# Mass vs Mass as a Force (Weight)

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Apparently, we exist in a paradigm (the "everyday world') wherein pounds and kilograms are assumed to refer to "weight". Numbers are given units of "lb" or "kg" without distinction. Why that is so is irrelevant to the practical problem solver. It may be incorrect terminology, but we seem to be stuck with the terminology.

Therefore, it seems that the correct answer to the confusion would be in the form of a question to be asked before attempting to solve a problem. It would be something like: "Is that a unit of weight or mass?"
The proper distinction is not between weight and mass. It is between force and mass. Outside the physics classroom, the term "weight" can be ambiguous.

The kilogram is always a unit of mass.

In the physics classroom, "weight" is a force -- the [apparent] local force of gravity on an object. In the grocery store, "weight" is a mass. Products sold by "weight" are officially labelled in units of mass. On the bathroom scales we do not distinguish between force and mass. Whether our "weight" is the 150 pounds force on the scale or whether it is the 150 pounds mass that we pretend that the scale is reporting does not matter. It's 150 either way. In the doctor's office, we'll use a balance scale and get our "weight" measured in pounds mass.

In the physics classroom, the pound is usually treated as a unit of force and is deprecated. In the grocery store, the pound is treated as a unit of mass. It is widely used in this manner in the U.S. When clarity is called for, the terms pound-force and pound-mass can be used for disambiguation.

Out working in the field, we do not distinguish between a stone that requires 100 pounds force to lift and a stone that has a mass of 100 pounds mass. For the practical purposes of the person moving the stone, it just doesn't matter.

Similarly, we do not stress much on whether a 15 pound line will provide 15 pounds force or will suffice to support a 15 pound mass. Or whether a 20 ton jack will provide 20 tons of force or will support a truck with a gross mass of 20 tons.

[If you are selling a truckload of grain at the elevator, you can bet that the scales will be calibrated to pay you for the grain you delivered by the ton mass rather than by the ton force. Though they may dock you for the moisture content]

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• dextercioby
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Thank you for trying to help me understand. If you will, please try to clarify the following dilemma for me:

I am asked how much force is required to accelerate 1kg to 30m/s. Do I assume the 1kg to be mass or to be weight? The calculation will be different, depending on which is used, right?

I do not like having to assume. I could give two answers, one for each case I suppose.
kg is always mass.

A very important skill I learned in first year chemistry is dimensional analysis. If you know the dimensions of everything in an equation, you have a good chance of getting the answer you are looking for.

The unit of force is the Newton. A Newton is derived from kg*m / s^2 which is the basis of F = m *a.
A unit of mass is the kilogram.
A unit of velocity is m/s.
A unit of acceleration, a, is v/s or m/s^2.

If you understand all the units in an equation, you can easily see what will fit in each spot. This also allows you to derive other equations for other problems.

So, if F = m * a, then the units will look like N = kg * m/s^2 or (kg*m)/s^2 = kg * m/s^2 which you can easily see is true. By removing the values and looking at JUST the units/dimensions, you can tell if you are using the correct ones or not.

• jbriggs444
Gold Member
Apparently, we exist in a paradigm (the "everyday world') wherein pounds and kilograms are assumed to refer to "weight". Numbers are given units of "lb" or "kg" without distinction. Why that is so is irrelevant to the practical problem solver. It may be incorrect terminology, but we seem to be stuck with the terminology.
The terminology is not incorrect. The word "weight" used in medicine and in commerce is synonymous with what a physicist calls mass. The reason it's not incorrect is because it is defined that way by law.

Quester
The terminology is not incorrect. The word "weight" used in medicine and in commerce is synonymous with what a physicist calls mass. The reason it's not incorrect is because it is defined that way by law.
Now I am confused, again! Are you telling me that 10 pounds of potatoes have a mass of 10 lbm? I thought I would have to divide the 10 pounds by 32+ to approximate the mass in lbm.

Gold Member
Now I am confused, again! Are you telling me that 10 pounds of potatoes have a mass of 10 lbm?
Yes. The pound used in the USA is, by definition, 0.453 592 37 kg.

• jbriggs444
Quester
Yes. The pound used in the USA is, by definition, 0.453 592 37 kg.
Then why do all calculations for acceleration, energy, and so forth made using pounds require that the pounds be divided by the acceleration due to gravity?

Quester
kg is always mass.

A very important skill I learned in first year chemistry is dimensional analysis. If you know the dimensions of everything in an equation, you have a good chance of getting the answer you are looking for.

The unit of force is the Newton. A Newton is derived from kg*m / s^2 which is the basis of F = m *a.
A unit of mass is the kilogram.
A unit of velocity is m/s.
A unit of acceleration, a, is v/s or m/s^2.

If you understand all the units in an equation, you can easily see what will fit in each spot. This also allows you to derive other equations for other problems.

So, if F = m * a, then the units will look like N = kg * m/s^2 or (kg*m)/s^2 = kg * m/s^2 which you can easily see is true. By removing the values and looking at JUST the units/dimensions, you can tell if you are using the correct ones or not.
It is very frustrating to not be able to get past what is "correct". I know what is correct. Even in the dark ages we learned what was called "canceling terms" or what you refer to as "dimensional analysis". What I am trying to get help with is dealing with what is "incorrect" and learning how to differentiate.

