# Mass and Newton's Law

1. May 9, 2015

### 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.

2. May 9, 2015

### Staff: Mentor

Why do you believe that such an example might exist?

3. May 9, 2015

### ravikannaujiya

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

4. May 9, 2015

### Staff: Mentor

You can use a balance scale.

5. May 9, 2015

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.

6. May 9, 2015

### DrStupid

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

7. May 9, 2015

### 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?

8. May 9, 2015

### jbriggs444

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

9. May 9, 2015

### DrStupid

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

10. May 9, 2015

### jbriggs444

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

11. May 9, 2015

### DrStupid

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

This applies to all objects.

12. May 9, 2015

### Staff: Mentor

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.

Last edited: May 9, 2015
13. May 9, 2015

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

14. May 9, 2015

### 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)
Mass-energy (also you have ruled out)
I'm not sure where we go from here. Is there a fifth option?

Last edited: May 9, 2015
15. May 9, 2015

### Staff: Mentor

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?

Last edited: May 9, 2015
16. May 9, 2015

### DrStupid

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.

17. May 10, 2015

### ravikannaujiya

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.

Last edited: May 10, 2015
18. May 10, 2015

### Staff: Mentor

Yes. Wasn't that what you wanted?

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).

Last edited: May 10, 2015
19. May 10, 2015

### 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).

20. May 10, 2015

### Staff: Mentor

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.

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.

Last edited: May 10, 2015