A fish maintains its depth in fresh water by adjusting the...

A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of $1.08 \mathrm{~g} / \mathrm{cm}^{3}$. To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water?

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Key Concepts

Volume Fraction Adjustment

Volume fraction refers to the proportion of an object’s total volume that is occupied by one of its components. By increasing or decreasing the volume fraction of a component with a distinct density, one can systematically alter the overall density of the object, which is a key principle in buoyancy control and material design.

Composite Density Calculation

When an object consists of materials with different densities, its effective density is determined by the weighted average of the densities of its individual components. This concept is important for understanding how altering the proportions of components with varying densities can adjust an object's overall density.

Density

Density is defined as mass per unit volume and is a fundamental property in physics that determines how substances interact with fluid environments. It is used to predict whether objects will float, sink, or remain suspended when immersed in a fluid.

Neutral Buoyancy

Neutral buoyancy occurs when an object’s average density matches that of the surrounding fluid. In this state, there is no net upward or downward force acting on the object, allowing it to remain at a constant depth without expending energy to adjust its position.

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