Archimedes Crown Density Calculation

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SUMMARY

The discussion revolves around calculating the density of a crown to determine if it is made of gold. The crown displaced 410 cm³ of water and has a mass of 2.42 kg, leading to a calculated density of 0.006 kg/cm³. However, the method is deemed inaccurate due to water's surface tension effects, which complicate density measurements for small objects. The consensus is to follow the advice of user HallsofIvy and assume the method works for the sake of the homework assignment.

PREREQUISITES
  • Understanding of density calculation (Density = Mass/Volume)
  • Familiarity with Archimedes' principle
  • Knowledge of the density of gold (approximately 19.32 g/cm³)
  • Basic principles of fluid mechanics, particularly surface tension
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  • Research the effects of surface tension on fluid displacement measurements
  • Learn about Archimedes' principle in greater detail
  • Investigate methods for accurately measuring the density of irregular objects
  • Explore the properties and applications of gold in various fields
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Students studying physics or chemistry, educators teaching density concepts, and anyone interested in the historical applications of Archimedes' principles.

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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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Look up the density of gold, of course.
 
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:
 

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