Archimedes “displacement” eureka.

[Vexer]

Archimedes “displacement” eureka, I don’t get it.

 

The story I know is this:

 

Archimedes was asked by his king to find out if a ‘gold’ crown he had been gifted was really solid gold. Archimedes’ answer was ‘displacement’.

 

How does the amount of water the crown displaces, indicate density?

 

Couldn’t he just weigh it?

 

 

I’m prepared to be embarrassed. But I don’t get it.

[thedarkshade]

I don't remember the story good, but I think that when Archimedes released the crown into the water, the crown didn't drown equal at all sides, indicating the it was not made of completely the same material.

[timo]

Dunno the story. But since density is mass divided by volume, knowing either the mass (by weighting) or the volume (by measuring the amount of water it displaces) alone will not result in knowing the density. You need both values to determine the density. A guess of mine would be that the weighting is not mentioned because it's kind of simple while measuring the volume via displacement in water is a pretty smart and not-so-straightforward idea.

[swansont]

This is the story where Archimedes realizes the displacement trick when he gets into the bath and sees the water rise/overflow. He then runs around, naked, shouting, "Eureka!"

 

Weighing it was the easy part, but it was finding the volume that was difficult, because of the irregular shape.

[Aeternus]

To clarify, wasn't the issue that the people making the crown could have added some silver into the crown so that it would weigh the same as a gold crown but they could pocket the surplus gold.

 

Therefore Archimedes realised that gold and silver are different densities and so if they weighed the same, the volume would be different but doing this by eyesight, with such a difference, would be rather hard and so the bath trick comes in where he can put a gold bar into some water, and then put the crown in (seperately) and if the water doesn't rise by the same amount, then it's off with the jewellers/goldsmiths head

 

http://en.wikipedia.org/wiki/Archimedes

[Country Boy]

Archimedes “displacement” eureka, I don’t get it.

 

The story I know is this:

 

Archimedes was asked by his king to find out if a ‘gold’ crown he had been gifted was really solid gold. Archimedes’ answer was ‘displacement’.

 

How does the amount of water the crown displaces, indicate density?

 

Couldn’t he just weigh it?

 

 

I’m prepared to be embarrassed. But I don’t get it.

To reiterate, yes, he did weigh the crown. But you can make two crowns weighing exactly the same thing from different percentages of gold and silver just by having the one with more silver slightly larger.

 

Archimedes did not use "displacement" to measure weight, he used it to measure the volume of the crown so that he could calculate density = weight/volume.

[Vexer]

Thanks all, but:

 

Wouldn't a plastic crown displace the same as a gold one? My point, really.

 

I still can't see what displacement has to do with it.

[insane_alien]

a plastic crown of the same mass would not displace the same as a gold crown. that is the point.

 

the crowns are necessarily of the same weight(mass) as this measurement is trivial and would be carried out to make sure the maker was not cheating the king out of his gold by using base metals.

 

for this to happen, the crown will be slightly larger. if it was made of plastic, to acheive the same effect it would be noticably larger. probably hulahoop size

[Vexer]

…a plastic crown of the same mass would not displace the same as a gold crown.

 

If fully submerged, it would, in fact, was my point. Displacement is a measure of volume - not anything else. A plastic crown would displace as much as a gold one.

 

I don’t see how volume has anything to do with it.

 

 

I’ve read what all you-all have said, but I still don’t get it.

 

Again, why couldn’t he just weigh it?

[iNow]

…a plastic crown of the same mass would not displace the same as a gold crown.

 

If fully submerged, it would, in fact, was my point. Displacement is a measure of volume - not anything else. A plastic crown would displace as much as a gold one.

But how would it become fully submerged if it were less dense than the water and floated on top?

[Vexer]

Again, why couldn’t he just weigh it?

[timo]

How would you determine the density from the weight?

[Vexer]

"Dense" *means* heavy.

[SkepticLance]

Gold is very dense. Gold with silver added is less dense. If you can measure the density, you can tell if there is anything in it apart from gold.

 

Archimedes had to weigh the crown (easy, even back in those days) and also measure its volume, since density is weight divided by volume. The problem was that he had no way to measure the volume of an irregular object like a crown. His 'eureka' moment came when he realised that even an irregular object would displace exactly its own volume in water.

 

To measure volume, he filled a jug to the point of overflowing with water. He then lowered the crown very slowly and gently, on the end of a length of cord, into the water. The water overflowed. He collected the water that overflowed and poured it into a measuring vessel to measure its volume - something like a modern day measuring cylinder.

 

He knew the displaced water would have the same volume as the crown. Thus, he had measured the volume of the crown.

Density = wt/vol. Eureka! He had the density.

 

He proved the crown was not pure gold, and the villains who were trying to cheat the king quite literally lost their heads.

[iNow]

"Dense" *means* heavy.

 

Care to elaborate? In short, I disagree.

[Vexer]

Thus, he had measured the volume of the crown.

 

Wouldn't a styrofoam crown have given the same volume?

 

 

Thanks for the excellent description of what I'm talking about. Yes, that's it.

 

 

Seriously, I don't see how weighing it is any different.

 

So you don't understand it either, iNow.

 

I feel better. If you did, you would have said.

 

(I'm not being *intentionally" dumb, BTW)

[timo]

How would you determine the density from the weight?

"Dense" *means* heavy.

Perhaps you can see that your reply was not an answer to my question. If not, then let's talk numbers: What's the density of an object with a mass of 300 g? Perhaps you might consider the idea that I asked the question for a reason (albeit I start to have doubts in the reason considering it has been said that density is mass divided by volume in almost every post in this thread, by now).

[swansont]

"Dense" *means* heavy.

 

Density is mass/volume

 

You need both mass and volume in order to determine the density. Archimedes discovered a way of determining the volume. Weighing was the easy part.

[Vexer]

So, he already had weighed the crown, but (as has been said) that in itself means nothing much. Then he measured the volume via the water thing.

 

A two-step operation, you're saying. (Which, if I may say, the original story does not at all make clear, or even mention, in it's popular version).

 

So the displacement of a stryofoam crown must be compared with it's separately determined weight.

 

hm

 

 

Athiest

 

Perhaps you can see that your reply was not an answer to my question. If not, then let's talk numbers: What's the density of an object with a mass of 300 g?

 

Ok, Athiest. It's density could be anything. I was thinking that in the context of 'sinking' (displacing) water, density, is weight.

 

 

 

 

 

I wonder why this was/is so hard for me to ‘get’.

[Country Boy]

More specifically "density" is "weight divided by volume". In order to determine the density- to see if it matched that of gold, Archimedes had to determin BOTH.

[Vexer]

A styrofoam crown would have fooled Archimides.

[insane_alien]

no, it wouldn't. it would have made discovering that the king was being cheated spectacularly easy as not only would it float unlike a gold crown, it would easily crumble in your hands.

[Vexer]

So a silver crown would have floated.... a bit more.

[insane_alien]

no a silver crown would have sank. silver is denser than water, polystyrene foam is not.

[SkepticLance]

The key was density. Archimedes weighed the crown, and then used immersion in water and displacement to find its volume. Then he divided weight by volume to get the density.

 

A styrofoam crown would have been of very low density - hence not gold. In Archimedes time styrofoam did not exist, but it is vaguely possible someone might have carved a crown from wood or stone and gilded it. This too would have been detected by Archimedes technique.

 

Archimedes method was precise enough to detect a crown that was mostly gold, but also containing silver - hence less dense.