What Is Buoyancy? - Explanation & Equation

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  • 0:01 What Is Buoyancy?
  • 0:52 Archimedes' Principle
  • 2:34 Example Problem
  • 4:24 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain what buoyancy is and use Archimedes' Principle to calculate the buoyant force on a submerged object. A short quiz will follow.

What is Buoyancy?

Buoyancy is the ability or tendency of an object to float in a fluid, which can be a liquid or a gas. This happens because fluid pressure increases with depth. Fluid pressure is the amount the molecules in a fluid hit an object. If you go underwater, diving down deeper and deeper, the molecules are closer and closer together. Because of this, they hit you more. So the pressure gets bigger the deeper you go. If you put an object underwater, there will be more pressure on the bottom of the object than on the top, because the bottom is deeper underwater. And this creates an upwards force.

The upwards force that an underwater object feels is called the buoyant force. But how can we predict how strong that force will be? Force is measured in newtons, so how can we figure out how many newtons of buoyancy an object will feel?

Archimedes' Principle

Archimedes' Principle is how we put a number to the buoyant force. It says that the buoyant force on a submerged object is equal to the weight of the liquid displaced by that object. What does this mean?

Well, whenever you put an object underwater, that object is displacing, or replacing, the water that would be there if you hadn't put it underwater. A bigger object will displace more water than a smaller object. If we can take the water it is displacing and figure out the force of gravity that acts on it, we will know how strong the upwards buoyant force on the object will be.

The force of gravity is given by the equation F = mg, where m is the mass of the object in kilograms, and g is the acceleration due to gravity, which is roughly 9.8 meters per second on the surface of the earth. So we just need to know how much the displaced water would weigh in kilograms, and we can work out the buoyant force.

To solve problems using Archimedes' Principle, we also need to know about density. Density is a measure of how compact the mass of a substance or object is. The density of an object or substance can be calculated from this equation: density in kilograms per meter cubed is equal to mass in kilograms, divided by volume in meters cubed. We discuss density in more detail in another lesson.

The density of water is 1000 kilograms per meter cubed. Normally in physics memorizing numbers isn't really important, but this one is a very useful number because we usually don't have the mass of the displaced water to plug into F = mg. More often we know the volume of the displaced water. But with volume and density, we can use the density equation to find the mass of the displaced water.

Example Problem

Let's go through an example of how to use Archimedes' Principle. Let's say you have a ball made of some unknown material. It floats with exactly one half of the ball in the water and one half of the ball out of the water. If the ball has a volume of 0.1 meters cubed, and the density of water is 1000 kilograms per meter cubed, what is the buoyant force on the ball?

Well, first of all we should write down what we know. The volume of the ball, Vball, is 0.1 meters cubed, and the density of water, rho-water, is 1000. And we're trying to find Fb, the buoyant force on the ball.

From Archimedes' Principle, we know that Fb will be equal to the force of gravity on the water displaced. The force of gravity on the water displaced is equal to mg, where m is the mass of the water displaced and g is 9.8. But we don't know the mass.

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