I guess when I buy Hungarian salami next time I’ll point all this out to the deli clerk.
“Remember!!! Hungarian salami ain’t steel, eh? Adjust your scale accordingly!!”
For my ordinary every day purpose, I’m not too bothered. But it’s very interesting to learn, just the same. Thanks.
So a 400-sided polygon would be a gon-gon?
All measurements include error. (I once took a course on measurement)
I’ll bet the error is a lot less than you are contemplating.
You’ve suggested that the mass of steel used for calibration is the standard. Its not.
If you go way back, you’ll find that the definition of a gram is based on a specific volume of water under specific conditions.
Thus is derived the Internation Prototype Kilogram of Platinum and Iridium constructed in 1889.
At the time, I’m fairly certain that the IPK was measured against a liter of water under normal atmospheric pressure and not calibrated under vacuum conditions.
So the IPK is off a little.
Given the IPK is denser than steel, the steel is somewhat less off than the IPK but still off.
So when measuring deli meat, which is way closer than steel to the density of water, we are getting a more accurate reading on the scale than if we were measuring steel.
tee hee
No. The IPK is 1 kg by definition. It’s not “off” at all.
The gram was defined as the mass of a cubic centimeter of water under certain circumstances. But it turns out that lumps of metal can be made more repeatably than those conditions of temperature and pressure could be, so when they made the prototype kilogram, they changed the definition (while matching it as closely as they could to the old definition, of course). And in any event, when you’re working with high-precision standards like that, you do it in vacuum, so as to avoid buoyancy (and air currents and dust contamination and whatever else) entirely.
TFD:
An analytical balance is adjusted and calibrated in place using a NIST-traceable set of steel weights. You need not concern yourself with how these standard weights are calibrated; just assume they’re pure steel and the mass of each is known to a very high degree of accuracy.
When you use the balance to measure the mass of an object, the balance essentially “assumes” the object has the density of steel. If the object *does *have the density of steel, then the reading will be correct (except for random error, of course). If the object’s density is *not *the same as the density of steel, there will be systematic error. This, of course, is due to the difference of buoyancy between the object (with its actual density) and the buoyancy of the same object if it were made of steel.
The buoyancy error is very real for analytical balances. However, it should be stated that the error is due to the way the balance measures mass. This is because an analytical balance doesn’t really measure mass… it measures weight. If it can be assumed the force due to gravity does not change over time for a particular balance (because the balance doesn’t move), then the balance simply converts weight to mass. This is done during the calibration of the balance using the standard weights… the balances measures the *weight *of each standard weight, and then is programmed to report the *mass *of the weight.
If you had a balance that directly measured mass - and not weight - then you would not need to do a buoyancy correction.
Thanks for lesson:rolleyes: Look, you’ve completely missed my point. Following your line of reasoning, as long as you use steel to calibrate your ballance then you already have built in a “systemic error”. based on the different buoyancy between steel and platinum.
I can’t imagine such an animal.
Huh? What’s platinum got to do with anything?
The true, absolute, no-BS mass of the standard steel weights are known. That’s all you have to be concerned with.
Let’s use an example.
Say I have two standard weights. Each weight is pure steel. The weights were calibrated by NIST. The calibration record provided by NIST says Weight A is 50.000173 grams and Weight B is 500.00034 grams. Each of these values has an error, of course, but we won’t concern ourselves with it - we will assume they’re exact. Most importantly, each of these values represents a pure, true, absolute, no-BS mass value.
After putting my balance in calibration mode, I plop Mass A on my balance and type “50.000173” into the balance’s keypad. Let’s assume the output of an electrical circuit inside the balance is 124.1234 mV after the weight is placed on the pan. Thus the microcontroller inside the balance knows 124.1234 mV equates to 50.000173 grams.
I plop Mass B on my balance and type “500.00034” into the balance’s keypad. Let’s assume the output of the same electrical circuit inside the balance is now 285.9671 mV. Thus the microcontroller inside the balance knows 285.9671 mV equates to 500.00034 grams.
