what is the science behind calibration weights ? How can we be so sure that the weight we’ve been using to calibrate is exact and not a few decimals off, which would make the concept of density completely wrong ?



what is the science behind calibration weights ? How can we be so sure that the weight we’ve been using to calibrate is exact and not a few decimals off, which would make the concept of density completely wrong ?

In: Physics

Weight is a unit of force, the SI unit for it is Newton. A bit simplified it is the force of gravity on a mass on the surface of the earth. Because gravity depends on the location on earth, the difference is on the surface of Earth is 0.7% The result is the weight of an object depends on where you are on earth.

The mass has the SI unit of the kilogram, weight is mass * gravitational acceleration. Calibration weights that you use to calibrate a scale are made to have a specific mass, not a specific weight because weight is location-dependent.

The same way density is not weight/volume but mass/volume.

Between 1889 and 2019 the kilogram was defined as the mass of the [https://en.wikipedia.org/wiki/International_Prototype_of_the_Kilogram](https://en.wikipedia.org/wiki/International_Prototype_of_the_Kilogram) All other masses were derived as a comparison to it. There is always a level of accuracy so not two-kilogram prototype had the exact same mass. There was a small change in mass over time because if you use them they need to be clean and there was a drop of around 1micro gram per cleaning, which is a change of 1 in one billion.

Any good calibration weight will have documentation so you can trackback what is was compared to and when. That way any errors and inaccuracies can be tracked.

Because of problem like this the kilogram was redefined in 2019 as

>”The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10^−34 when expressed in the unit J s, which is equal to kg m^2 s −1, where the metre and the second are defined in terms of c and ∆ν_Cs.”[1]

Today mass is determined by a physical constant.

So any real physical object will not have a mass that is exact. The object made with higher accuracy will cost more.

Any density measurement of material will have one accuracy limit and I assume it is the volume that is harder to determine than the mass.

Calibration weights are correct by definition, within a known tolerance.

Unlike a lot of other basic units, mass is annoyingly difficult to quantify in any absolute terms that we can usefully employ. Saying “1kg is equal to 1 cubic decimeter of water at such and such temperature and pressure” (the original definition) is perfectly rigorous but really hard to implement, because you’ve just turned the problem into one of measuring volume instead of mass.

So in the late 1890s they switched to a physical artifact…they made a platinum iridum bar and *defined* it to be 1kg. Later that got replaced by a cylinder that was used to calibrate everything else. It can’t be wrong, because it’s the definition. Then you just compare other weights to *the* kilogram and keep track of the tolerances of your measuring devices to make calibration weights for general use. The problem with this approach is that if your reference mass changes you get into a fight about which one is right.

Very recently (2019) we redefined the kilogram in terms of the Planck constant, the second, and the meter (which all have really vigorous definitions that don’t depend on a physical artifact). This lets us check reference weights against other things we can directly measure.

If you use a different calibration weight, you are essentially using a different unit of measurement despite calling it the same name. Thus, as long as people keep their units under control when transferring data between people, there will be no problem.

Numbers are totally arbitrary. If I say that my body weight is now 1 firakegram, then it is. And if you then use the force which my body weighs down on a scale to measure the weight of two smaller people you might find that they are 1.8 firakegrams. Weight itself is a fundamental property of an object, but how the numbers and units we use to represent it are completely arbitrary. We don’t need to know the “actual” (and we can’t know it, anyway. What units does the universe use?) weight of something as long as we know what other people mean when we give them our representations of the objects weight.

The ELI5:
Calibration weights are mostly made by a single company and that company does a very good job of making all their weights the same. There’s a whole business of making ‘official’ standard weights and measures. And organizations that get together to compare and certify these standard weights and measures.

Depending on how accurate you need your measurement determines how fancy your calibration weight must be.