A material will float on the surface of a liquid if the...

A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately $1.0 \mathrm{~g} / \mathrm{mL}$, will a block of material having a volume of $1.2 \times 10^{4} \mathrm{in}^{3}$ and weighing $350 \mathrm{lb}$ float or sink when placed in a reservoir of water?

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Key Concepts

Density

Density is the measure of how much mass is contained in a given volume of a substance. It is calculated as mass divided by volume, and it provides a basis for comparing different materials. In floating and sinking problems, determining whether an object will float typically involves comparing its density to that of the surrounding fluid.

Buoyancy

Buoyancy is the upward force that a fluid exerts on an object immersed in it. According to Archimedes’ principle, an object will float if the buoyant force, which is equal to the weight of the displaced fluid, is greater than or equal to the weight of the object. This concept is central in assessing whether an object will float or sink.

Unit Conversion

Unit conversion is a critical step in solving real-world problems involving physical quantities when they are provided in different unit systems. In problems involving density, weight, and volume—especially when given in units like pounds and cubic inches—it is necessary to convert these quantities into consistent units to make accurate comparisons, such as comparing the density of a material to that of water.

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