In this thread, I want to review and demonstrate a method of identifying materials (mostly metals) using Archimedes' Principle.
I'm not targeting all metals (especially NOT gold, for which Archimedes thought up this whole idea to start with!) but mainly distinguishing between aluminium alloy and the zinc-based die-casting alloys (aka 'Zamak').
In my own situation, this facility helps me fend off any scrap metal dealer who tries to avoid paying me the aluminium price for my old computer hard drive chassis by claiming that they are zinc-based. I suggest that the method will also be useful to Mad Modders who do their own casting.
What Archimedes realised was that an object immersed in a liquid experiences a reduction in weight equal to the weight of the liquid it displaces, i.e. a quantity of the liquid that has the same volume as the immersed object. Using this principle enables us to determine the specific gravity of the object - knowing the specific gravity, we can consult any of the various tables of physical properies of materials and hence identify the metal.
Specific gravity is defined as the ratio of the weight of a given volume of the material to the weight of the same volume of water. If you're a physicist, you'd want that to be pure water at Standard Temperature & Pressure (aka 'STP') but I'm a Mad Modder and so I'm using ordinary tap water!
I plan to explain three methods of getting to the specific gravity of our 'mystery object', the first one requires a weighing machine that suspends the object rather than having it in a scale pan. The fisherman's spring balance would do, I've used a modern digital gizmo (see photos, below).
(My scales read in grams or kilograms but pounds will work too, you just have to use the same units for all measurements. If your scales read in pounds and ounces, you'll have to express the ounces as decimal parts of a pound. So, for example, 2 lbs 4 oz = 2.25 lbs.)
The second & third methods substitute a ruler and a counterweight for the weighing machine. All three methods require a bucket of water and some string. All three methods require the 'mystery object' to be of only one material, so if it's mostly e.g. aluminium, you need to remove any nuts, bolts, brackets, pins etc., etc., that are made of steel or other material different from that comprising the bulk of the object. But then if your mystery object is destined for either the crucible or the scrap metal dealer, you'd have to have done that anyway!
The first method is very simple, first weigh the object. Note its weight - call it 'D'. Then lower the object into the water, ensuring that it doesn't touch the sides or bottom of the bucket. Also, make sure the object isn't trapping any air. Again, note the weight - call it 'W'.
Now, from Archimedes' Principle, the weight of the 'same volume of water' is the difference between D and W, i.e. in mathematical terms (D-W). So the specific gravity of our 'mystery object' is given by D/(D-W). In my physics classes, years ago, we used the symbol ρ to denote specific gravity.
OK so far? Here's an example:
Object #1, dry weight:
then, object #1, immersed weight:
Sorry about the fuzzy focus. So, we have D=510 grams and W=315 grams, so (D-W)=195 grams. So the specific gravity, ρ=315/195=2.62 From my reference tables, aluminium alloys have specific gravity values around 2.6 so object #1 is aluminium alloy.
Now here's another example:
Object #2, dry weight:
then object #2, immersed weight:
So, we have D=275 grams and W=240 grams, so (D-W)=35 grams. So the specific gravity, ρ=275/35=7.8 From my reference tables, zinc-based alloys have specific gravity values around 7 to 8 so object #2 is zinc-based alloy.
Notice that the denser the material of the 'mystery object', the smaller is the relative change in weight.
I wrote earlier that I'm using ordinary tap water. If all you have is sea water, you could use that - you'd just have to multiply the (D-W) term by the specific gravity of sea water, i.e. 1.02, but that's probably splitting hairs!
In my next post, I'll explain methods two and three. I'll post that as soon as I've drawn and scanned some diagrams to illustrate the methods.
Methods #2 & #3 are going to involve some algebra but if you don't 'do' maths just trust me and go straight to the conclusion!