Relating buoyancy to displacement, Archimedes principle forms the basis of the relationship between solid objects and surrounding fluids. Fluids can be either a liquid or a gas, but we’ll be sticking to liquids for this article.
Archimedes principle states that any floating object displaces its own weight of fluid. In more general terms, it can also be stated as: “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.”
This explains why wood floats and a steel bar doesn’t. The object’s density will determine its behavior when placed in a liquid – whether it will float or sink. As a rule of thumb, if an object has a higher density than water, it will sink, if lower, it will float.
Then Why do Steel Ships Float?
Good question. Steel will float only if its shape allows it to hold enough air to where its density lowers below that of water. This is why a steel bar will sink rapidly, whereas say, a steel bowl of the same mass will float. They both weigh the same amount, but the bowl holds more air within it than the bar and therefore will float due to its lower density.
In contrast, wood doesn’t have to displace as much water for it to float, as it is considerably less dense, and therefore doesn’t need as much force to keep it afloat. Both of these materials obey Archimedes principle.
Deriving an Object’s Volume from its Buoyancy
If an object is square or an otherwise “simple” geometric shape, its volume can be calculated fairly easily. But irregular shapes such as a crown for example, are more difficult. But good news! An object’s volume can be calculated by simply subtracting its mass when it’s submerged from its mass when it’s not, and multiplying by the density of water – which is one.
The weight of an object immersed completely in water is known as its apparent weight, called such because it’s not actually decreasing in weight, but only seems so due to the buoyant force which is simply pushing upward on the object and causing it to seem lighter than it really is. As we learned from Archimedes principle, buoyant force is equal to the weight of the displaced water.
This means that a floating ship is displacing its total mass in water! Imagine looking at a ship from underneath the surface of the water. Now imagine that the part of the ship that is submerged beneath the surface is a container – that has zero thickness.
If you were to fill this container with water and weigh it, this weight would equal the force of buoyancy that is working in the opposite direction to keep the ship afloat. So the greater the liquid displacement, the more steel you can have for your ship. Just remember that the only thing that is going to keep the steel afloat is the assumed fact that there is sufficient air “trapped” within it to where its density is lowered below that of water.