Eureka.....did Archimedes get it wrong?

[Imnotdutcheither]

Ok I know that this is just a story, but it is the popular version of the story that is used to teach many children about displacement. I want to know whether the science behind it is right.

"The story: Some 2000 years ago, King Hiero II of Syracuse asked the Greek mathematician Archimedes (287-212 BC), to determine the amount of silver in the royal crown.

Though the crown appeared to be made of gold, the King suspected that the goldsmith might actually have hidden a large percentage of silver in it. Archimedes was at loss: How would he determine the "gravity" of the metal in the king's crown? While bathing one day, the mathematician noticed that as he stepped into his bath, which was too full, there was a certain amount of water displacement onto the floor -- and the answer instantly hit him. He realized that a crown made of pure gold would displace more water than would one made of an alloy. He ran out stark-naked into the street, shouting "Eureka! I have found it!" (perfect tense of the Greek word heuriskein, to find).

Archimedes then went back to his bath, plopped himself down into the water, and thought to himself that he could determine the amount of silver that was in the stately crown: He could put the King's crown into the water, and then he could place equal amounts of gold and silver in the water separately and observe the difference in the displacement of water. "

Now it says that the gold crown would displace more water due to its greater mass (gold is heavier than silver). However, in the popular version of the story (as many teachers teach it) the crown is shown as being immersed in water. In which case both the fake crown and the real crown would displace equal amounts of water as they occupy the same volume (assuming they are identical aside from the materials from which they are made).

The only way to reconcile the info is to float something on the water (say a piece of wood). Then put the crown on top. The wood would have to float still but would sit lower in the water. A heavier crown (gold) would make the wood sit lower in the water. Hence, the real gold crown would displace more water. This could be compared to the amount of water real gold and silver displace (using the same volume of metal as in the crown).

Did I miss something.........?????????

 

[Imnotdutcheither]

Wassup? Too many big words for ya?

So is the popular story right or am I right?



































































ya dont know do ya.........eh?

 

[Deleted member 33117]

No, he could determine how much water a sertain amount (weight/mass) of gold or silver would displace, and since they have different specific gravities, 1 lbs of gold will displace less water than 1 lbs of silver. He could do this to determine how much a given weight of each displaced (thus determining the specific gravity for the material), then weigh the crown, and see how much water it displaced, to determine its specific gravity. Using this he could compair it to gold and silver (no need for a second crown to be made for any measurements), and determine what % of the crown's mass was gold and how much was silver. He would be able to tell if it were say 60% silver and 40% gold instead of 100% gold as it should have been. Understand now?

 

[Imnotdutcheither]

Got it. He effectively worked out the crowns density by getting the volume from displacement and the mass from weighing it. Then he could compare than value to pure gold and silver. From there he could calculate the percentage.

Now that makes perfect sense. Thanks.

Next question: why the fuck do they tell this story to primary school kids (age 5 - 10)? They would not understand this at all. We dont even teach specific gravity in school in this country.

No, he could determine how much water a sertain amount (weight/mass) of gold or silver would displace, and since they have different specific gravities, 1 lbs of gold will displace less water than 1 lbs of silver. He could do this to determine how much a given weight of each displaced (thus determining the specific gravity for the material), then weigh the crown, and see how much water it displaced, to determine its specific gravity. Using this he could compair it to gold and silver (no need for a second crown to be made for any measurements), and determine what % of the crown's mass was gold and how much was silver. He would be able to tell if it were say 60% silver and 40% gold instead of 100% gold as it should have been. Understand now?

 

[Deleted member 33117]

Ok, your second question is more of a philosphical one. My favorite philosophers are Hobbs and Nietzche... so do you really want an answer?

 

[danielson]

but surely a 1m3 block of aluminum displaces the same amount of water (in volume) as a 1m3 block of lead, or say iron from a neutron star (most dense metal i can think of the top of my head)

as far as im aware the eureka can can only measure displacement (giving you a value for volume) and you have to know the density of the material you hold to ascertain the mass

if they used some sort of weighing scale to ascertain the mass of each crown, then did the eureka thing to get the volume they could check the densities and see i it was the correct value (thereby differentiating between the crowns)? correct me if i'm wrong because i havent done physics in a while

 

[Imnotdutcheither]

This was my point. There had to be more to it than simple displacement. The two crowns would displace the same amount of water. You are right in saying that you would need the masses too.........and pure samples for comparison.

but surely a 1m3 block of aluminum displaces the same amount of water (in volume) as a 1m3 block of lead, or say iron from a neutron star (most dense metal i can think of the top of my head)

as far as im aware the eureka can can only measure displacement (giving you a value for volume) and you have to know the density of the material you hold to ascertain the mass

if they used some sort of weighing scale to ascertain the mass of each crown, then did the eureka thing to get the volume they could check the densities and see i it was the correct value (thereby differentiating between the crowns)? correct me if i'm wrong because i havent done physics in a while

 

[Imnotdutcheither]

Ok, your second question is more of a philosphical one. My favorite philosophers are Hobbs and Nietzche... so do you really want an answer?

lol.........

Any recommended reading? I need brain fodder.........

 

[Deleted member 33117]

Anything from Nietzche other than "Why I am so brilliant" would be good reading. If I remember correctly, he wrote that once he started having mental problems from a very advanced case of syphilis, which eventually killed him.

 

[Imnotdutcheither]

Thanks remind to hit you with some green tomorrow.

Just added 'Beyond Good and Evil: Prelude to a Philosophy of the Future' to my heavy reading list from Amazon lol. Most people there recommended it as a good introduction.