# Archimedes' Law

## The force exerted by a fluid on a floating or submerged object is equal to the weight of the water displaced.

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The Weight of Gold

### The Weight of Gold

Credit: Domenico Feitt
Source: http://commons.wikimedia.org/wiki/File:Domenico-Fetti_Archimedes_1620.jpg

As a philosopher, mathematician, inventor, and engineer, Archimedes contributed to the field of physics with his formulations on hydrostatics and statics. He is perhaps best known for defining what is now known as the buoyant force.

#### Amazing But True

• The buoyant force is best described as an upward force on an object that is partially or fully submerged in a liquid. This upward force is caused by the difference between the pressures on the top and bottom of the object. By measuring the weight of an object in air and water, you can accurately determine its density, as Archimedes did for the crown of King Hiero II.
• According to one legend, King Hiero II tasked Archimedes with determining whether his crown was made of solid gold or whether the goldsmith had swindled the king by adding some silver to the mix. Because finding the crown's volume without transforming its original shape was not possible at the time, Hiero's assignment called for novel techniques. Archimedes used what is now known as the Archimedes' principle, which states that a submerged object will experience a buoyant force equal to the weight of displaced fluid, to confirm the crown's purity. By submerging a scale that balanced the crown and solid gold block of equal weight, a difference between densities would tip the scale, revealing any impurity. However, If the crown was made of pure gold, the buoyant forces on both the crown and block would be equal, keeping the scale in balance.

#### Can You Apply It?

Using the information provided above, answer the following questions.

1. Would the effects seen by Archimedes suggest that water is compressible or incompressible?
2. There are two blocks that are submerged in a body of water. The first block is sitting at the bottom of the body of water while the other block is just under the surface. Which block experiences a greater buoyant force?
3. If the mass of an object is 10 kg, what volume would it need to have a density of 1 kg / m3?

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