What factors play a role in the buoyancy of a substance or object?

Answer

Dear Remy,

To start with, we don’t take the surface tension of water into account (see the answer at the bottom of the question what this has as an effect). So we assume that we completely submerge an object in water.

To better understand Archimedes’ law, imagine that you could isolate a quantity of water (eg the volume of water that would fit in a bottle, 1 liter) from a larger quantity of water (eg a flooded bath). So in your mind you see the bottle shape in the bath. The water in the bottle shape stays nicely in place: it is in balance with the rest of the water. If it is in equilibrium, this means that the sum of the forces acting on it is zero. The forces acting on the bottle shape are:

• the “pressure” of the water above the bottle shape
• the “pressure” of the water under the bottle shape
• the gravity of the water in the bottle shape
• the “pressure” of the water to the left of the bottle shape
• the “pressure” of the water to the right of the bottle shape
• the “pressure” of the water for the bottle shape
• the “pressure” of the water behind the bottle shape

You notice that all these forces do not act in the same direction. In order to have balance in the total, there must also be balance in every direction. In other words, the pressure to the left must be equal to the pressure to the right, the pressure to the front must be equal to the pressure to the rear and the sum of the pressure upwards, the pressure downwards and the force of gravity must also be equal to zero. And it is precisely those last three components that determine Archimedes’ law: gravity + the pressure above the bottle shape = the pressure below the bottle shape. In other words, the bottle shape experiences an upward force from the water below and the magnitude of that force is equal to the weight of the water in the bottle shape.

Now if we replace the bottle-shaped water with a bottle of air, the pressure of the water underneath will still be the same (the bottle still occupies the same volume). The gravity that the bottle of air experiences is smaller (the bottle of air is not as heavy as the bottle-shaped water). As a result, the upward force will be greater than the downward force, so that the bottle of air is pushed upwards until it is on the surface (= floats).

On the other hand, if we replace the bottle-shaped water with a bottle of mercury (much heavier than water), the gravity will be greater than the bottle-shaped water, while the buoyancy through the water under the bottle is still the same. The downward force is thus greater than the upward force and the bottle will be pushed downwards.

In other words, if a material weighs more than the same volume of water, it will sink and if it weighs less, it will float. How much a material weighs for a given volume is called (mass) density (mass density = mass / volume).

So: materials with a lower density than water (= most oils, most woods, feathers, a bottle filled with air, …) will float and materials with a higher density (= a complete block of iron, most stones, …) will sink.

Then why doesn’t a ship sink? Isn’t it mostly iron? That is correct, but there is also a lot of air on the inside of the fuselage. And with a ship you have to compare the weight of the entire ship (iron + air) with the volume of water it replaces = the entire volume (iron + air) that is under water.

One last word of explanation about surface tension of water: at a microscopic level, water consists of long chains (a kind of train of magnets). That way you can put something on it and it won’t sink immediately. Try very carefully to place a (copper) coin flat on a water surface (for example in a glass): it will float. If you put the coin in it, it will sink. So mass density does not explain everything about floating and sinking.

It’s a lot of explanation, but hopefully you understand now.

Bart