Applications

You will be aware that some objects float in water and that others sink. When you swim you feel that you are lighter and more buoyant. The general concept that governs floating and sinking is called Archimedes' principle.

Sinking ships-

The Plimsoll Problem

Why do steel ships float?

It's obvious that a piece of steel will sink in water, yet ships made of steel float. There must be some other factor that comes into play to explain this. Applying Archimedes' principle to the problem the upthrust of the water must be greater than the mass of the ship, so somehow a great mass of water has to be displaced. This is done by shaping the hull of the ship in such a way that as the ship sinks into the water it displaces more and more liquid until a balance is reached between the mass of water displaced and mass of the ship. This general principle applies to any object made from a material that is more dense than the liquid it is in.

In the past, some European ships sank when they entered the tropics for the first time. All was well when the cargo was put aboard in cold, salty waters, but then the ship sank when it reached warmer, less salty seas. The problem was that Archimedes' principle had not been taken into account. When the ship was first loaded it floated because cold, salty water has a relatively high density. This meant that less water had to be displaced to equal the mass of the ship. As the ship steamed to warmer, less salty waters, more water had to be displaced to maintain equilibrium. The ship dropped lower in the water, sometimes dropping below the waterline, and sinking. This was overcome by Samuel Plimsoll who marked his ships with what became known as the Plimsoll Line.

How do submarines float and sink?

How do helium balloons work?

Using Archimedes' Principle and the law of floatation, it is clear that a change in mass of an object affects how much liquid has to be displaced. In submarines, this is controlled by ballast tanks. When the tanks are empty, the submarine has less mass and it floats like a normal ship. As water is allowed into the tanks, the mass of the submarine increases, the downward gravitational force on the submarine increases and the submarine begins to sink. Careful balancing of the water ballast enables the craft to stay at any chosen depth. The swim bladders of fish work in a similar manner.

Most of us feel comfortable with the idea of something floating in water. We see that happen every day. In fact, people themselves float in water, so we have a way of directly experiencing water flotation. The reason why things float in water applies to air as well, so let's start by understanding water flotation.

Let's say that you take a plastic 1-liter soda bottle, empty out the soft drink it contains, put the cap back on it (so you have a sealed bottle full of air), tie a string around it like you would a balloon, and dive down to the bottom of the deep end of a swimming pool with it. Since the bottle is full of air, you can imagine it will have a strong desire to rise to the surface. You can sit on the bottom of the pool with it, holding the string, and it will act just like a helium balloon does in air. If you let go of the string the bottle will quickly rise to the surface of the water.

The reason that this soda bottle "balloon" wants to rise in the water is because water is a fluid and the 1-liter bottle is displacing one liter of that fluid. The bottle and the air in it weigh perhaps an ounce at most (1 liter of air weighs about a gram, and the bottle is very light as well). The liter of water it displaces, however, weights about 1,000 grams (2.2 pounds or so). Because the weight of the bottle and its air is less than the weight of the water it displaces, the bottle floats. This is the law of buoyancy.

Helium balloons work by the same law of buoyancy. In this case, the helium balloon that you hold by a string is floating in a "pool" of air (when you stand underwater at the bottom of a swimming pool, you are standing in a "pool of water" maybe 10 feet deep -- when you stand in an open field you are standing at the bottom of a "pool of air" that is many miles deep). The helium balloon displaces an amount of air (just like the empty bottle displaces an amount of water). As long as the helium plus the balloon is lighter than the air it displaces, the balloon will float in the air.