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# Archimedes' Law

## The buoyant force acting on an object equals the weight of the fluid displaced by the object.

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Archimedes' Law

Do you see the man sitting on top of this tanker truck? He gives you a sense of how big the truck is. What’s behind the truck? Is it a huge apartment complex? It’s just as massive as a very large building, but it’s not even resting on land. It’s a giant cruise ship, and it’s floating on water. The ship weighs about 100,000 metric tons. How can such a tremendous weight float on water? Why doesn’t it sink to the bottom of the ocean instead? Archimedes’ law explains why.

### Archimedes Takes a Bath

Did you ever notice when you get into a bathtub of water that the level of the water rises? More than 2000 years ago, a Greek mathematician named Archimedes noticed the same thing. He observed that both a body and the water in a tub can’t occupy the same space at the same time. As a result, some of the water is displaced, or moved out of the way. How much water is displaced? Archimedes determined that the volume of displaced water equals the volume of the submerged object. So more water is displaced by a bigger body than a smaller one.

Q : If you jump into swimming pool, how much water does your body displace?

A : The water displaced by your body is equal to your body’s volume. Depending on your size, this volume might be about 0.07 m 3 .

### Displacement and Buoyant Force

Objects such as ships may float in a fluid like water because of buoyant force. This is an upward force that a fluid exerts on any object that is placed in it. Archimedes discovered that the buoyant force acting on an object equals the weight of the fluid displaced by the object. This is known as Archimedes’ law (or Archimedes’ principle). For an entertaining video presentation of Archimedes’ law, go to this URL:

### Floating Objects and Archimedes’ Law

Archimedes’ law explains why some objects float in fluids even though they are very heavy. It all depends on how much fluid they displace. The cruise ship pictured above is extremely heavy, yet it stays afloat. If a steel ball with the same weight as the ship were placed in water, it would sink to the bottom. This is modeled in the Figure below . The reason the ball sinks is that its shape is very compact, so it displaces relatively little water. The volume of water displaced by the steel ball weighs less than the ball itself, so the buoyant force is not as great as the force of gravity pulling down on the ball. Thus, the ball sinks.

Now look at the ship’s hull in the Figure above . Its shape causes the ship to displace much more water than the ball. In fact, the weight of the displaced water is greater than the weight of the ship. As a result, the buoyant force is greater than the force of gravity acting on the ship, so the ship floats.

Q : Why might you be more likely to float in water if you stretch out your body rather than curl up into a ball?

A : You would displace more water by stretching out your body, so there would be more buoyant force acting on it. Therefore, you would be more likely to float in this position.

### Summary

• Archimedes determined that an object displaces the same volume of fluid as its own volume.
• According to Archimedes’ law, the buoyant force acting on an object equals the weight of the fluid that the object displaces.
• The shape of an object may affect how much fluid it displaces and therefore the buoyant force acting on it. This explains why one object may sink while another object with the same weight but a different shape may float.

### Vocabulary

• Archimedes’ law : Law stating that the buoyant force acting on an object equals the weight of the fluid displaced by the object.

### Practice

Practice applying Archimedes’ law by doing the brainteaser at this URL:

### Review

1. What is Archimedes’ law?
2. Fill in the missing word in the following sentence: An object will float in a fluid when the weight of the fluid displaced by the object is _______ than the weight of the object.
3. Demonstrate how the shape of an object affects its ability to float using a container of water and two pieces of aluminum foil that are the same size and therefore the same weight. (Hint: Form the two pieces of foil into different shapes.)

### Vocabulary Language: English

Archimedes’ law

Archimedes’ law

Law stating that the buoyant force acting on an object equals the weight of the fluid displaced by the object.