# archimedes law

## 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 in the opening image 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 1.1. 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 ships hull in the Figure 1.1. 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.

## 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 cant 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 bodys volume. Depending on your size, this volume might be about 0.07 m3 .

## 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).

## instructional diagrams

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## questions

archimedes was a greek mathematician who lived more than 2000 years ago.

``````-->  a. true

b. false
``````

archimedes determined that the volume of water displaced by an object placed in the water is equal to the objects

``````a) weight.

-->  b) volume.

c) mass.

d) density.
``````

a bigger object displaces less water than a smaller object.

``````a. true

-->  b. false
``````

according to archimedes law, the buoyant force acting on an object equals the

``````a) weight of the object.

-->  b) weight of the displaced fluid.

c) volume of the object.

d) volume of the displaced fluid.
``````

archimedes law explains why some very heavy objects can float on water.

``````-->  a. true

b. false
``````

## diagram questions

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