Is it possible to measure SQRT(2) kg with a scale?

[littlemathquark]

Homework Statement

İs it possible to measure $\sqrt{2}$ kg with a scales?

Relevant Equations

None

Because of $\sqrt{2}$ be a irational numbers I think it is impossible and there is no scales that can measure irational quantity. May be approximately. But 2 kg can be measurable. İt is my efforts and thougts.

 

[kuruman]

Because of $\sqrt{2}$ be a irational numbers I think it is impossible and there is no scales that can measure irational quantity. May be approximately. But 2 kg can be measurable. İt is my efforts and thougts.

It's impossible, but not because the number is irrational. To what accuracy do you propose that this measurement be made? Any measurement is impossible to make beyond a given accuracy.

 

[pines-demon]

I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of $\sqrt{2}$ units.

 

[kuruman]

I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of $\sqrt{2}$ units.

I repeat, to what accuracy?

 

[pines-demon]

I repeat, to what accuracy?

As good as your square is. If you make it really straight, thermal fluctuations may average any irregularity out.

Edit: What you are not allowed to do is take a regular scale and try to find $\sqrt{2}$ units in that scale.

 

[PeroK]

It's impossible, but not because the number is irrational. To what accuracy do you propose that this measurement be made? Any measurement is impossible to make beyond a given accuracy.

If it's impossible for $\sqrt 2$, then it's impossible for any number. Every measurement has a margin of error.

 

[PeroK]

Edit: What you are not allowed to do is take a regular scale and try to find $\sqrt{2}$ units in that scale.

I don't see why not. You use your trick to get a length of $\sqrt 2$ and then use that on a scale.

 

[Orodruin]

I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of $\sqrt{2}$ units.

No it doesn’t. You have an object that is $\sqrt 2$ units within the errors of your construction.

As good as your square is. If you make it really straight, thermal fluctuations may average any irregularity out.

On the contrary. Thermal fluctuations add to the construction error.

If it's impossible for $\sqrt 2$, then it's impossible for any number. Every measurement has a margin of error.

obviously…

 

[kuruman]

On the contrary. Thermal fluctuations add to the construction error.

There is also thermal expansion.