[spacemule]

Thanks for answering. I'm not even an amateur in physics, so forgive me for this elementary follow-up question. Why does it not balance in water? It would seem to me that the same weight it on each side of the scale, so the same force is pushing down on each side of the scale.

[malcolp]

You're right there is the same force pushing down on each side. But there's also an additional force in water pushing up. It's called upthrust. It's equal to the weight of displaced water. If the densities are different the samples with the same weight will have different volumes and different upthrusts.

This can be quite a useful phenomenon practically. Anyone who has learned to scuba dive will know that if you take a deep breath in from your air tank you increase your volume without changing your weight and will be able to slightly change your bouyancy and float upwards or downwards without moving your limbs. Submarines also use the same phenomenon.

[hughesjj]

> Submarines also use the same phenomenon

For clarity, the submarines fix their voice but adjust their weight by pumping or flooding their ballast tanks

[Terr_]

> Why does it not balance in water?

Technically, it doesn't balance an air either, but it's just harder to notice the effect.

For an exaggerated example, imagine a 1-kg cube of styrofoam and another 1-kg cube of steel, each placed on opposite trays of a balance-scale.

The scale will be truly balanced in vacuum, and in air will appear balanced to the unaided human eye.

However when you submerge the entire system underwater, the differences will be shockingly visible... especially when the styrofoam floats up and off the scale entirely! It isn't because of negative mass or negative weight, just buoyancy that can no longer be ignored.

By conducting the "weighing" experiment again in a denser fluid (water) any subtle differences in density/ displacement become easier to measure.

[Lanzaa]

That is not how a balance scale works. The two sides balance, because the weigher makes them balance. That can be done in a vacuum, air, or water.

The trick being described has the weigher balance the scale in air, with unknown mass A and some mass of gold B. The two sides are equal in weight in air, different from mass. Then the entire balance system is submerged. The difference in density of A and B, and therefor volume, leads the balance to become unbalanced.

It would be wise to add mass to the lighter side to try and measure how imbalanced. I would bet most adulterants are about half the density of gold or less. In g/cm3: Gold is 19.3, silver 10.5, lead 11.3, copper 9.0, nickel 8.9.