Question

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

Short answer

Explain your answer using buoyancy force and density as key factors.

Step-by-step solution

Understand the buoyancy force

Buoyancy force is the upward force exerted by a fluid (in this case, water) that opposes the weight of an immersed object (ship). According to Archimedes' principle, the buoyancy force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The overall effect is that the object appears to weigh less when submerged in the fluid.

Determine the density of freshwater and seawater

The density of a fluid is essential in calculating the buoyancy force exerted on an object. Fresh water has a density of approximately 1000 kg/m³, while seawater has a higher density, which is around 1025 kg/m³. The higher density of seawater is due to the dissolved salts in it.

Compare the buoyancy force in freshwater and seawater

Using the information from Step 2, we can see that the density of seawater is greater than that of freshwater. Since the buoyancy force depends on the density of the fluid, a ship submerged in seawater will experience a greater buoyancy force than a ship submerged in freshwater.

Relate the buoyancy force to the depth of the hull in water

Since the buoyancy force is equal to the weight of the fluid displaced by the object, a greater buoyancy force implies a greater volume of displaced fluid. In order to displace the same volume of fluid, the hull of a ship sailing in seawater will sink deeper compared to when it is sailing in freshwater. This is because the extra buoyant force exerted by the seawater is needed to balance the ship's weight, allowing the ship to stay afloat.

Answer the question

In conclusion, the hull of a ship will sink deeper in seawater than in freshwater due to the greater buoyancy force exerted by the seawater, which has a higher density than freshwater.

Key concepts

Archimedes' Principle

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.

Fluid Density

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 versus Seawater Density

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.