# Archimedes - volume, density, weight, what?

#### pfaction

##### Full Member
10+ Year Member
TBR: Archimedes realized he could determine the volume of the crown by placing it in a comtainer of water and then measuring the amount of water compared to an equal volume of pure gold and pure silver.

Milski and I had a discussion: If I fill a 10L bucket with water and put a 1m^3 bowling ball, 1m^3 iron ball, 1m^3 steel ball, the volume displaced will be 1m^3.

So what the **** is going on here? How can you tell the difference volume displaced of a golden, silver crown if the volumes are the same?

#### MrNeuro

##### Full Member
7+ Year Member
TBR: Archimedes realized he could determine the volume of the crown by placing it in a comtainer of water and then measuring the amount of water compared to an equal volume of pure gold and pure silver.

Milski and I had a discussion: If I fill a 10L bucket with water and put a 1m^3 bowling ball, 1m^3 iron ball, 1m^3 steel ball, the volume displaced will be 1m^3.

So what the **** is going on here? How can you tell the difference volume displaced of a golden, silver crown if the volumes are the same?

archimedes used weight not just volume

the formula used in determining that is
W/B = p obj / p medium

W= pobj Vobj g
B= pfluid Vobj g

so what he did was measured the volume of the crown first multiplied it by the density of the fluid to get B
then divided B by the weight of the crown and by doing so the ratio he got for the crown if it was pure gold would have to be the same as the fraction seen w/ any block of gold equivolumetric or not

because when you divide the Weight by the Buoyant force you're essentially getting a specific gravity and comparing that to the specific gravity of gold

#### pfaction

##### Full Member
10+ Year Member
Okay, because another site said this: He took an exact weight of the crown, and equal weights of pure gold and silver. He noted one of them was larger in volume. Thereafter, he submerged both and saw the water fell out a certain amount. On submerging the crown he found blah blah.

I was like, that makes more sense. The exact weight will correspond with density to get the same volume.

TBH I have difficulty understand what you're saying: it's 1:20 AM, so.

#### milski

##### 1K member
5+ Year Member
Ah, so this is about the fake crown. Disregard the long PM that I sent you.

This is only about density/volume, it really has nothing to do with buoyancy (except that it's nice that the crows sink on their own). He just used submerging them as a fancy way to measure the volume of the crown. It would be rather tricky to do otherwise with an object with such a complicated shape.

About the Ads

#### pfaction

##### Full Member
10+ Year Member
"Disregard it?" Gonna read it at tomorrow and not 1:30 AM. So but was I right overall on the volume thing of objects heavier ? And my second post?

#### milski

##### 1K member
5+ Year Member
"Disregard it?" Gonna read it at tomorrow and not 1:30 AM. So but was I right overall on the volume thing of objects heavier ? And my second post?

Well, it's not wrong, it just goes into details about buoyant force and floating of objects. That's not relevant here.

Yes, second post seems good. Basically, the crowns weighed the same (good fake?) but since one was less dense, it had bigger volume. He put them in water, displacing volume equal to the volume of the crown, to determine which one was which.

#### pfaction

##### Full Member
10+ Year Member
Good. Thanks for clearing that up, because I vividly remember the other topic and had a mental breakdown when TBR said he did it by pure volume of the crown. It is WEIGHT they did it by, not volume, because volume would result in the same thing when pobj>pliq.

#### milski

##### 1K member
5+ Year Member
Well, if the V1=V2, use weights to determine which one is lighter and fake.
If M1=M2, submerge in water to see which one has larger V and is fake.

(Assuming the fake material has lower density).

#### Dasypus

##### Full Member
Well, if the V1=V2, use weights to determine which one is lighter and fake.
If M1=M2, submerge in water to see which one has larger V and is fake.

(Assuming the fake material has lower density).

Gold is denser than all but four or five naturally occurring elements, and is much denser than silver, copper, zinc, and lead (lead's the densest of those, and gold's nearly twice as dense), so this seems like a good assumption

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