Why do some objects float while others sink? One of the factors that determines this is the density of the object. The density of an object is related to another important factor called specific gravity, which will be the main focus of this lesson.
What Is Specific Gravity?
When we go out in the summer to enjoy the pools and the rivers, we always have to make sure that all of our equipment and safety measures are working and in place. When we go to the river and get on our boats, we make sure the boat has no leaks and we have our safety vests on. For young children who are still learning how to swim, we make sure they have their floaters on or we swim with them in a swim ring to make sure they do not sink. Why is it that boats and swim rings both float? There are many factors that determine if an object will sink or float in water, and one of these factors is what we call the specific gravity.
The specific gravity is the ratio between the density of an object, and a reference substance. The specific gravity can tell us, based on its value, if the object will sink or float in our reference substance. Usually our reference substance is water which always has a density of 1 gram per milliliter or 1 gram per cubic centimeter.
What is Density?
So, what is density, anyway? An object’s density is a measure of how compact or heavy it is, in a given volume. We measure density in mass per unit volume which is written using measures like grams per milliliter (g/mL), grams per cubic centimeter (g/cm^3), or kilograms per liter (kg/L).
Here are two objects with different densities. On the left is an object highly packed with particles. That means it has a high density. On the right is an object with a low density. You can see that the particles are not packed tightly but that there are fewer particles occupying the same volume. To find the density of an object, we divide its mass by its volume.
For example, take an object with a volume of four liters and a mass of one kilogram. We plug these numbers into the density formula and discover that its density is 0.25 kg/L.
The Formula for Specific Gravity
The formula for specific gravity, given that the reference substance is water, is the density of the object divided by the density of the water. Here, we use the Greek symbol Rho to indicate density.
Specific Gravity Formula
The specific gravity has no unit because the units of the numerator and the denominator are the same, so they just cancel each other out. Let’s look at an example. Here, the density of the object is 19 g/mL and the density of water is 1 g/mL. We cancel the unit g/mL because this unit is present in both the numerator and the denominator:
Specific Gravity: No Unit
High and Low Density
Formula for Density
The density is directly related to the mass of the object (unit: usually in grams but can be measured in kilograms or pounds), so the specific gravity can also be determined by dividing the mass of the object by the mass of the water.
Specific Gravity Formula
The mass itself is directly related to the weight of an object, measured in units called Newtons. So, the specific gravity can also be solved by dividing the weights of the object and the water.
Specific Gravity Formula
Note that in all of these the units are the same so the result will have no units as they’ll cancel each other out.
When we throw pennies in water fountains to make a wish, the pennies sink to the bottom. That’s because the pennies are denser than water. If we plug the pennies into the specific gravity formula as our object, we’d find that the specific gravity would be greater than one. When the specific gravity is greater than one, the object will sink, and when the specific gravity is less than one, then the object will float. If the specific gravity is equal to one’, this means that the object will neither sink nor float — it will hover in the liquid.
Pennies will sink in water because their specific gravity is greater than 1
Specific gravity is an important tool in the jewelry business. Let’s imagine that Julie the Jeweler wants to make a piece with a gold ring. She buys the gold online and wants to know for sure that it’s real, not a different metal that looks like gold. If the gold is genuine, then it should be denser than water — the density of gold is 19 g/mL and the density of water is one g/mL. The specific gravity will be greater than one, so the gold should sink in water and displace a specific volume of water based on the weight of the gold.
Julie can place the gold in an amount water, observe whether it sinks and measure the amount of water displaced. This will tell her if it’s real gold.
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