1. Why a Lump of Iron Sinks but an Iron Ship Floats
The density of iron is about 7.9 grams per cubic centimeter, which is much larger than water's density of about 1.0 gram. Because of this, a lump of iron sinks [2]. However, a ship made of iron floats. The material is the same, but the result is opposite. This is the starting point for understanding buoyancy.
The answer lies not in the name of the material, but in the average density when the whole ship is viewed as one object. To understand this, we must first look at what water does to objects.
2. Why Water Pushes Up on Objects: Pressure Increases With Depth
Why do your ears hurt at the bottom of a pool? In water, pressure becomes stronger in deeper places. This is why your ears hurt at the bottom of a pool. The difference in pressure between the top and bottom creates buoyancy. An object in water experiences a force pushing down on its top surface and a force pushing up on its bottom surface. Because the bottom surface is deeper, the upward force is stronger. This difference is the buoyant force that lifts the object [1]. The forces pushing from the sides are equal in size and cancel each other out.
If the buoyant force is greater than the object's weight, it rises. If it is smaller, it sinks. If they are equal, it stays still [1]. So, what determines this buoyant force?
3. Buoyancy: The Upward Force Equal to the Weight of Displaced Water
An object in water receives a buoyant force equal to the weight of the water it displaces. This is Archimedes' principle [2]. Buoyancy does not depend on the density of the object itself. If you submerge iron and wood of the same size, they receive the same buoyant force. The difference is in the weight of the objects.
There is a famous story about this principle. According to a story written by the ancient Roman architect Vitruvius, Archimedes was asked by a king to check if a gold crown had silver mixed in. Archimedes noticed water overflowing from a bathtub and reportedly ran out shouting "Eureka!" [8]. However, this is a legend based on Vitruvius's description [7].
If the weight is different, the result changes. Even if the buoyant force is the same, heavy objects sink and light objects float. Objects with a density lower than water float, while those with a higher density sink [1]. How can we explain heavy iron ships?
4. Why an Iron Ship Counts as One Object Including the Air Inside
One liter (1000 cubic centimeters) of water weighs about 1 kilogram. Since iron is about 7.9 times heavier than water, 1 kilogram of iron has a volume of only about 127 cubic centimeters. This is an approximate value calculated by dividing 1000 by 7.9. The water displaced by this lump is about 127 cubic centimeters. The buoyant force is only about one-eighth of the iron's weight, so it sinks.
If you take the same 1 kilogram of iron and stretch it thin to make a container filled with air, you can increase the volume of the part submerged in water. If it becomes large enough to displace 1000 cubic centimeters of water, the buoyant force reaches the weight of 1 kilogram. When viewed as the whole ship, the average density of the iron and air combined becomes smaller than water, so it floats [2]. Clay sinks when rolled into a ball but floats when shaped like a boat, using the same idea [2]. By stretching iron thin and filling the inside with air, only the volume increases.
5. How Eggs and Fish Float: Changing the Water or Changing the Body
The density of an egg is about 1.08 g/cm³, while fresh water is about 1.00 g/cm³. Therefore, an egg sinks in fresh water. If you dissolve salt to make the water's density larger than the egg's, the egg floats [3]. This is a method of changing the water, not the object.
Fish adjust their bodies. A fish's body is slightly heavier than water and is said to sink easily if nothing is done. Fish with swim bladders regulate buoyancy by storing or releasing gas in them [4]. When gas enters, the average density of the whole body approaches that of water. It is said that some types take in air at the surface, while others have organs that produce gas [4]. The structure of a ship and a fish's swim bladder both work on the principle of matching the average density to water. This idea is also used in the actual safety of ships.
6. The Load Line: The Mark That Warns a Ship Against Overloading
On the side of a ship, there is a line called the load line (Plimsoll mark). This is a limit line to prevent the ship from sinking too deep due to overloading [5]. There are separate lines for seawater and freshwater because freshwater provides less buoyancy than seawater, causing the ship to sink slightly deeper for the same weight [5]. Lines for summer, winter, and other seasons are separated because the risks of waves, wind, and ice accumulation on the hull differ by season [5]. Note that the difference is not just due to seasonal changes in seawater density.
The international convention on load lines was adopted in 1930. Its purpose is to set limits on cargo and ensure reserve buoyancy [6]. The understanding of buoyancy connects to actual safety standards.
7. A Home Experiment: Making Clay Float in a Bowl of Water
Try comparing two shapes made from the same clay in a bowl of water. Rolled clay sinks, but clay shaped like a boat with high sides floats. Even with the same weight, the volume of the submerged part changes. If it floats, try placing small beads or clips on it one by one. How much it can hold is like the ship's "maximum load." If you add too much, it sinks. Lay a towel on the floor to protect against splashes.
You can also test if an egg floats. Dissolve salt little by little in a cup of water and observe where the egg rises. As salt increases, the water around the egg becomes heavier, and at a certain point, it floats up [3]. For a deeper understanding, the Ministry of Land, Infrastructure, Transport and Tourism's page on the load line convention contains the rules for ship safety [6].