a 1.0m^3 block of ice floats in fresh water. 92% of its volume is below the surface of the water. What is the magnitude of the buoyancy force acting on the block?

To determine the magnitude of the buoyancy force acting on the block of ice, we can apply Archimedes' principle. This principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. In this case, since the ice block is floating, we can calculate the buoyancy force based on the volume of water displaced by the submerged portion of the ice.

Calculating the Buoyant Force

First, let's break down the information provided:

• The volume of the ice block is 1.0 m³.
• 92% of its volume is submerged in water.

Step 1: Determine the Volume of Water Displaced

Since 92% of the ice block is below the water's surface, we can calculate the volume of water displaced:

Volume of water displaced = 92% of 1.0 m³ = 0.92 m³.

Step 2: Calculate the Weight of the Displaced Water

Next, we need to find the weight of the water that corresponds to this volume. The density of fresh water is approximately 1000 kg/m³. Using this density, we can calculate the mass of the displaced water:

Mass of displaced water = Volume of displaced water × Density of water

Mass of displaced water = 0.92 m³ × 1000 kg/m³ = 920 kg.

Step 3: Calculate the Buoyant Force

The buoyant force can be calculated using the weight of the displaced water. The weight is given by the formula:

Weight = Mass × Gravitational acceleration (g)

Assuming g = 9.81 m/s², we find:

Weight of displaced water = 920 kg × 9.81 m/s² = 9019.2 N.

Final Result

Thus, the magnitude of the buoyancy force acting on the block of ice is approximately 9019.2 N. This force is what keeps the ice floating, balancing the weight of the ice block itself.

In summary, by understanding the relationship between the volume of water displaced and the buoyant force, we can effectively analyze floating objects in fluids. This principle is fundamental in various applications, from ship design to understanding natural phenomena in aquatic environments.