5 ms·
Wikipedia has a good paragraph on this. It describes a very cool alternative method that has higher accuracy, and according to Galileo it's probable that Archim
by hddqsb 3y ago
Wikipedia has a good paragraph on this. It describes a very cool alternative method that has higher accuracy, and according to Galileo it's probable that Archimedes used this method:
> The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement. Archimedes may have instead sought a solution that applied the hydrostatics principle known as Archimedes' principle, found in his treatise On Floating Bodies: a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.[34] Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly.[12] Galileo Galilei, who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."
-- https://en.wikipedia.org/wiki/Archimedes#Archimedes'_principle https://en.wikipedia.org/wiki/Archimedes#Archimedes'_princip...
- spacemule 3y ago> then immersing the apparatus in water I'm having trouble picturing what's going on here. I'm not sure what the apparatus is. The best I can figure, it's two containers of water with the reference gold in one and the crown in the other. However, this wouldn't be any different than just weighing the two pieces of gold (which are already known to be the same mass). I tried searching for "hydrostatic balance," but nothing relevant to this came up. Since you seem to understand this, would you mind explaining (or pointing to an explanation of) Archimedes's probable solution?
- mafuy 3y agoThe apparatus is the scale, on which the crown and the gold were placed. They balance out when it is in air. They do not (for a fake crown), when the scale is submerged in water.
- spacemule 3y agoThanks for answering. I'm not even an amateur in physics, so forgive me for this elementary follow-up question. Why does it not balance in water? It would seem to me that the same weight it on each side of the scale, so the same force is pushing down on each side of the scale.
- malcolp 3y agoYou're right there is the same force pushing down on each side. But there's also an additional force in water pushing up. It's called upthrust. It's equal to the weight of displaced water. If the densities are different the samples with the same weight will have different volumes and different upthrusts. This can be quite a useful phenomenon practically. Anyone who has learned to scuba dive will know that if you take a deep breath in from your air tank you increase your volume without changing your weight and will be able to slightly change your bouyancy and float upwards or downwards without moving your limbs. Submarines also use the same phenomenon.
- hughesjj 3y ago> Submarines also use the same phenomenon For clarity, the submarines fix their voice but adjust their weight by pumping or flooding their ballast tanks
- Terr_ 3y ago> Why does it not balance in water? Technically, it doesn't balance an air either, but it's just harder to notice the effect. For an exaggerated example, imagine a 1-kg cube of styrofoam and another 1-kg cube of steel, each placed on opposite trays of a balance-scale. The scale will be truly balanced in vacuum, and in air will appear balanced to the unaided human eye. However when you submerge the entire system underwater, the differences will be shockingly visible... especially when the styrofoam floats up and off the scale entirely! It isn't because of negative mass or negative weight, just buoyancy that can no longer be ignored. By conducting the "weighing" experiment again in a denser fluid (water) any subtle differences in density/ displacement become easier to measure.
- daniel-cussen 3y ago[dead]
- hddqsb 3y agoSure! (My explanation is basically equivalent to the combined explanations by @mafuy and @malcolp, but I'll post it anyway.) The idea is to balance a scale with the crown on one side and an equal mass of gold on the other side (no water yet), and then submerge the entire scale in water. Now there will still be the same mass on each side, but there will additionally be a buoyancy force on each side proportional to its volume. So if the volume of the crown is different from the volume of the reference gold, the buoyancy forces will be different and the scale will tip.