being displaced. After it has inside it will be greater, thus causing the balloon to fall
sunk into the water to the point at which a cubic meter of to the floor, just as the boat filled with water sank to the
water has been displaced, it feels an upward force ex- bottom.
actly equal to its weight, 9,800 newtons. At this point the But now suppose we blew hot air, or a light gas such
upward buoyant force exactly equals the downward as helium, into the balloon. Heated air and light gases
weight, so there is no longer any net downward force on like helium are less dense than regular air, so they weigh
the boat. By Newton's first law, described in chapter 1 of less per unit volume. If we inflate am balloon to the
this unit, objects with no net force on them tend to re- same size as before, the same upward force as before
main at rest. Thus, our boat would now float, assuming would be felt by it. But the downward weight force
there were still some part of it above watel; called the would be less. The balloon, therefore, would rise into the
freeboard. The line around the boat where the surface of air, since there is an unbalanced upward net force on it.
the water meets it when it floats is called the waterline. In the case of a large balloon launched into the ahno-
Now suppose a hole were drilled in the hull of our sphere, as the balloon rises the air gets thinner, so eventu-
boat belnw the waterline, allo\ving the ,vater to flow in. ally at some altitude the upward buoyant force decreases

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