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Identifying Materials Using Archimedes' Principle.
Pete W.:
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! :lol: :lol: :lol:
Pete W.:
OK, now let's deal with the case where we don't have any scales.
I don't want to confuse anyone but I'm changing the numbering system slightly, this method is method 2a).
What we need is a rigid beam and some string. Suspend the beam using one piece of string from approximately its mid-point - support it in any way that's convenient. Then suspend the 'mystery object' on one side of the beam and a second object, used as a counter-weight, on the other side of the beam. The string supporting the 'mystery object' needs to be long enough for the object to be immersed in the water in the bucket during the second phase of the operation; for now, leave both the 'mystery object' and the counter-weight swing clear in the air. Adjust the positions of the pieces of supporting string so as to bring the system into balance.
When the 'mystery object is immersed in the water, it will lose weight so its suspension will have to be moved further out from the main suspension point to restore balance - take this into consideration in positioning the 'mystery object' and the counter-weight.
Now, with the system in the air, measure the distance of the 'mystery object' from the main suspension point of the beam. Note the value. (If you wish, you can also measure the corresponding distance to the counter-weight but it doesn't get used!)
Next, either raise the water-filled bucket or lower the beam's main suspension so as to immerse the 'mystery object' in the water. The same precautions regarding contact with the sides or bottom of the bucket and regarding trapped air apply here as in Method #1.
Immersing the 'mystery object' disturbs the balance of the system and you will need to re-adjust - in this method, you move ONLY the position of the suspension of the 'mystery object', leave the position of the counter-weight unchanged.
When you're satisfied with the new balance conditions, measure the distance of the 'mystery object' suspension from the main beam suspension point again, note the value.
To follow the next bit, you need to understand 'moments'. It's not difficult, it's all to do with leverage. Consider a see-saw with one side twice as long as the other - then it'll need two people sitting on the short side to balance one person sitting on the long side. At balance, both sides have the same 'moment' about the pivot. The 'moment' is equal to the force multiplied by the distance at which it acts.
Now here comes the algebra:
The volume of the 'mystery object' is represented by the symbol 'V', the specific gravity by the symbol 'ρ' and the acceleration due to gravity by the symbol 'g'. The measured lengths are represented by the symbols on the diagrams that follow.
(I hope that my algebra is readable.) Remember, in algebra, a point means 'multiplied by'.
In my next post, I'll proceed to Method 2b) in which the 'mystery object' remains in the same place but it's the counter-weight suspension that's moved to restore balance. That means a similar but slightly different bit of algebra!
Pete W.:
I hope you're all still with me! Here comes method 2b)
The procedure is basically the same as in method 2a) except that to restore balance, it's the counter-weight suspension that's moved and the 'mystery object' suspension is left unchanged.
This needs a slightly different set of algebra, with symbology consistent with that used in method 2a), as follows:
I hope that what I've written is clear - if not I'll try to answer questions.
Right now, I've just been called for the evening meal!! :ddb: :ddb: :ddb:
awemawson:
I'm definitely sticking with my Analloy Analyser:
http://madmodder.net/index.php/topic,9244.msg102310.html#msg102310
I seem to remember that aluminium and zinc based alloys can be distinguished by their reaction to acids quite easily
BTW do you have huge quantities of disc chassis, or is this a theoretical analysis?
Pete W.:
Hi there, Andrew,
Thank you for your post. I did intend to refer to your marvellous gadget in my introduction - it must be a useful asset but it's one not many of us have.
Regarding your question - why do you want to know?
(There's an anecdote lurking in the undergrowth of that topic but I'm not sure I should recount it on-list!) :ddb: :ddb: :ddb:
But here's a clue: Some time ago, my lovely but shy assistant sold quite a few neodymium-iron-boron magnets on eBay - the buyers were motorcyclists whose tank-bags wouldn't stay on at speed.
One buyer came back with the report that with 'our' magnets, his tank-bag would stay on at 100+ mph, I always wondered how he knew!! :lol: :lol: :lol:
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