B What is Mass?

[AxisCat]

TL;DR Summary

Best Way to Understand What Mass is?

Like the title says, I am really struggling to have an intuitive understanding of what mass is. I know how silly that statement is as I consider myself to be a fairly smart guy. It started as I was working through some fluid dynamic equations for water flow through pipes and such. Being a HVAC contractor I am required to do some basic calculations for sizing pumps and piping. Mostly just using Bernoulli's equation.

But it occurred to me that I just really don't have a firm grasp on what mass is. Mass is very fundamental to how the equations describe the nature of fluid flow. And even if not directly used as a unit it is buried in the other units I solve for feet, pounds and the like. For whatever reason I have an intuitive feel to what weight is, like I know when I pick something up i can say, yup.... that weighs about 25 lbs. And I am very aware of the difference between weight and mass. It is hard to explain.

I have read all the definitions both metric and imperial. I live in the imperial world of units so I just glossed over the metric definition. And it just seems like mass is a circular definition. Force, gravity, slugs, acceleration; I can memorize the definitions but honestly don't have a clear understanding. I am a visual person and just can't 'see' it.

If you have ever watched the movie Idiocracy; the scene when they are discussing what plants crave. Brawndo's got what plants crave: It's got electrolytes! But what are electrolytes? And the one dude raises his hand and says its whats Brawndo has. Because it has electrolytes!! I probably screwed up how that went but it was hilarious. When I first watched that move years ago I never thought it would almost become prophetic in certain ways.

So I am beginning to think mass is just made up of electrolytes.......

 

[PeroK]

In classical physics, like fluid mechanics, mass is the amount of a substance. Its main characteristic is that the more massive an object, the more force it takes to accelerate it at some fixed rate.

Each substance has a certain amount of mass per unit volume. Water has a mass of 1kg per liter at some standard temperature.

It's true that in Newton's second law mass and force tend to be defined together. But, that shouldn't cause any conceptual difficulty.

It's also true that if you delve into fundamental physics, mass can be a slippery concept. But that shouldn't affect your understanding at a macroscopic level.

 

[berkeman]

Paging @russ_watters for an HVAC perspective on this question...

 

[TensorCalculus]

I'm not some kind of expert, just a student, but I've always liked to think of mass as a measure of an object's inertia (i.e. a measure of it's reluctance to change its current state it's in) - for example objects with higher mass require more force to achieve the same acceleration as something with less mass. It's not particularly technical but it does feel somewhat intuitive, at least for me.
Just imagine a 100000kg cube - it's got a lot of mass, so when you try to push it or change it's current state, you can't - not without something that can apply a lot of force to it. On the contrary, a 1kg cube doesn't take a huge effort to push - it doesn't have that much mass.

 

[symbolipoint]

In classical physics, like fluid mechanics, mass is the amount of a substance. Its main characteristic is that the more massive an object, the more force it takes to accelerate it at some fixed rate.

Each substance has a certain amount of mass per unit volume. Water has a mass of 1kg per liter at some standard temperature.

It's true that in Newton's second law mass and force tend to be defined together. But, that shouldn't cause any conceptual difficulty.

It's also true that if you delve into fundamental physics, mass can be a slippery concept. But that shouldn't affect your understanding at a macroscopic level.

Maybe this is just a feeling, but a thing or an idea like "mass" is something like one of those undefined "primitive notions" in Geometry like "point",?

 

[jbriggs444]

Intuitively, I agree with the idea expressed by @TensorCalculus. Mass is a number that quantifies an object's resistance to acceleration. To make this work, we can adopt the notions of "force", "distance" and "time" as primitive concepts and "mass" as a derived concept.

So $\sum F = ma$ can be thought of as defining mass in terms of force and acceleration.

It turns out to be hard to create a reproducible standard of force without referencing mass or acceleration. So we normally treat mass as primitive and force as derived instead.

Significantly, as @PeroK points out, the mass of a substance is proportional to how much of that substance you have. Two bricks glued together have twice the mass of either brick separately. 7.5 liters of water has 7.5 times the mass of one liter of water.

Under Newtonian mechanics it is something of a miracle that the force of gravity is proportional to mass. General relativity provides clarification for this -- both passive gravitational mass and inertial mass are just Newton's second law in action. [Active gravitational mass turns into part of the stress-energy tensor. Which under every day circumstances is dominated by rest energy which is in turn another name for invariant mass]

In commerce we have historically used passive gravitational mass as a measure for "amount of substance". This is how balance scales work. This practice continues to the present day. Products are normally labelled by passive gravitational mass. Usually in grams and kilograms.

