Measuring Mass without Newton's Law: Possible?

  • Context: Undergrad 
  • Thread starter Thread starter ravikannaujiya
  • Start date Start date
  • Tags Tags
    Law Mass Newton's law
Click For Summary
SUMMARY

This discussion centers on the measurement of mass without relying on Newton's laws of motion. Participants highlight that mass can be measured using a balance scale, which operates on the principle of comparing gravitational forces without directly invoking Newton's laws. The conversation also touches on the concept of operational definitions, particularly in the context of SI units, where mass is defined in terms of the kilogram. Ultimately, it is established that while traditional methods like balance scales are effective, they do require a uniform gravitational field for accurate measurements.

PREREQUISITES
  • Understanding of balance scales and their operation
  • Familiarity with the concept of gravitational force
  • Knowledge of operational definitions in physics
  • Basic principles of mass measurement and SI units
NEXT STEPS
  • Research the principles of balance scales and their applications in different gravitational fields
  • Explore operational definitions in physics and their implications for measurement
  • Study the differences between inertial mass and gravitational mass
  • Investigate alternative methods for measuring mass in microgravity environments
USEFUL FOR

Physicists, educators, and students interested in the fundamental concepts of mass measurement, as well as those exploring alternatives to Newtonian mechanics in experimental physics.

ravikannaujiya
Messages
38
Reaction score
0
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.
 
Physics news on Phys.org
Why do you believe that such an example might exist?
 
because mass is a fundamental quantity so we must have a way to measure it irrespective of knowledge of force.
 
You can use a balance scale.
 
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.
 
MohammedRady97 said:
(this is called an operational definition)

What makes you sure that this is a definition for mass?
 
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?
 
ravikannaujiya said:
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.
 
jbriggs444 said:
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?
 
  • #10
DrStupid said:
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.
 
  • #11
jbriggs444 said:
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

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

This applies to all objects.
 
  • #12
ravikannaujiya said:
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.

ravikannaujiya said:
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.
 
Last edited:
  • Like
Likes   Reactions: jbriggs444
  • #13
DrStupid said:
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.
 
  • #14
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?
 
Last edited:
  • #15
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.
 
Last edited:
  • #16
MohammedRady97 said:
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.
 
  • #17
DaleSpam said:
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.
 
Last edited:
  • #18
ravikannaujiya said:
so, here we have relative scale to measure mass using gravity
Yes. Wasn't that what you wanted?

ravikannaujiya said:
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.
:rolleyes: 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:
  • #19
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
ravikannaujiya said:
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.

ravikannaujiya said:
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.
 
Last edited:
  • #21
ohk.. thanks.
 
  • #22
officialmanojsh said:
Mass is nothing but calculation of amount of matter present in a body.

What do you mean with "amount of matter"?
 

Similar threads

Undergrad Newton's 2nd Law confusion: mass times acceleration is not a force?
  • · Replies 39 ·
2
Replies
39
Views
3K
High School Inertial Mass vs Gravitational Mass
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Are Newton's Laws just definitions?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Spring balance analysis from a system point of view
  • · Replies 24 ·
Replies
24
Views
2K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
  • · Replies 0 ·
Replies
0
Views
2K
High School Newton’s second law as one complete law
  • · Replies 27 ·
Replies
27
Views
2K
Undergrad Extending Newton's laws -- Is the concept of force still defined?
  • · Replies 35 ·
2
Replies
35
Views
5K
Undergrad Newton's Third Law: Action & Reaction Along the Line Connecting Two Objects
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Covariance of Newton's 2nd Law under Galilean boosts
  • · Replies 38 ·
2
Replies
38
Views
5K
Undergrad Newton's second law for rotations
  • · Replies 9 ·
Replies
9
Views
1K