Archimedes' principle can be used to calculate the density...

Archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid. (a) What mass of fluid does the iron displace? (b) What is the volume of iron, using its density as given in Table 11.1 (c) Calculate the fluid's density and identify it.

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Key Concepts

Archimedes’ Principle

Archimedes’ Principle asserts that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. This concept is pivotal for determining the densities of fluids or solids by correlating the loss of an object's apparent weight when submerged to the mass of the fluid displaced.

Buoyant Force and Apparent Weight

The buoyant force is the upward force experienced by an object in a fluid, counteracting gravity. The apparent weight of a submerged object is its actual weight minus this buoyant force, and the difference can be used to calculate the weight, and hence the mass, of the displaced fluid.

Density

Density is defined as the mass per unit volume of a substance. It is a key property that allows comparison between different materials and is critical for determining the identity of a fluid or the volume of a solid when one of these properties is known.

Volume Calculation

Calculating the volume of an object typically uses the relationship between mass and density, where volume equals mass divided by density. This calculation is essential when applying Archimedes’ principle, as the volume of the displaced fluid must equate to the volume of the immersed object.

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