# the definition of mass

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What is the definition of mass??

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Well in classical physics ie mechanics mass is the constant of proportionality that connects force or momentum and velocity.

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As for the second law of Newton's dynamics:

"The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass of the body."

The mass is the "quantity of matter" in a body, and in classical physics is assumed to be constant. Therefore, we can write this relation for the second law of dynamics:

$\vec{F}=k\vec{a}$

Or, rather

$\vec{F}=m\vec{a}$

Where m is the mass, a scalar and constant quantity.

Edited by Ityrus

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As for the second law of Newton's dynamics:

"The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass of the body."

The mass is the "quantity of matter" in a body, and in classical physics is assumed to be constant. Therefore, we can write this relation for the second law of dynamics:

$\vec{F}=k\vec{a}$

Or, rather

$\vec{F}=m\vec{a}$

Where m is the mass, a scalar and constant quantity.

What is the quantity of matter

Well in classical physics ie mechanics mass is the constant of proportionality that connects force or momentum and velocity.

What is momentum

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here's something i came across a time ago,

mass

physics- physical quantity: the property of an object that is a measure of its inertia, the amount of matter it contains, and its influence in a gravitational field.

quantity

amount: an amount or number of something

physics- particular magnitude of something: the product of a measurable phenomenon such as electric current or radiation intensity and the time during which the phenomenon is measured

magnitude

greatness of size: greatness of size, volume, or extent

mathematics- number assigned to mathematical quantity: a numerical value that describes the amount of something, usually expressed in terms of a multiple of standard units, or the item measured in this way

dilation

expanding of something: the act or process of widening or being widened, enlarging or being enlarged, or stretching or being stretched

expanded condition: a condition in which something is widened, enlarged, or stretched

expanded thing: something, especially a part of something else, that has become widened, enlarged, or stretched

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here's something i came across a time ago,

mass

physics- physical quantity: the property of an object that is a measure of its inertia, the amount of matter it contains, and its influence in a gravitational field.

quantity

amount: an amount or number of something

physics- particular magnitude of something: the product of a measurable phenomenon such as electric current or radiation intensity and the time during which the phenomenon is measured

magnitude

greatness of size: greatness of size, volume, or extent

mathematics- number assigned to mathematical quantity: a numerical value that describes the amount of something, usually expressed in terms of a multiple of standard units, or the item measured in this way

dilation

expanding of something: the act or process of widening or being widened, enlarging or being enlarged, or stretching or being stretched

expanded condition: a condition in which something is widened, enlarged, or stretched

expanded thing: something, especially a part of something else, that has become widened, enlarged, or stretched

What is matter

What is a number of something

What is greatness of something

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What is matter

What is a number of something

What is greatness of something

seriously ??

edit-

ahh i see what you are doing here..

Edited by krash661

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What is matter

What is a number of something

What is greatness of something

Are you just trying to be obnoxious? In classical physics, mass is the constant of proportionality relating how much an object accelerates to how much net force was applied to it. On Earth, the easiest way to determine the mass of something would be to place it on a scale (measure its weight), then divide by the acceleration due to gravity at Earth's surface which is ~9.8 m/s2. If you don't have the luxury of being able to measure something's weight (if you're in orbit around a planet, in deep space, etc.), then I suppose the next easiest way to determine mass is to attach the object to the end of a spring with known spring constant, then set it into simple harmonic motion. If you measure its period to good accuracy, then its mass is $m=T^2 k /4 \pi^2$.

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Are you just trying to be obnoxious? In classical physics, mass is the constant of proportionality relating how much an object accelerates to how much net force was applied to it. On Earth, the easiest way to determine the mass of something would be to place it on a scale (measure its weight), then divide by the acceleration due to gravity at Earth's surface which is ~9.8 m/s2. If you don't have the luxury of being able to measure something's weight (if you're in orbit around a planet, in deep space, etc.), then I suppose the next easiest way to determine mass is to attach the object to the end of a spring with known spring constant, then set it into simple harmonic motion. If you measure its period to good accuracy, then its mass is $m=T^2 k /4 \pi^2$.

