When will the hull of a ship sink in water deeper: when the ship is sailing in fresh water or in seawater? Why?

Archimedes' principle is a law of physics fundamental to fluid mechanics and lays the groundwork for understanding why objects like ships float. The principle states that any object, wholly or partially submerged in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

This principle can be a bit tricky to grasp, so imagine you're taking a bath and you decide to submerge a rubber duck into the water. As the duck goes in, water spills out of the tub. Archimedes' discovered that the weight of this spilled water is actually the same as the upward force pushing on the duck, which we call buoyancy. This is why the duck doesn't just sink to the bottom but floats at the surface.

In the context of the ship, when it's placed in water, it pushes water aside in an amount that would weigh the same as the ship. This interaction determines whether the ship will sink or float. By knowing this, you're a step closer to unlocking the secret behind how huge vessels can sail across the oceans without diving beneath the waves.

The density of a fluid, such as water, is an essential concept when discussing buoyancy and Archimedes' principle. Density is defined as mass per unit volume and is generally expressed in kilograms per cubic meter (kg/m³). In simpler terms, density tells us how much 'stuff' is packed into a certain space.

Why Does Density Matter?

For any object floating in water, from a leaf to an ocean liner, the fluid's density is a deciding factor in how well the object floats. A fluid with higher density exerts a greater upward buoyancy force on the object submerged in it. Now, linking back to the buoyancy force, remember that the density of this fluid directly influences the weight of the displaced water (and therefore the strength of the buoyancy).

Higher density fluids can support heavier objects because they can exert a stronger buoyancy force. It's akin to trying to push a beach ball down into the water – the denser the water, the stronger the pushback you'll feel. So, when we're comparing different types of water, like fresh and saltwater, the density is what's going to determine the buoyancy effect on our ship.

Freshwater and seawater may seem similar at a glance but their densities tell a different story, which significantly influences buoyancy. Typically, freshwater has a density of approximately 1000 kg/m³. Seawater, due to its dissolved salts and minerals, is denser, with approximately 1025 kg/m³.

Since seawater is denser, it will exert a greater buoyancy force on objects compared to freshwater. This is why ships float better in seawater – they displace an amount of water that weighs as much as the ship, but because seawater is denser, this happens before the ship has to submerge as much of itself as it would in freshwater.

Think about it like this: if you're floating in a pool with a life jacket on, you'll sit higher in the water due to the pool's fresh water. If you were to float in the ocean with the same life jacket, you'd be even more buoyant, not because of anything you've changed, but because the seawater itself helps to keep you more afloat. In our original exercise, this means a ship's hull will not need to sink as deeply in seawater to displace the necessary volume of water to support its weight.