Archimedes Eureka

[michel123456]

During my strange peregrinations on the web, sourced by a thread on this forum I hit on the Wikipedia article about Archimedes Eureka.

 

At the end of article 2, we can read the following

 

For the problem posed to Archimedes, though, there is a simple method which requires no precision equipment: balance the crown against pure gold in air, and then submerge the scale with crown and gold in water to see if they still balance.[4]

 

My question is: is that correct?

 

In the source link [4] (from Galileo’s treatise) , we can read the full concept and in-between the following:

 

Let us suspend a [piece of] metal on [one arm of] a scale of great precision, and on the other arm a counterpoise weighing as much as the piece of metal in air. If we now immerse the metal in water and leave the counterpoise in air,(...)

 

Which looks more correct to me.

 

Your opinion?

[swansont]

Immersing one arm in water will unbalance it, since there will be a buoyancy force. Which is explained in the part you omitted

 

If we now immerse the metal in water and leave the counterpoise in air, we must bring the said counterpoise closer to the point of suspension [of the balance beam] in order to balance the metal.

 

The source is explaining a recipe for finding out how much silver is in the crown; that assumes the scales are unbalanced when both objects are immersed in water.

[michel123456]

Ok, today with a clearer mind:

 

Taking a simple scale exactly balancing 3kgs of silver on one side, 3 kgs of gold on the other side.

Immersing the whole system in water, we will see the gold part going down, and the silver up.

Because 3 kgs of silver take more volume than 3kgs of gold, when immersing, the Archimedes principle states that silver will move more water than gold and vertical push will be more important on silver than gold. The result is gold sinking.

 

That's it?

[swansont]

That's it.

[michel123456]

But that happens in air too. Air is also a medium, like water. I never heard that measuring weight in normal conditions should involve a factor of buoyancy, as small as it is.

[insane_alien]

liquids and solids tend to be a few orders of magnitude denser than air so historically the error in measurement from the instrument exceeds that from buoyancy.

 

it is important if you want super accurate results though.

[John Cuthber]

But that happens in air too. Air is also a medium, like water. I never heard that measuring weight in normal conditions should involve a factor of buoyancy, as small as it is.

The effect of buoyancy of air is real. It's easy enough to measure on a laboratory balance.

Typically the correction for air density is about 0.1%

Often, it's not worth troubling with but if you are really trying to get precise results you need to correct for it (and allow for the variation of air density with humidity and barometric pressure) or weigh things in a vacuum chamber.

[michel123456]

The effect of buoyancy of air is real. It's easy enough to measure on a laboratory balance.

Typically the correction for air density is about 0.1%

Often, it's not worth troubling with but if you are really trying to get precise results you need to correct for it (and allow for the variation of air density with humidity and barometric pressure) or weigh things in a vacuum chamber.

 

Thanks.

Either I never learned that or I forgot it .

[michel123456]