Measuring Mass without Newton's Law: Possible?

[ravikannaujiya]

Hi! I have been searching for examples where mass can be measured without using Newton's law but I could not find one. Please explain, can we measure mass without using Newton's laws? How?
PS: please don't explain using mass energy equivalence.

 

[Nugatory]

Why do you believe that such an example might exist?

 

[ravikannaujiya]

because mass is a fundamental quantity so we must have a way to measure it irrespective of knowledge of force.

 

[Dale]

You can use a balance scale.

 

[PFuser1232]

If you attach a mass $m_1$ to a spring on a horizontal surface, stretch the spring by a certain amount, let go, measure the acceleration $a_1$, then do the same for mass $m_2$, it is an experimental fact that $m_1 a_1 = m_2 a_2$.
You can therefore pick any arbitrary mass and measure other masses in terms of that mass using the procedure outlined above (this is called an operational definition).
In the case of the SI units, we express mass in terms of kilograms. What's a kilogram? Well, the kilogram is the hunk of metal kept in Sèvres, France.

 

[DrStupid]

(this is called an operational definition)

What makes you sure that this is a definition for mass?

 

[ravikannaujiya]

Balances use concept of gravitation force that's why pointer of a balance tilts towards the object with greater mass and it is not a universal instrument for the measurement of mass (as it doesn't work in space or in free fall). m1a1=m2a2. doesn't it smell like Newton's law. Let me reframe the question... can we measure mass of an object without changing its state of motion as the time we change the state of motion we get the idea of force?

 

[jbriggs444]

Balances use concept of gravitation force that's why pointer of a balance tilts towards the object with greater mass and it is not a universal instrument for the measurement of mass (as it doesn't work in space or in free fall). m1a1=m2a2. doesn't it smell like Newton's law. Let me reframe the question... can we measure mass of an object without changing its state of motion as the time we change the state of motion we get the idea of force?

We could (in principle) measure its active gravitational mass: Hold it steady and see how strongly it attracts nearby objects.

 

[DrStupid]

We could (in principle) measure its active gravitational mass: Hold it steady and see how strongly it attracts nearby objects.

How do you measure the attraction of nearby objects without using forces or changing their state of motion?

How about measuring the gravitational redshift or time dilation instead?

 

[jbriggs444]

How do you measure the attraction of nearby objects without using forces or changing their state of motion?

I was answering the reframed question which does not forbid us from having nearby objects move.

 

[DrStupid]

I was answering the reframed question which does not forbid us from having nearby objects move.

ravikannaujiya didn't mentioned it in his rephrased question, but he also wrote

m1a1=m2a2. doesn't it smell like Newton's law.

This applies to all objects.

 

[Dale]

Balances use concept of gravitation force that's why pointer of a balance tilts towards the object with greater mass and it is not a universal instrument for the measurement of mass (as it doesn't work in space or in free fall).

The actual gravitational force doesn't matter, as long as the field is uniform over the size of the balance. The same balance measurement will allow you to measure the mass on Earth, on the Moon, and on Jupiter despite the widely different gravitational forces involved. So a balance scale is not measuring gravitational force, it is in fact measuring mass. It does require a uniform gravitational field, but as long as the forces don't break the structure they are not important themselves.

can we measure mass of an object without changing its state of motion as the time we change the state of motion we get the idea of force?

Again, yes, use a balance scale. A balance scale is the traditional method for measuring mass.

 

[PFuser1232]

What makes you sure that this is a definition for mass?

I'm sure that's one way of defining inertial mass, according to Introduction to Mechanics by Kleppner and Kolenkow at least.

 

[Jilang]

Well,you have four choices:
Inertial Mass (which you have ruled out)
Active gravitational mass (very small so is hard to measure, though not impossible)
Passive gravitaional mass (already suggested)
Mass-energy (also you have ruled out)
I'm not sure where we go from here. Is there a fifth option?

 

[Dale]

I also think that this general approach is fairly pointless.

You can take any measurable quantity, and on personal whim decide to exclude different categories of measurement. If you keep indulging your whims then you will eventually exclude every possible measurement. You will then have a fiat "unmeasurable" quantity. So what?

In the end you learn more about your whims than about physics.

 

[DrStupid]

I'm sure that's one way of defining inertial mass, according to Introduction to Mechanics by Kleppner and Kolenkow at least.

With Galilean transformation it would be way of defining inertial mass. But with Lorentz transformation it results in something different which is not even a scalar.

 

[ravikannaujiya]

The actual gravitational force doesn't matter, as long as the field is uniform over the size of the balance. The same balance measurement will allow you to measure the mass on Earth, on the Moon, and on Jupiter despite the widely different gravitational forces involved. So a balance scale is not measuring gravitational force, it is in fact measuring mass. It does require a uniform gravitational field, but as long as the forces don't break the structure they are not important themselves.

Again, yes, use a balance scale. A balance scale is the traditional method for measuring mass.

First, if mass are different, force due to gravity is not same. Its only acceleration due to gravity is same, and that's why when we compare two masses in uniform gravitational field acceleration due to gravity cancels out from both side...so, here we have relative scale to measure mass using gravity without having the knowledge of acceleration due to gravity. When I said space I meant when object experiencing only force due to gravity, that is also the case of free fall. Balances experiences not only force due to gravity but also reaction/tension/normal (whichever kind of balance may be)from the ground (you can understand by free body diagram). So, you say, we can use balance to measure mass in free fall.

 

[Dale]

so, here we have relative scale to measure mass using gravity

Yes. Wasn't that what you wanted?

When I said space I meant when object experiencing only force due to gravity, that is also the case of free fall. Balances experiences not only force due to gravity but also reaction/tension/normal (whichever kind of balance may be)from the ground (you can understand by free body diagram). So, you say, we can use balance to measure mass in free fall.

OK, I could have worded my post more precisely. I should have specified that the scale should be at rest in the uniform field. That doesn't change the point that this is a measurement of mass (passive gravitational mass specifically).

 

[ravikannaujiya]

yes I want that but not on the expanse of changing the state of motion and it only works in presence of gravity. However, thank you very much guys for replying, I think I got my answer.
We cannot measure mass in Newton's laws without changing the state of motion of an object. and its almost given in the definition itself. as the reasoning goes:
Mass is a measurement of inertia.
Inertia is a tendency to resist a change in state of motion of an object.
So, if there is no change in state of motion, we would not observe any tendency to resist its state of motion.
so, we don't measure inertia (mass).

 

[Dale]

We cannot measure mass in Newton's laws without changing the state of motion of an object.

Sure we can. I gave you an example of a standard way to measure mass where the object is at rest and remains at rest so the state of motion is unchanged. You may choose to ignore that example on a whim, but that is your whim and not physics.

Mass is a measurement of inertia.

That is not all mass is, as was pointed out above by Jilang. Mass is also the source of gravitation, the thing affected by gravitation, and a measure of the energy of an object at rest.

Obviously, you cannot measure the a in F=ma without changing the state of motion, but you can measure the m. Not that this fact has any importance.

 

[ravikannaujiya]

ohk.. thanks.

 

[DrStupid]

Mass is nothing but calculation of amount of matter present in a body.

What do you mean with "amount of matter"?