Archimedes Crown Density Calculation

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In summary, the question is asking if Archimedes' crown was made of gold based on the information that the level of water rose by 410cm^3 when the crown was placed in it, and the crown had a mass of 2.42kg. The method to determine this is by calculating the density (mass/volume) and comparing it to the density of gold. However, due to the surface tension of water, this method may not be accurate for smaller objects like a crown.
  • #1
DizzyDoo
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[SOLVED] Archimedes Crown Question

Hi,

This is the last question on a homework sheet, based on that interesting Archimedes story.

"Archimedes put a golden coloured crown in some water an the level rose by 410cm^3. He then weighed it and found its mass to be 2.42kg. Was the crown made of gold?"

It's all to do with density, which is Mass/Volume right? Using the m and v given here, I get 0.006kg cm^3. How do I find out if that is gold or not?

Thanks for your time!
 
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  • #2
Look up the density of gold, of course.
 
  • #3
DizzyDoo said:
Hi,
How do I find out if that is gold or not?

You can't :rolleyes:
The problem is that the strong surface tension of water (which e.g. makes it possible to put MORE than 1000 cm^3 of water in a 1000 cm^3 volume bowl) makes this method very inaccurate for an object as small as a crown.

But since this is homework you should ignore this, pretend that the method works and just follow HallsofIvy's advice:wink:
 

FAQ: Archimedes Crown Density Calculation

What is the "Archimedes Crown Question"?

The "Archimedes Crown Question" is a famous mathematical problem posed by the ancient Greek mathematician, Archimedes. It involves determining whether a given crown is made of pure gold or if it contains other metals, using only a balance scale and the principles of buoyancy.

What is the story behind the "Archimedes Crown Question"?

The story goes that King Hiero II of Syracuse suspected a goldsmith of replacing some of the gold in his crown with silver. He asked Archimedes to find a way to prove or disprove his suspicions, leading to the creation of the "Archimedes Crown Question".

How did Archimedes solve the "Archimedes Crown Question"?

Archimedes solved the problem by using the principle of buoyancy, which states that an object will displace its own weight in water. He compared the weight of the crown in air to its weight in water, and determined that if it contained any silver, it would displace more water and therefore weigh less in water.

Why is the "Archimedes Crown Question" significant?

The "Archimedes Crown Question" is significant because it showcases Archimedes' ingenuity and his contributions to the field of mathematics. It also demonstrates the use of scientific principles to solve real-world problems.

Has the "Archimedes Crown Question" been solved in modern times?

Yes, the "Archimedes Crown Question" has been solved in modern times using more advanced techniques, such as X-ray fluorescence spectroscopy. This method allows for a more precise determination of the crown's composition without damaging it.

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