Too good to be true?

[Diver]

This truly is the dullest thread CUK has ever seen.

Wilmslow, please come back!

DP shut up!

Go and peddle some Doom in another thread

[TimberWolf]

This truly is the dullest thread CUK has ever seen.

Wilmslow, please come back!

[TimberWolf]

Archimedes was asked to determine whether a crown made for King Heron II was made of pure gold.
He determined and demonstrated that the crown was not pure gold, because although the crown and a nugget of the same weight balanced on scales in air, they did not do so in water because the crown has a lower density than the nugget. <------Displacement see

I was thinking more of proving it in a more fundamental way, e.g. with Newtons laws. If the story is true Archimedes found the principle experimentally (i.e. he didn't have a clue ), though he could equally have proved it vigorously too.

Here is a proof:

http://www.youtube.com/watch?v=ZdfLnxTQnqQ

HTH

[Diver]

I was thinking more of proving it in a more fundamental way, e.g. with Newtons laws. If the story is true Archimedes found the principle experimentally (i.e. he didn't have a clue ), though he could equally have proved it vigorously too.

Here is a proof:

http://www.youtube.com/watch?v=ZdfLnxTQnqQ

HTH

I actually sat right the way through that

The bit where he nips off camera saying "Let me just check"

[scooterscot]

Now this is fun science

[fzbucks]

P1 * V1 / T1 = P2 * V2 / T2.

Or something.

Why is this thread turning into something out of Physicsforums?

Cos a couple of geeks are having a pissing contest.

[hyperD]

P1 * V1 / T1 = P2 * V2 / T2.

Or something.

Why is this thread turning into something out of Physicsforums?

Because CUK is one of the last bastions of knowledge where we can discuss this.

Unlike MySpace.Thickos where everyone discusses:-

Phil moves back into the Vic
Ronnie has her first baby scan
Bianca surprises the kids with a holiday

[TimberWolf]

I actually sat right the way through that

The bit where he nips off camera saying "Let me just check"

I fast-forwarded through a lot of it, but found it entertaining nevertheless. The proof is actually quite simple. Here's the basics.

Using:

Pressure = Force / Area (P=F/A), therefore F=P*A
Density = Mass / Volume
Let d stand for water density, so the pressure at depth = d * g * depth

Pressure increases (linearly) with depth (P = d * g *depth), so for an object of height h the pressure on the top surface (P1) will be slightly less than on the bottom surface (P2) and so the pressure difference on the object (P2-P1). Using the first equation, this force equals (P2-P1)*A. Horizontal pressures are equal so are ignored.

Using the third formula this force equals (d * g * h) * A, and since volume is height * area, equals d*g*V. And since Mass = density * volume (2nd formula), equals mg.

Mg equals the weight of water displaced, so that's the buoyant force.

In algebraic terms: F= (P2-P1)A = pghA = pgV = mg

I think you have to do things like this yourself before they make sense but that's the basics.

[TimberWolf]

Note also that if the bottom surface isn't subjected to the water pressure, there will be no net buoyant force. Archimedes principle is not valid. For instance if the bottom surface is glued to a flat surface on the bottom. This situation doesn't appear to get discussed much though.

[TimberWolf]

Note also that if the bottom surface isn't subjected to the water pressure, there will be no net buoyant force. Archimedes principle is not valid. For instance if the bottom surface is glued to a flat surface on the bottom. This situation doesn't appear to get discussed much though.

p.s. I think I've done this when messing about with flat floats in the swimming pool. Put two floats under the water with one flat on top of the other. Just hold down the bottom one, and I think I've seen the top one remain stuck to the bottom one for a while. Archimedes principle not in action. Water works its way between the floats quite quickly though (and how quickly it does so depends on its pressure and therefore the depth), and so after a few seconds Archimedes principle takes over again.