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Archimedes' Principle: Definition, Formula & Examples

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  • 0:00 What is Archimedes' Principle?
  • 0:25 A Closer Look
  • 1:05 Example - The Battleship
  • 1:45 Example - Ice Cube
  • 2:20 Calculating the Displacement
  • 4:10 Lesson Summary
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Lesson Transcript
Instructor: Jeremiah Lewman
Archimedes' principle deals with the forces applied to objects by the fluids around that object. This applied force reduces the net weight of any object in a fluid, whether it be a liquid or a gas.

What is Archimedes' Principle?

Have you ever heard someone say, 'Whatever floats your boat'? Well, the answer should always be 'buoyancy.'

Buoyant force is the force applied upward on an object by any fluid. Archimedes' principle states that the buoyant force applied to an object is equal to the weight of the fluid the object displaces.

A Closer Look

Let's take a closer look at this definition. First, we need to understand 'displacement.'

As the story goes, Archimedes poured himself a warm bath one day, and when he got in, he realized the level of the water went up. He then determined that the more of his body he put in the bath, the higher the water level went.

This means the volume of his body that he put in the water had to move or displace the water so he could fit in the bath. Therefore, displacement in this context is when an object moves a fluid so it can occupy the volume the fluid originally occupied.

Example - The Battleship

Let's use a battleship as an example. A battleship is made of steel. Right about now, you may be saying, 'But steel doesn't float!' So how is it a battleship can float?

Look at the image of the battleship. Now imagine drawing a line where the water comes up on the hull of the ship. Then, fill the ship's hull with water up to that line. How much do you think the water would weigh? If you said 'a lot,' you're right. It would actually weigh as much as the entire ship!

Floating Battleship
archimedesbattleship

The weight of the water to fill up the hull of the ship weighs the same as the ship, so the water applies a buoyant force up on the ship with this much force. Therefore, the ship made of steel floats!

Example - Ice Cube

Let's look at another example. If you put an ice cube in a glass of water, the cube floats because ice is less dense than water. So, the ice underwater displaces that volume of water.

To make things easy, we will say that the ice cube is a perfect cube, where each side is 1 cm long. Let's also say the ice cube is floating so that 0.8 cm is under water. How much does the ice cube weigh? To determine that, let's go over some calculations.

Calculating the Displacement

Remember that Archimedes' principle states that the weight of the fluid displaced is the buoyant force. Therefore, we need to know how much water is displaced.

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