Whether an object sinks or floats in a fluid is determined by its density, which is the relationship between its mass and the volume it occupies. To answer the question of whether an object with a density of \(3.4 \text{ g/cm}^3\) will sink or float, we must first understand how density is measured and then compare it to the medium in which the object is placed. This simple comparison provides the definitive answer to the object’s behavior in a liquid.
Understanding Density
Density is a measure of how much matter is compressed into a defined space. It represents the concentration of mass within a volume and is often symbolized by the Greek letter rho (\(\rho\)). The formula for calculating density is mass divided by volume. The units used for the object in question, \(\text{g/cm}^3\), stand for grams per cubic centimeter, meaning a specific number of grams of material are contained within that space. Substances that are heavy for their size have a high density, while those that are light for their size have a low density.
The Critical Comparison Point
Determining if an object will sink or float is always a relative comparison between the object’s density and the surrounding fluid’s density. The rule is straightforward: an object sinks if its density is greater than the fluid’s, and it floats if its density is less than the fluid’s.
The most common medium for this comparison is water, which serves as a universal benchmark. Pure liquid water reaches its maximum density of approximately \(1.000 \text{ g/cm}^3\) at a temperature of \(4^\circ \text{C}\). For most practical purposes, the density of fresh water is rounded to \(1.0 \text{ g/cm}^3\).
When an object is submerged, it displaces a volume of fluid. The buoyant force pushing up on the object is equal to the weight of the fluid that was displaced. If the object’s weight is greater than the weight of the displaced water, it sinks because the net force is downward.
Applying the Rule to \(3.4 \text{ g/cm}^3\)
The object has a density of \(3.4 \text{ g/cm}^3\), and when placed in water, this value must be compared to water’s density of approximately \(1.0 \text{ g/cm}^3\). Since \(3.4\) is significantly larger than \(1.0\), the object will sink.
This outcome occurs because the object packs much more mass into the same volume than the water does. For every cubic centimeter of the object, there is \(3.4\) grams of mass, while an equal volume of water only contains \(1.0\) gram of mass.
The weight of the object is therefore much greater than the upward buoyant force generated by the displaced water. This density ratio means the object is over three times denser than the water, causing it to overcome buoyancy and descend. Common materials that have a density in this range and would also sink in water include aluminum (\(2.7 \text{ g/cm}^3\)) and iron (\(7.87 \text{ g/cm}^3\)).
When the Surrounding Medium Changes
The sinking outcome for the \(3.4 \text{ g/cm}^3\) object is only true when it is placed in a fluid with a density lower than its own, such as water. If the surrounding medium is changed, the result can be different, as the buoyant force changes relative to the new fluid’s density.
For instance, if the object were placed in a liquid like isopropyl alcohol, which has a lower density of about \(0.785 \text{ g/cm}^3\), the object would still sink, as \(3.4\) is greater than \(0.785\).
Conversely, the object could be made to float if it were placed in a liquid that is denser than \(3.4 \text{ g/cm}^3\). An object with a density of \(3.4 \text{ g/cm}^3\) would float on a liquid metal like mercury, which has a very high density of approximately \(13.6 \text{ g/cm}^3\). The liquid’s density must simply be greater than the object’s density for the floating action to occur.