Downward forces of 45.0 N and 15.0 N, respectively, are...

Downward forces of $45.0 \mathrm{~N}$ and $15.0 \mathrm{~N}$, respectively, are required to keep a plastic block totally immersed in water and in oil, respectively. If the volume of the block is $8000 \mathrm{~cm}^{3}$, find the density of the oil.

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Key Concepts

Archimedes' Principle

This principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. It is fundamental in understanding why a block or any submerged object appears lighter in a fluid than in air, as well as for calculating the magnitude of the buoyant force.

Buoyant Force Calculation

The buoyant force is computed by multiplying the volume of the displaced fluid by the density of the fluid and the acceleration due to gravity. This relationship is crucial in problems where the balance of forces on an immersed object is used to infer properties of the fluid, such as its density.

Fluid Density

Density is defined as the mass per unit volume of a substance. In the context of fluid mechanics, knowing the density of the fluid is essential because it directly affects the buoyant force experienced by objects immersed in it. When the buoyant force and the volume of the displaced fluid are known, the density of the fluid can be determined.

Unit Conversion

Accurate calculations in physics often require consistency in units. Converting units, such as from cubic centimeters to cubic meters, ensures that all quantities are in the SI system, allowing for the correct application of formulas like those derived from Archimedes' Principle.

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