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Density is a measure of how much mass is contained within a specific volume. It is described mathematically as \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). When calculating density, it's important to make sure that the mass and volume are in compatible units, such as kilograms and cubic meters, respectively.

In the context of our problem, we're determining the average density of a duck that is partly submerged in water. Knowing the proportion of the duck's volume that is under water helps us calculate its density by leveraging its buoyancy.

• The mass of the duck is equal to the mass of the water displaced by the submerged part.
• The average density of the duck can be calculated by comparing its density to that of water, considering the percentage of the duck's volume that is submerged.

Remember, a floating object's average density is always less than the fluid it displaces.

Objects float when their density is lower than the density of the fluid they are placed in. When something floats, it means the gravitational pull downward is balanced by an upward buoyant force. This buoyant force is generated because the object pushes aside, or displaces, enough fluid to equal the object's weight.

It is helpful to think of an iceberg as an example; the portion above the water is supported by the much larger submerged section. Similarly, 75% of our duck's volume stays above the lake water's surface, indicating that it is less dense than the water.

• When floating, the sum of forces (gravity and buoyancy) remains in equilibrium.
• An object remains buoyant as long as the density is lower than the displaced fluid.

This principle explains why a boat, despite its weight, can float on the sea. Its shape ensures its average density is less than water.

Archimedes' principle is a fundamental concept in fluid mechanics that explains why objects float or sink. It states that a body wholly or partially submerged in a fluid experiences a buoyant force that is equal to the weight of the fluid displaced by the body.

For our duck, which is floating with 25% of its volume submerged, Archimedes' principle helps us understand that the weight of the duck is precisely balanced by the weight of the water it displaces. This equilibrium is why the duck does not sink.

• The submerged fraction of the duck equals the ratio of its density to the fluid's density.
• In our example, 25% of the duck's density is equal to water density, illustrating perfect balance as described by Archimedes.

This principle is foundational to understanding flotation and is widely applicable, from balloons in the air to submarines under the sea.