Cavendish balance and mass of objects

[Ranku]

The Cavendish balance measures the gravitational constant G. To do so requires us to know the magnitude of the smaller and larger masses in the apparatus. However, mass is derived from the weight of an object, which is the gravitational force upon an object, which in turn requires the value of the gravitational constant. So, how to measure the mass of an object (whose magnitude is required to measure the gravitational constant) without requiring the gravitational constant?

 

[Ibix]

Newton's second law.

 

[Bystander]

https://en.wikipedia.org/wiki/Cavendish_experiment
What don't you understand?

 

[Ranku]

Newton's second law.

Newton's second law.

To derive the mass of an object by observing its acceleration, we need to know the magnitude of the applied contact force. However, the contact force itself has to be carried by a mass, whose magnitude we need to know, by weighing it, which takes us back to the initial problem.

One possible way to resolve this dilemma could be to use a grocer's scale, to designate the magnitude of mass of objects from scratch, by the purely physical method of visual observation. By placing a 'reference mass' of unknown magnitude on one side of the balance and by observing its equality with another mass on the other side of the balance, we may designate each of the two masses as constituting a 'standard unit of mass'. Next we transfer the two masses to one side of the balance, and compare them with another single mass on the other side of the balance, and designate the new mass as representing a greater mass by a factor of 2, and so on.

 

[Ibix]

That's basically what a unit system is. I pick an arbitrary stone and say "this stone is our standard mass". All masses are then quoted in multiples of the mass of that stone. We use kilograms instead of stones these days.

 

[Ranku]

That's basically what a unit system is. I pick an arbitrary stone and say "this stone is our standard mass". All masses are then quoted in multiples of the mass of that stone. We use kilograms instead of stones these days.

Ya, although the history and technology of definition of the 'kilogram' is a bit more elaborate and sophisticated.

 

[jbriggs444]

However, mass is derived from the weight of an object

Historically, merchants have bought and sold objects and bulk goods using balances.

Balances do not measure gravitational down-force. They compare the gravitational down-force of an unknown test object against the gravitational down-force of a known reference mass. In this manner the mass of the test object becomes known while its gravitational down-force is left unknown.

There is a good reason that "weight" in commerce is normally used as a synonym for mass. It reduces the motivation to do gold bullion arbitrage between Singapore (g = 9.7806 m/s²) and Helsinki (g = 9.825 m/s²) at a nominal profit of $344.52 per kg.