Archimedes Crown Density Calculation

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To determine if Archimedes' crown is made of gold, the density must be calculated using the given mass of 2.42 kg and the volume displacement of 410 cm³, resulting in a density of approximately 5.9 kg/cm³. This density is significantly lower than the density of gold, which is about 19.3 kg/cm³. However, the accuracy of this method is questioned due to the effects of water's surface tension, which can lead to inaccuracies in measuring small objects like a crown. For the purposes of the homework, it is suggested to proceed with the calculations as if the method is valid. The conclusion is that based on the calculated density, the crown is not made of gold.
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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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