Density is a fundamental concept in physics and engineering. Not only is it intimately tied to the mass of an object, but density is also central to determining whether something will float when placed on the surface of a fluid. While density may not be important in the same way as the fundamental forces, it is still one of the most important things you can know about a substance.
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Density is defined as ρ = m ÷ V, where ρ is density, m is mass and V is volume. Density is important when working out if something will float in water, and it can also be useful for calculating the mass of a specific volume of a substance.
What Is Density?
Density is the mass of a substance per unit volume. In the form of an equation, this means:
ρ = m ÷ V
The Greek letter rho, ρ, is traditionally used to represent density; m is the mass; and V is the volume. The units of density are kg per cubic meter, or something equivalent to this in other units such as pounds per cubic foot.
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Water is a good example for density because at everyday temperature, its density is close to 1,000 kg/cubic meter or 1 g/cubic centimeter. Stainless steel, on the other hand, has a density of 8,000 kg/cubic meter. This fits with everyday experience, because a block of stainless steel is heavier than an equal-sized block of water.
You can change the density of something by compressing it in volume (i.e., reducing the volume) or increasing the amount of mass within the same volume.
Density in General
Although density usually refers to mass per unit volume, in some situations the term can be used differently. For example, the “number density” of objects is the number of whatever it is you’re counting within a unit of volume. The charge density is the amount of electric charge per unit of volume. Population density is also used as a measure of the number of people per unit area or volume. In general, density means the amount of something within a certain amount of space.
The Importance of Density: Buoyancy
Density has obvious importance when it comes to the buoyancy of objects. Broadly, if something is denser than water (having a density over 1,000 kg/cubic meter) it will sink, but if something has a lower density than water, it will float.
More technically, something will start to float when the weight of the water it displaces (due to the surface area making contact with the water and how far it pushes the water down) matches the weight of the object, but if this never happens it will sink. If the object is denser than water (for example, a block of steel), the weight of the water it displaces can never match the weight of the object, so it will continue to sink.
Aluminum is a good example. It is denser than water, but a piece of aluminum foil stretched out will float on water because of the large surface area making contact with the water. However, if you roll the same amount of foil up into a ball, the surface area in contact with the water becomes much smaller and the mass is concentrated above it, so the greater density of aluminum wins out and the foil will sink. This is why boats made of denser materials than water will float, even though a single block of the material will sink: The whole structure has a lower density than the block because it contains a lot of air or less dense material too.
The difference in density is also why oil floats on the surface of water. The density of oils range from around 0.91 to 0.93 g per cubic centimeter, just less than the density of water. You can perform many experiments on this simple basis, showing that more dense liquids will sink to the bottom of a container of water while less dense liquids will float.
The Importance of Density: Calculating Mass
Since density and mass are so closely related, you can calculate the mass of a certain amount of a substance easily provided you know its density and the volume of the substance. This can be useful in engineering and other applications. Use the simple formula:
m = ρ × V
To work out the mass of the substance. For example, using the density of steel quoted earlier, 0.5 cubic meters of steel has a mass of:
m = ρ × V = 8,000 kg/cubic meter × 0.5 cubic meters = 4,000 kg
This is useful in many different situations. For example, if you know how much space there is in a van and what the maximum safe load the van can carry is, you can work out whether filling it with a specific material will be safe. You could also use the ρ = m ÷ V version of the equation to work out what the densest material you could safely transport is.