How could a test for density be used to separate counterfeit coins? How do vending machines do it?
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If a coin is trying to be counterfeit, then it’s probably trying to look exactly the same in which case, all that you need to measure is mass (weight). If it weighs differently than the real thing it’s wrong.
But if you want to look specifically at density, if you had a weird coin that had a volume of 1 cubic centimeter and weighed 1 gram, its density would be 1 g/cc, because Density = Mass / Volume.
So you have your 1 g/cc coin.
You grab a coin that looks exactly the same, but when you weigh it, it only weighs 0.5 g. Density is now 0.5g/cc.
Testing another coin is twice as heavy (mass), with a density of 2g/cc.
Obviously, comparing these densities shows that they are not "real" 1g/cc coins. But like I said, calculating density doesn’t matter, if the volume is constant, as it probably would be on a fake coin.
But let’s say that you have a really bad counterfeiter. He uses the *exact* same mass of material, but keeps getting the shape of the coin wrong. First, he has a volume of 0.5cc. The next one has a volume of 2cc. Now you compare this against your known density, using M/V;
Density of the first one = 1g / 0.5cc = 2 g/cc
Density of the second one = 1g / 2cc = 0.5 g/cc
So once again, pretty obvious which ones are wrong against your 1 g/cc.
But *mathematically* density isn’t perfect. Let’s say that you have an obviously counterfeit coin. It’s *huge*! Weighs 100 grams! Has a volume of 100 cubic centimeters! But when you put that together into your density equation, you get:
100 g / 100 cc = 1 g/cc
See the problem? Now, again, if you were searching for a counterfeit coin, no one would have a problem seeing it. I’m just pointing out that *mathematically* speaking, density testing isn’t a perfect system.
So that’s how it works.
Old-style vending machines had fairly simple sensors that measured the mass as the coin passed through (weight is easy, right?). They also use optical scanners to determine the volume of the coin, then put it together and compare it against an internal bank of coins. If it’s a US coin, it processes it.
Most modern vending machines use magnetic scans to read coins as well. If you put in a quarter, the coin passes through an electromagnetic field that reads its thickness and metallic properties. Its profile corresponds to a profile programmed in the machine’s central computer (yes a vending machine with a central computer core), which recognizes these properties as belonging to a quarter. The computer also stores knowledge of the properties for nickels, dimes, and pennies. Once the machine accepts the coin as valid, it sends the coin to a cash box at the back of the machine, and digitally stores the value of money that you’ve put in, so that it can hang up and not actually spit out that Snickers bar that you wanted when you hit D-6.
Note… if someone tries to put in a Canadian quarter, or a Mexican peso, both of which are quite similar in size (obviously different to look at them side by side, of course) to a US quarter, the machine processes it, and if it doesn’t register the coin within its database, it does one of two things: (1) Spits the coin back at and the jerk who tried to use it (2) sucks it into a second hopper in the back next to the genuine coins without giving it back — people who own the vending machine get more money, without having to give out any goods, and I guess that the unfortunate vending machine client just gets screwed.