Archimedes's principle (Crown)

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In summary, Archimedes used a method of measuring the apparent mass of a crown when submerged in water to determine its volume. He then used the difference between the actual mass and the apparent mass to calculate the buoyant force, which revealed the volume of the crown. This method was later refined to become known as Archimedes' principle. Additionally, Archimedes' famous exclamation of "Eureka!" came from his realization that the volume of water displaced by his body was equal to the volume of his submerged body, providing a solution to the problem of measuring irregular objects.
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hanson
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Hi all, I am so confused by the famous Archimedes's story of telling if the crown is made of pure gold.

As far as I understand from information posted in the internet, such as http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html

Archimedes first determines the volume of the crown by measuring the apparent mass when the crown is immersed into water by a mass spring for example.
Then the difference between the actual mass and the apparent mass will be the buoyant force, which is given by the volume of the crown * density of water.
From this, we know the volume of the crown.

And we can divide the actual mas of the crown by the density of water to get the density of the crown.

But can't one just measure the volume of the water displaced when the crown is immersed into the water, and that should be equal to the volume of the crown?
Can we get the volume of the crown that way?
 
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Yeah, I can see your confusion.

Wikipedia's article on the word Eureka: http://en.wikipedia.org/wiki/Eureka states
'he reportedly proclaimed "Eureka!" when he stepped into a bath and noticed that the water level rose—he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. This meant that the volume of irregular objects could be measured with precision, a previously intractable problem.'​

And that is how he originally determined the density of the crown.


I think that later on he continued researching it and came up with the whole buoyancy force is the difference between the actual weight and apparent weight, which is the weight of the displaced water deal. And that is known as the Archimedes' principle (described in http://en.wikipedia.org/wiki/Archimedes'_principle)


Hope that clarifies things a bit.
 

1. What is Archimedes's principle?

Archimedes's principle states that when an object is fully or partially submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces.

2. How does Archimedes's principle apply to the crown?

Archimedes's principle can be applied to the crown to determine its purity. When submerged in water, the crown's weight in air will be equal to the weight of the crown plus the weight of the displaced water. If the crown is made of pure gold, it will displace more water and therefore weigh less in water compared to a fake crown made of a less dense material like brass.

3. How did Archimedes use this principle to solve the crown mystery?

According to legend, Archimedes used this principle to solve the crown mystery by comparing the weight of the crown in air and in water. He realized that the crown was less dense than pure gold, indicating that it was made of a mixture of materials rather than solid gold.

4. Can Archimedes's principle be applied to other objects besides the crown?

Yes, Archimedes's principle can be applied to any object that is submerged in a fluid, whether it is a liquid or a gas. For example, this principle is used in designing ships and submarines, as well as in determining the density of various materials.

5. Is Archimedes's principle always accurate?

In an ideal scenario, where the fluid is incompressible and the object is fully submerged, Archimedes's principle is always accurate. However, in real-world situations, there may be other factors that can affect the accuracy of the principle, such as the shape of the object and the presence of air pockets.

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