Using these two points, the balance draws a straight line and simply calculates the y=mx+b equation for the line. When you put an unknown object on the balance, the balance will measure the output of the electrical circuit inside the balance and calculate mass based on the y=mx+b equation. In actuality it’s a bit more complicated that that, but this is essentially how it’s done.
And as mentioned previously, if what you’re plopping on the balance is not steel, there will be error.
Just an FYI, but Googling around, there seem to be at least stainless steel, cast iron, and brass calibration weights available, for various NIST class ratings. See here, for example. This doesn’t affect the point of what Crafter_Man is saying, there’d just be a slightly different buoyancy correction.
90% of the IPK is made up of platinum.
Show me that a buoyancy correction was made for platinum to steel by NIST.
Expanding a bit on Zen’s post.
Say I have two standard weights. Each weight is made of Styrofoam. I send the weights to NIST for calibration. NIST sends them back, along with a certificate stating the true, absolute, no-BS mass of each weight. Can I use these Styrofoam weights to calibrate my balance using the same procedure I provided in my previous post? Yep! Would it be valid? Yep! Afterwards, if I use the balance to measure something that has the same density as Styrofoam, the mass reading will be correct. If I use the balance to measure something that does not have the same density as Styrofoam, the mass reading will have an offset error.
The reason I focused on steel in my previous posts is because almost all standard weights are made of steel.
BTW: Assuming your balance was calibrated with steel weights, is it always necessary to do a buoyancy correction? No. Instead of doing a buoyancy correction, you can simply write down the mass value displayed by the balance, and state that the value is “based on the density of steel” or something like that. This is what’s usually done. The reason is because you often have no idea what the density of the sample is. Instead of trying to measure the sample’s density, or estimating what you *think *the density is, it’s much easier - and you cover your ass - by stating “the mass value is based on the density of steel” and leaving it at that. If your customer wants to know the *true, absolute *mass of the sample, tell them you’ll have to charge them a lot more money for accurately measuring the sample’s density.
I’m very confident NIST has gone to ***extreme ***lengths to measure the absolute, true mass of their “best” in-house weights vs. the IPK. The buoyancy corrections they made are probably trivial compared to other corrections and calculations they had to make.
Nope, it doesn’t do that, either. All the scale measures is the normal force on it. If there are any other forces on the object being measured, or if the system is accelerating, the normal force will be different in magnitude from the weight.
I think it would be possible to construct a device that measures mass by moving the load around and measuring the force required to accelerate it.
Any balance type scale measures mass. Go to the moon, take along a laboratory balance and set of gram weights, and you’ll find everything has the same mass there as it does on Earth. I’m not sure but I think a standard springless medical scale would be the same.
I’m going to give that. It was easy enough for me to calculate the the air weight of the additional displacement for a kilogram of water over a kilogram of steel . It surprised me that it came to 1.2 grams.
Whoopie! I’m getting a free gram when I buy a kg of black forest ham. And from now on I’m gonna make sure none of the meat hangs over the scale plate at the Deli. 
Here’s a picture of NIST’s state-of-the-art high precision mass comparator in use.
I couldn’t find a good description of it on the NIST site, but the Romanian National Institute of Metrology provides a description of their mass comparator (italics mine),
Yep, you’re correct, of course. But the assumption is that no other force is acting on it besides mass*gravity.
I´m not sure if this has been mentioned so far but…
As the system works there’s need for a standard reference mass to derivate all other measurements, that would be the IPK. It makes sense to make it weighting 1Kg instead of 1 gram for a resolution point of view, basically, the 1Kg mass has 3 orders of magnitude better precision than it would be achived with a 1 gram mass.
That is to say, it would be very difficult (impossible at the time the first was made) to make a 1 gram reference mass with the same accuracy than a 1Kg mass since both should have the same manufacturing tolerances.
In any case it would be a fascinating read to know how the first IPKs where made in the 18th and 19th centuries.