[Colin2B]

It is not physically possible to detect a 2ug force in 1797.

Ignoring the incorrect 2μg, it is incumbent on those who find Cavendish's experiment incredible, to explain why it yielded a value of G within 1% of the current best measurements.

We often find people speculating on visiting aliens with advanced technology and whether we would be capable of understanding that technology. Here we have someone from 2019 incapable of understanding technology from 1797!

[Bored chemist]

Here we have someone from 2019 incapable of understanding technology from 1797!

I'm not sure if it's not that they can't understand but that they actively refuse to.
The OP has refused, consistently, to even try to do the maths which shows how it would work.

[Colin2B]

I'm not sure if it's not that they can't understand but that they actively refuse to.
The OP has refused, consistently, to even try to do the maths which shows how it would work.

Maybe he can’t do the maths, or maybe he's trolling

[alancalverd]

https://en.wikipedia.org/wiki/Cavendish_experiment gives a very succinct account of the arithmetic involved in deriving G from the angular displacement of an idealised torsion suspension. Since it involves square roots and Greek characters θ and π , it is obviously magic, not science, which is probably why the OP refuses to study it.

[evan_au]

Show a a 2ug force is measured today in modern physics.

Without quite going to the spectacular lengths of using resonating carbon nanotubes to count the nucleons in an atom....

A more common technology is to use resonating silicon micromechanical structures (MEMS) to detect chemicals in the environment. The chemicals adhere to the end of the beam, and it changes its resonant frequency. And time/frequency is the unit we can measure with the greatest precision.

Using this technique, one team was able to measure changes in mass of an attogram (10^-18 grams).
This is a millionth of a millionth of a microgram.

Silicon MEMS is the technology already used in your smartphone as an accelerometer.

See: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5399360/

[alright1234 (OP)]

 a standard analytical balance is 100 times less sensitive; i.e. it is limited in precision to 0.1 milligrams.

That being the case how did Cav measure a 2ug force?

[alright1234 (OP)]

Here we have someone from 2019 incapable of understanding technology from 1797!

I'm not sure if it's not that they can't understand but that they actively refuse to.
The OP has refused, consistently, to even try to do the maths which shows how it would work.

What math are you talking about? The question is how did Cav measure a 2 ug force in 1797? This is not a math problem------ this is a physics problem.

[Bored chemist]

How far should the beam have moved? is a maths problem.

Answer it.

[alright1234 (OP)]

How far should the beam have moved? is a maths problem.

Answer it.

What\? can you explain it to me?

[alancalverd]

RTFM.
Cavendish wrote a very comprehensive account, which has allowed many people to replicate his experiment. The Wikipedia reference I gave earlier is more thorough than most undergraduate textbooks.
I think they have the Ladybird Book of Hard Sums in  the Harvard library, but it's probably a bit advanced for your friend.

[alright1234 (OP)]

How far should the beam have moved? is a maths problem.

Answer it.

Cav experiment is a physics experiment not a mathematical problem. Example, weighing the mass of a penny is a physics experimental problem not a mathematical problem. How would you weigh the mass of a penny to 2 ug in 1797? You would use a scale not a pen and parchment to do some mathematics.

[Bored chemist]

How would you weigh the mass of a penny to 2 ug in 1797?

With the help of a time machine.
Obviously that would be tricky.

It would also be irrelevant.
Nobody is saying that he measured the mass or weight of anything to that precision.
So, stop posting straw men.

However, because I can do maths (and physics) I can calculate how far the beam of Cavendish's apparatus would move when acted on by a force of 2µg at the end(s) of that beam.

You are tacitly claiming that the movement is too small to measure.
In reality, he measured it.

Why don't you address the issue once and  for all by actually doing the godforsaken maths and showing that the movement is too small to measure?
Are you not clever enough, or are you scared that it will show you are wrong?

[alright1234 (OP)]

The fact that Cav is measuring a force of 2 ug has precedence before anything else.

[Bored chemist]

The fact that Cav is measuring a force of 2 ug has precedence before anything else.

Yes, he measured a very small force.
He did it by applying that small force to the end of a long lever and using it to twist a long thin wire.
and then he measured the angle through which it twisted.

You seem to think that angle would be too small to measure.
Well, as I keep saying, why don't you calculate it?
That way we would all know if it is too small to measure.

[alright1234 (OP)]

Not physically possible in 1797. Admit it.  It does not matter what the angle is if the original force is impossible to measure in 1797.

[Bored chemist]

Not physically possible in 1797. Admit it.  It does not matter what the angle is if the original force is impossible to measure in 1797.

Do you understand that the angle IS the measure of the force?
Do you simply not understand how the experiment worked at all?

[alright1234 (OP)]

An angle represents a magnitude in degrees but a force is depicted in Newton or grams.

[Bored chemist]

An angle represents a magnitude in degrees but a force is depicted in Newton or grams.

Yes, but if I want to measure a force- for example the weight of something, I can do so by applying the force to a spring and measuring how much the spring stretches.
So, what I measure is a length.
But that allows me (via a calibration) to calculate a force.

In the case of this experiment, rather than stretching a spring, they twisted it.
The angle it twists through is a measure of the force (strictly speaking, the torque).
The clever bit is that by twisting a vertical wire any effect of the Earth's gravity doesn't affect the measurement because that's downward, but the twist is sideways.

[alright1234 (OP)]

It is not physically possible to measure a 2ug force in 1797 no matter what method you use.

[Kryptid]

Not physically possible in 1797. Admit it.  It does not matter what the angle is if the original force is impossible to measure in 1797.

It is not physically possible to measure a 2ug force in 1797 no matter what method you use.

https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/49/Argument-by-Repetition