I did not ask : How we measure mass ,but how we define mass

Howevetr if we define mass as the constant of proportionality connecting force and accelaration,then i will ask you what is force or accelaration.

Then you will say : force is the product of mass accelaration .That will lead us into a never ending cycle,because then i will ask you what is mass

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I did not ask : How we measure mass ,but how we define mass

I did define it.

Howevetr if we define mass as the constant of proportionality connecting force and accelaration,then i will ask you what is force or accelaration.

Then you will say : force is the product of mass accelaration .That will lead us into a never ending cycle,because then i will ask you what is mass

No, that is not how I will define force, and that's not how Newton defined it either. Newton gave F=ma as an equation of motion, not a definition of force. He defined force as a quantifiable "push or pull," and he gave an example of a force: gravitation. The Lorentz force is another example. F=ma is not, nor has it ever been, a definition of force. Acceleration is absurdly simple to define: the time derivative of velocity.

Before we continue, I think we deserve to know what point you're trying to make. Because you're coming across as an obnoxious troll who just wants to argue for the sake of arguing. It's clear you didn't come hear because you were confused and wanted clarification, you came here to be annoying.

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I did define it.

No, that is not how I will define force, and that's not how Newton defined it either. Newton gave F=ma as an equation of motion, not a definition of force. He defined force as a quantifiable "push or pull," and he gave an example of a force: gravitation. The Lorentz force is another example. F=ma is not, nor has it ever been, a definition of force. Acceleration is absurdly simple to define: the time derivative of velocity.

Before we continue, I think we deserve to know what point you're trying to make. Because you're coming across as an obnoxious troll who just wants to argue for the sake of arguing. It's clear you didn't come hear because you were confused and wanted clarification, you came here to be annoying.

iN an axiomatic development we have the udefined or primitive concepts.

For example in Modern Geometry the primitive or undefined concepts are: point ,line,on,between,congruent.

So in an axiomatic development of Newtonian Physics i was trying to establish what are the primitive concepts .

Is mass one of the undefined concepts??

In your definition of force what is a pull or push??

Notiice in any definition if we do not have some udefined concepts the definition is worthless

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In post#1 you asked as short specific question without qualification.

What is the definition of mass

This seems a serious question and four members, including myself, took your question in that vein and responded seriously.

You responded to each member in such a way as to make them believe your original intent was facetious.

So far this process has been pretty counterproductive and we have reached your post#11.

I am going to take post#11 as serious and supplying some of the missing context.

There are two concepts of mass in classical physics.

Gravitational mass as used in Newton's law of gravitation.

Inertial mass as generally so far offered here.

On of the deep questions of physics is to understand the reason that these two concepts coincide.

Engineers don't bother to worry as to why they just attach constants to make bring about this coincidence.

If you want an introductory discussion of this issue in modern physics both classical and relativistic/quantum, look at

The lightness of Being by Frank Wilczek.

The book is largely about the subject of mass in physics.

If you want a good pragmatic development of inertial mass look at

The Mechanics of Flight by A.C. Kermode, OBE

Which developes the use of mass as the constant in Newton's laws.

If you would like to post further details of your viewpoint classical or relativistic/quantum we can discuss the matter further.

Yes you are correct you need to establish some givens to develop a formal system of mechanics.

One of these concerns motion, which necessitates the concepts of space and time.

The concept of a body brings in the issue of what is moving and leads to mass amongst other properties.

Formal mathematics eg time derivatives are also permissible.

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In classical physics there are two kinds of mass;

Inertial mass- "a measure of an object's resistance to acceleration". This is the mass in $F=ma$.

Newtonian gravitational mass- "the property that allows bodies to interact gravitationally". This is the M and m in $F = -G mM/r^{2}$. Or in terms of gravitational potential $V= -m G/r$.