 

[gmax137]

Those with a philosophical or historical bent may like
Concepts of Mass in Classical and Modern Physics, by Max Jammer
(https://en.wikipedia.org/wiki/Max_Jammer)

It's been a long time since I read this book. I may have to give it a re-read...

 

[256bits]

TL;DR Summary: Best Way to Understand What Mass is?

Force, gravity, slugs, acceleration;

The slug is not a common unit expressed in everyday language with those using the imperial system.
The would be the reason for the difficulty - unfamiliar terminology.

One slug would accelerate at 1 foot per second per second when a pound force is acting on it.
On earth, a slug weighs approx 32.17405 pounds. ( where g, the acceleration of gravity 32.17405 ft/s2.

Similarly,
A pound force would accelerate a pound mass at a rate of 32.17405 ft/s2.
This form you may be more familiar with. You probably have an intuition what a 'pound' is.

Drop a pound mass on earth and it will accelerate at the rate of g, 32.17405 ft/s2.
Drop a slug (32 pound mass ), and it will accelerate at the rate of g, 32.17405 ft/s2.

So, from one pound force, a slug( 32 pound masses ) accelerates at 1 ft/s2.
Or, from one pound force, a pound mass ( 1/32 of a slug ) accelerates at 32.17405 ft/s2

 

[WWGD]

Maybe the amount of matter assuming fixed density? I smell an Infinite Regress awaiting.

 

[jbriggs444]

Maybe the amount of matter assuming fixed density? I smell an Infinite Regress awaiting.

We can compare passive gravitational masses with a balance. Archimedes knew how to measure volume.

 

[cianfa72]

It's true that in Newton's second law mass and force tend to be defined together. But, that shouldn't cause any conceptual difficulty.

I'd advise to take a look at Feynman's discussion about force and mass.

Namely, according Feynman, force is supposed to have some independent properties, that were not completly described by Newton himself. Just in the specific case of gravitation, Newton gave the complete law. Another property forces have is given by Newton's third law.

 

[WWGD]

We can compare passive gravitational masses with a balance. Archimedes knew how to measure volume.

It may not be a necessary way or the only way of doing so, but I believe it works nonetheless.

 

[Lnewqban]

It started as I was working through some fluid dynamic equations for water flow through pipes and such. Being a HVAC contractor I am required to do some basic calculations for sizing pumps and piping. Mostly just using Bernoulli's equation.

For that purpose, volume, pressure and temperature of the fluid are parameters easier to measure with normal instruments than its mass.

Mass is the number of reference for your thermal and flow calculations.

In any closed-loop hydronic system, mass (number of molecules) is conserved, regardless changes in the temperature, velocity and pressure of the flow.

The pumps transfer mechanical energy from a motor into the mass of the fluid, rather than to its volume.

Mass is what absorbs or releases heat at the coils.

Please, see:
https://www.engineeringtoolbox.com/mole-d_1255.html

https://www.engineeringtoolbox.com/fluid-mechanics-equations-d_204.html

https://plumbingandhvac.ca/simplified-math-behind-hydronics/

 

[AxisCat]

I am overwhelmed with the replies to my question. Thank you to everyone that contributed their insight. I am going to take some time and reread through all of this; I am probably just making it harder than it really is.

 

[WWGD]

Just let Catholic priests decide between them, I say!

 

[berkeman]

Just let Catholic priests decide between them, I say!.

Took me a couple beats to get it...

 

[jtbell]

Just let Catholic priests decide between them, I say!.

An appropriate response on St. Patrick's Day.

 

[Andrew Mason]

Newton could have defined "mass" of a free body as the applied force divided by its resulting acceleration. But defining "mass" as "inertia" in that sense would be circular, as force is defined by change in quantity of motion per unit time and quantity of motion is mass multiplied by change in velocity.

Newton's definition contained in his 1687 Principia Mathematica was:
"DEFINITION I.
The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. ... It is this quantity that I mean hereafter everywhere under the name of body or mass."

Newton's concept of matter was that all matter was made up of different arrangements of the same fundamental constituent units, each having the same inertia. This was why he was fascinated with alchemy - he thought that if one could just re-arrange those little fundamental units one could turn iron into gold! (He was right of course. It is just that you need to process them inside of a Supernova).

