Why did Archimedes shout ‘Eureka!’ when he saw water overflowing, and how does the principle of buoyancy relate to inertia and density?

This article explains the principle of buoyancy, as discovered by Archimedes, through the lens of two physical properties: inertia and density. Buoyancy is the force exerted by an object equal to the weight of the water it repels, and inertia and density are important concepts for understanding the nature of this force.

 

Eureka! Can you think of who it was that exclaimed these words? Socrates? Achilles? A Tyrannosaurus Rex? Among the many similar names that sound like you’ve heard them before, the first name that comes to mind is Archimedes. This great ancient Greek mathematician and physicist is said to have realized the principle of buoyancy while taking a bath and watching the water overflow. “Eureka!” was his exclamation of joy at that moment. Buoyancy is a force that’s well known to us thanks to Archimedes’ anecdote, but not many people can explain what it is exactly.
The definition of buoyancy is: “The force exerted by an object when it is immersed in water is equal to the force equal to the weight of the water repelled by the volume of the object.” This definition is not easy to grasp what it means after reading it once. To understand this complex definition of buoyancy more clearly, it is necessary to first understand the basic concepts of physics. To make the concept of buoyancy easier to understand, this article will explain two physical properties – inertia and density – and give you a close-up example of how they permeate our everyday lives. Once you understand these two concepts, the definition of buoyancy will come naturally.
First, let’s talk about a principle of Mother Nature called “inertia.” Inertia is the tendency of an object to stay in its original state: an object that is at rest tends to stay at rest, and an object that is in motion tends to stay in motion. For example, it’s hard to push a heavy boulder, because it tends to stay in its original state of rest, so it’s hard to move it with force. Conversely, it’s also hard to stop a moving object: it takes a lot of force to stop a moving bus suddenly, for example. This is also due to inertia.
Inertia is something we can easily observe in our daily lives. For example, when a car stops suddenly, we feel like we’re bouncing forward. This is because our body is trying to maintain its original state of motion, which is moving forward. Inertia is a fundamental property of all objects, so understanding it can help us better understand buoyancy and other physical phenomena.
Second, let’s talk about “density.” Density is the mass per unit volume of a substance; in other words, it’s a measure of how tightly packed the particles that make up a substance are. The substances around us are categorized into gases, liquids, and solids based on their density, and they exist in different forms depending on their properties. For example, air is light because it has low density, and water is relatively heavy because it is denser. Density is strongly related to buoyancy. The reason an object floats is because its density is less than the density of water. Conversely, the reason an object sinks is because its density is greater than the density of water.
To better understand the concept of density, consider the difference between salt water and fresh water. Salt water is denser than fresh water because of the salt dissolved in it, which is why you experience floating more easily in salt water. An object of the same volume will experience greater buoyancy in salt water because the denser water pushes against it with a greater force.
Now, let’s rethink buoyancy based on the concepts of inertia and density. When an object is submerged in water, the amount of buoyancy it experiences is proportional to the amount of water it pushes away. This is known as Archimedes’ principle. For example, if you put a 10-liter ball in a bathtub, it will push out 10 liters of water and take up that much space. The force with which the pushed water tries to regain its place – a force equal to the weight of the pushed water – is buoyancy.
The principle of buoyancy is very simple, but the applications are endless. It’s why boats stay afloat and why balloons float in the air. It’s even what allows submarines to float or sink underwater. As you can see, buoyancy plays a very important role in our daily lives and in science and technology.
Finally, let’s illustrate the relationship between density and buoyancy with a more extreme example: what happens if you put a 10-liter ball in a bathtub full of mercury instead of water? Because mercury is 13 times denser than water, it creates much more buoyancy than water. The ball pushing off the 10 liters of mercury would receive a much greater buoyant force and would float more easily. Buoyancy is highly dependent on the density of a substance, and there are many scientific applications that take advantage of this.
Now that you have a clearer understanding of Archimedes’ principle and the concept of buoyancy, science is an amazing tool that brings together these simple principles to explain our world. Buoyancy isn’t just the force that keeps you afloat, it’s an important example of how the laws of nature work. We hope this explanation has helped you understand how buoyancy works.
There are many scientific principles all around us that don’t have to be mechanically memorized if you put a little thought into them. Hopefully, this article has made you feel more comfortable with the concept of buoyancy.