What's the most significant digits, mass measurement, possible of an iphone X?

Inspired by this thread :

Whats the best possible accuracy, of an off the shelf weighing machine, that can measure an object approximately as big as the iphone X (~0.4 lbs or 0.2 kg) ?

By off the shelf, I mean a balance that is currently being manufactured / used for similar weight objects.

Here’s one with .002mg readability:

They way I’m reading that page, it says that they make balances with a capacity of up to 520 grams, and they make balances with a precision of 0.002 mg (2 µg), but it doesn’t say that the same model can do both. Did you find one with a 200-g capacity and a 2 µg precision?

This has two ranges:

0 g to 120 g with 0.005 mg readability

0 g to 41 g with 0.002 mg readability

Also keep in mind that readability (resolution) is not the same as uncertainty.

And when using an instrument such as this, you should also do a buoyancy correction, which means you must have a calibrated temperature and RH meter next to the balance. You must also know the density of the specimen.

The best I could find was this model, which can weigh a 200-gram mass to within 10 µg. That’s still 5 orders of magnitude less precise than would be required to detect the mass difference between a charged iPhone and a discharged iPhone.

IIRC from that other thread, and assuming it’s correct, you’d need one that can get down to .000000001 mg, to get into the picogram range. Even then, a few specks of dust could throw it off by hundreds of thousands of picograms.

If you could weigh, what, a million batteries at the same time, you might be able to start registering a difference in mass between them being charged vs uncharged. Of course then you’d have to find a scale that can weigh into the 30,000kg range with picogram resolution.

Wouldn’t it be easier to just look at the battery display on the screen?

It’s not just dust you have to worry about, either. Does an iPhone contain any magnetic materials? (trick question: All materials are magnetic). How do those materials interact with the magnetic field of the Earth? Likewise, does anything in the experiment have an electric charge (or dipole, or any higher-order multipole)? Is light pressure an issue?

Excellent points. Thanks

You could mitigate some of that by finding it’s mass instead of it’s weight. Even if it means taking X number of charged batteries and X number of uncharged batteries and putting them on opposite sides of a balance.
Of course, if the magnetic pull of the battery is different based on it’s state of charge that would further complicate things. Though the magnetic pull of the charge is probably a lot easier to empirically find than the mass of the charge.

I think that the goal here isn’t actually to measure the mass precisely, per se, but to measure the change in mass. Taking two mass measurements and subtracting them is one way to do that, but it’s not the only way. To that end, I’d be inclined to put a single phone in our apparatus, and then let it discharge its battery while in the apparatus, and seeing what changes. That way, we wouldn’t have to worry about what motes of dust are on the phone, just that it remains the same motes of dust, which is somewhat easier.

Though yes, the electromagnetic moments are likely to change with the discharge of the battery (or at least, I certainly wouldn’t rule out that they might change), which means that we’d still have to try to measure that somehow and control for it.

I don’t know where or how, but at this point heat might come into play.

Of all things, I think that would be the easiest. I’m guessing it wouldn’t take much more than an off the shelf EMF (or just magnetic field) detector to see if it changes and calculate those changes. Magnetic force is a whole lot stronger than gravity and should have a much larger, and thus easier to detect, effect on the battery.

Really high end balances are often called ‘mass comparators.’

The OP references both significant digits and accuracy, but these are not the same thing. A high-quality device will not show precision beyond its ability to do so accurately but theoretically these are two different things.

By definition they are different.

For the parent OP, accuracy is not important. But precision and resolution are. The question is more like “What is the best we can do to measure the delta in mass for a phone sized object?” The absolute value of the mass is not so important and is allowed to vary from the true value by much more than the delta is resolved. Often this kind of relaxation of the task allows better precision and/or resolution to be achieved, but how much we might improve, I have no idea.

The OP used the word “accuracy” which is why I got all nitpicky about it. As early as 8th grade the difference was drilled into me by science teachers.