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When an object is submerged in a fluid, a force acts upon it pushing it up, countering gravity. This is known as the buoyant force. In simple terms, the buoyant force is what allows objects to float, and it's all due to the pressure difference exerted by the fluid on different parts of the submerged body. Think of how a ball pushes back up when you try to push it underwater.
This force can be calculated using Archimedes' principle. Archimedes taught us that the buoyant force is equal to the weight of the fluid that the object displaces. When you place an object in water, it pushes some of the water out of the way. The volume of this displaced water determines the buoyant force.
Key points about buoyant force include:

• It acts in the upward direction.
• The magnitude of the buoyant force is equal to the weight of the displaced fluid.
• It's what makes objects float or sink depending on their density relative to the fluid.

This is why understanding the concept of buoyant force is essential in determining how objects behave in fluids, like our iceberg example.

Density is a measure of how much mass exists per unit volume. In the context of our iceberg example, the density of the water plays a crucial role due to the nature of the buoyant force.
Water density varies depending on its salinity. Saltwater is denser than freshwater because it contains dissolved salts. This means that more mass is packed into the same volume compared to freshwater.
Let's consider how this affects the iceberg:

• Saltwater has a density of approximately \(1024 \: \mathrm{kg/m}^3\), while freshwater is \(1000 \: \mathrm{kg/m}^3\).
• This higher density of saltwater offers more buoyant force per unit volume displaced than freshwater. As a result, an iceberg displaces a smaller volume of saltwater to balance its weight compared to freshwater.

This difference in densities is why icebergs appear to float higher in saltwater than in freshwater.

The fraction of an object's volume submerged refers to the proportion of the object that is beneath the surface of the liquid. It depends on both the object's density and the density of the fluid it's in. For an iceberg floating in water, this is a practical application of how buoyant force and density work together.
Using Archimedes' principle, you can determine how much of the iceberg is submerged in either saltwater or freshwater. By calculating the ratio of the density of ice to the density of the water, we find out what fraction of the iceberg remains below the water's surface.
Let's break it down further using our iceberg example:

• For saltwater, the submerged volume fraction is calculated as \( \frac{917}{1024} \approx 0.895 \), meaning 89.5% of the iceberg is immersed.
• In freshwater, it is \( \frac{917}{1000} \approx 0.917 \), indicating 91.7% of the iceberg is submerged.

The result is that more of the iceberg stays below the surface in freshwater compared to saltwater. Thus, even small differences in fluid density can significantly impact the visibility and stability of floating objects.