So for Newton, mass was just a measure of the quantity of matter - the number of these fundamental particles contained in a body. Newton's insight was remarkable. If you think of nucleons being Newton's fundamental particles the mass of a substance is, to a very close approximation, determined by the number of nucleons it contains.

AM

 

[cianfa72]

Newton could have defined "mass" of a free body as the applied force divided by its resulting acceleration. But defining "mass" as "inertia" in that sense would be circular, as force is defined by change in quantity of motion per unit time and quantity of motion is mass multiplied by change in velocity.

I like the viewpoint from Feynman: the force is an independent concept having some properties. Then experimentally turns out that for a given body in any inertial frames the ratio between applied force and coordinate acceleration is always the same and doesn't change across inertial frames (i.e. it results to be frame invariant). That constant/invariant ratio actually defines the body's inertial mass.

 

[A.T.]

But defining ... would be circular

So what? Physics has no problem postulating several related entities like:
- Charge is what is affected by electric fields.
- Electric fields are what affects charge.

As long the quantitative predictions are right, it doesn't matter what is defined in terms of what. And doesn't matter if the definitions seem "circular", because such related definitions only make sense together, stated simultaneously. They don't have to chronologically build on each other, with some being more "fundamental" than the others.

 

[PeroK]

Newton could have defined "mass" of a free body as the applied force divided by its resulting acceleration. But defining "mass" as "inertia" in that sense would be circular, as force is defined by change in quantity of motion per unit time and quantity of motion is mass multiplied by change in velocity.

Newton's definition contained in his 1687 Principia Mathematica was:
"DEFINITION I.
The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. ... It is this quantity that I mean hereafter everywhere under the name of body or mass."

Newton's concept of matter was that all matter was made up of different arrangements of the same fundamental constituent units, each having the same inertia. This was why he was fascinated with alchemy - he thought that if one could just re-arrange those little fundamental units one could turn iron into gold! (He was right of course. It is just that you need to process them inside of a Supernova).

So for Newton, mass was just a measure of the quantity of matter - the number of these fundamental particles contained in a body. Newton's insight was remarkable. If you think of nucleons being Newton's fundamental particles the mass of a substance is, to a very close approximation, determined by the number of nucleons it contains.

AM

So, how is the mass of a fundamental particle defined? If you were stuck defining a dollar, then defining it as one hundred cents doesn't address the issue of defining what money is.

 

[Andrew Mason]

So what? Physics has no problem postulating several related entities like:
- Charge is what is affected by electric fields.
- Electric fields are what affects charge.

It’s not particularly insightful to define mass as inertia. Newton understood that there was a relationship between gravity and inertia. If he had defined mass as inertia he would need a different definition for mass as the source of gravity. So he defined mass to be something that was common to both gravity and inertia: quantity of matter.

Newton concluded that the inertia of inertia units was additive and the gravitational effect of gravity units was additive. (In fact, it turns out that he was wrong - close though). And so he postulated that gravitational effects and inertial effects are proportional to the same thing: mass, being the quantity of fundamental units of matter.

It was not obvious that gravitational effects and inertial effects of matter should be proportional to the same thing. But that was Newton’s theory based on observation. So far, no one has shown that he was wrong.

AM

 

[Andrew Mason]

So, how is the mass of a fundamental particle defined? If you were stuck defining a dollar, then defining it as one hundred cents doesn't address the issue of defining what money is.

The mass of a basic unit would be one kilogram divided by the number of such units in a kilogram. The problem Newton had was that he did not know that that basic unit was.

At the time, it was by no means obvious that all matter consisted of the same basic units. Gold was dense and had other properties that bore no resemblance to air or water. But all matter had inertial and gravitational properties. What was it that made a handful of gold have more inertia and gravity than a handful of feathers?

Newton’s theory was that at some level all matter consisted of the same basic units in different configurations, and each unit possessed the same inertial and gravitational properties. The differences between bodies in their inertial/gravitational properties then was simply explained as differences in the number of these fundamental matter units they contained. That number - the quantity of matter as Newton called it - determined its “mass”.

AM

 

[Herman Trivilino]

Think of the previous definition of the kilogram. We measure the mass of something by comparison to something with the mass of one kilogram. The most precise way to do the comparison is still by use of a balance pan.

I'm sure there's an equivalent way of doing it with the new definition, but it's convoluted.

Anyway, what I'm describing is an operational definition, which is the best that physics can do for you.