It turns out that to be best of our knowledge, these two species of mass are the same. This is the weak equivalence principle.

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I'll assume that we are talking about classical physics so far.

Newton's 2nd law says that there is a constant proportion between the force on an object and its acceleration. The acceleration of an object can be defined easily; force isn't quite so simple. The third law gives us a better idea of force; it says that any force on one object from another is balanced by an opposite force on another object. Put that with the first law, and we get that the total force on all objects is 0.

Put all together, and what we get out is that Newton's three laws are equivalent to the following statement: that there is a constant of proportionality for each object (which we call mass) such that the sum of the velocities of each object multiplied by that constant is conserved over time. That gives us a definition of mass, based on a position function over time.

=Uncool-

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I think it's all been said in this thread so far.

But something which never ceases to amaze me is that scientists like Newton, Gallileo etc came up with some of these concepts like mass, force and so on from first principles. They must have had extraordinary insight, especially for the time, which is of course a mark of their genius.

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They must have had extraordinary insight, especially for the time, which is of course a mark of their genius.

Indeed. What is also very pleasing is that the notion of mass, either inertial or gravitational, is a measure of the "amount of stuff", which is really should be our intuative feeling about any notion of "mass".

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Indeed. What is also very pleasing is that the notion of mass, either inertial or gravitational, is a measure of the "amount of stuff", which is really should be our intuative feeling about any notion of "mass".

Yes. The interesting thing too is that we can define mass and say quite a lot about what it does, how it behaves etc., but not really what it actually is. In fact maybe the concept of what something actually is is meaningless. Maybe this is an apocryphal story but I seem to recall reading that Newton was asked what is gravity to which he replied he had no idea.

Edited by Griffon

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iN an axiomatic development we have the udefined or primitive concepts.

For example in Modern Geometry the primitive or undefined concepts are: point ,line,on,between,congruent.

So in an axiomatic development of Newtonian Physics i was trying to establish what are the primitive concepts .

Is mass one of the undefined concepts??

!

Moderator Note

If that's the question you want to ask, then admit that this is the question you want to discuss. Because, as has been observed, the tactic of moving the goalposts comes off as troll-ish

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iN an axiomatic development we have the udefined or primitive concepts.

For example in Modern Geometry the primitive or undefined concepts are: point ,line,on,between,congruent.

So in an axiomatic development of Newtonian Physics i was trying to establish what are the primitive concepts .

Hilbert's 6th problem, they call that.

The first set of primitives come from geometry, so, point, line, and plane would be primitives in mechanics as well. The rest you can get from this link. I'm sure mass and time are two.

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The interesting thing too is that we can define mass and say quite a lot about what it does, how it behaves etc., but not really what it actually is.

But I would say that this not really any different to other concepts in physics. You have a physical concept, that you will have to put into the langauge of mathematics or even the concept fell out of the mathematics. You then see it this has a clear interpretation, which hopefully ties into to your intuative idea of the original physical concept.

Mass is a good example of this, but it is not teh only concept like this.

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Mass is pretty much everything that can be sized down to particles or is a particle. You can use F=m*a to get mass: m=F/a

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Mass is pretty much everything that can be sized down to particles or is a particle. You can use F=m*a to get mass: m=F/a

Well, classically you like to think of particles as point masses, but we know that there are particles with zero mass, the photon. But yes, m = F/a is the definition of inertial mass.

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But yes, m = F/a is the definition of inertial mass.

Don't you think that a definition that admits the possibility of division by zero is kinda worrying?

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Don't you think that a definition that admits the possibility of division by zero is kinda worrying?

Really we should view the mass as the constant of proportionality between the force and acceleration for a point mass. If a=0 then F=0 also, so we cannot say anything about the mass. So, okay we should make the proviso that a is not equal to zero if we want to make this a proper definition.

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What's the mass of a quark?

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