Everyone here seems to be stuck on kilograms ALWAYS meaning mass. I understand that in the scientific world. It is apparently not true in the day to day world. If 1 lb of weight is the same as 1 lbm, then why add the "m"? I thought I just learned that "lb" by itself is meaningless in the scientific world.

• weirdoguy
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https://physics.nist.gov/cuu/pdf/sp811.pdfIt is very frustrating to not be able to get past what is "correct". I know what is correct.
The problem is not what we don't know. It's what we know for sure that just ain't so.

Everyone here seems to be stuck on kilograms ALWAYS meaning mass.
Yes. Everyone here does agree on that.
I understand that in the scientific world. It is apparently not true in the day to day world. If 1 lb of weight is the same as 1 lbm, then why add the "m"? I thought I just learned that "lb" by itself is meaningless in the scientific world.
In the every day world, there are likely folks who sometimes use the kilogram as a unit of force (the kilogram-force). One need not worry much about meeting them.

The two things that you have to worry about are unit "pound" and the quantity "weight". The meaning of those are ambiguous. One needs to use context to disambiguate.

I would not say that "lb" is meaningless, exactly. It has meaning. It's just that the meaning depends on context. If you see it in the grocery store, it is a unit of mass. I hold here in my hands a bottle of ketchup with a label saying "1 lb 8 oz". That's mass.

NIST (the U.S. standards authority) is pretty good about using "lb" to mean pounds mass and "lbf" to mean pounds force. But I do not trust everyone to be that careful.

Quester
One needs to use context to disambiguate.

I would not say that "lb" is meaningless, exactly. It has meaning. It's just that the meaning depends on context. If you see it in the grocery store, it is a unit of mass. I hold here in my hands a bottle of ketchup with a label saying "1 lb 8 oz". That's mass.
Great, something concrete to discuss!

If the marking on the bottle signifies 1.5 lbm, and I want to accelerate that bottle at 20 ft/sec2, then applying f=ma, I would have to apply a force of 30 lb-ft/sec2 ? :

1.5 lb X 20 ft/sec2 = 30 lb-ft/sec2

In the old physics classes I had, the calculation would be:

1.5 lb/(32 ft/sec2) X 20 ft/sec2 = .9375 lbf

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• jbriggs444
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Great, something concrete to discuss!

If the marking on the bottle signifies 1.5 lbm, and I want to accelerate that bottle at 20 ft/sec2, then applying f=ma, I would have to apply a force of 30 lb-ft/sec2 ? :
Yes. [I share your sentiment about actual calculations versus nattering about definitions. But on to the nattering...]

To avoid confusion, there is a unit called the "poundal" which is equal to a pound(mass) foot per second. Just as you write, 30 poundals applied to 1.5 pounds mass will yield 20 ft/sec2 acceleration.

One system of engineering units uses the pound(mass), the poundal, the foot and the second. Another system of engineering units uses the slug, the pound(force), the foot and the second. Both are "coherent" systems of units in which the ##F=ma## formula works as-is.

[The poundal is about 1/32 of a pound force. The slug is about 32 pounds mass. The 32 is, of course, the standard acceleration of gravity in feet per second squared].
1.5 lb X 20 ft/sec2 = 30 lb-ft/sec2

In the old physics classes I had, the calculation would be:

1.5 lb/(32 ft/sec2) X 20 ft/sec2 = .9375 lbf
Yes.

The U.S. customary system of units (pound mass, pound force, foot, second) is not "coherent". You have to stick the acceleration of gravity into the ##F=ma## formula if you use such a system.

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I think the other confusing factor is that SI units don't actually have ANY definitions or terms about 'weight'.

Weight is not really the same as force. Weight is 'the gravitational force characteristic of a given mass on the Earth's surface'. You have to go to earlier agreements between specific countries (like 1959 between US, CA, UK, AUS, NZ) that defined the letters (not ambiguous, guys!) and meanings.

The rest of the international community did not define a unit of 'weight', thus was created the confusion. In the absence of a unit of 'weight' what does one do next. Well, the Napoelonist-metricists co-opted the kilogram as a unit of weight.

That's how I see the confusion being spawned, anyway. Feel free to tell me what the real cause was if you know it.
Any system of units has its specific choice of "base units". All other quantities are then measured by "derived units", which are defined in terms of products of powers of the base units.

Which units you choose as base units is arbitrary, but the SI has as an intrinsic constraint that the powers in the derived units should be integer. This is the reason, why in the SI we have so "unnatural" units for electromagnetism, i.e., that's why we introduce a base unit for electric charge with an additional fundamental constant fixed. In the new SI of 2019 that's the elementary charge, i.e., the charge of a proton, which has since then a fixed value when measured in the base unit unit Coulomb, C; for historical reasons in fact in the SI the unit of electrical current, Ampere (A), is the base unit and then ##1\text{C}=1 \text{A} \, \text{s}##.

The unit of force is a derived unit in the SI. For convenience one gives it a name, Newton, by defining ##1\text{N}=1 \text{kg}/(\text{m} \, \text{s}^2)##.

A weight is a force, namely the gravitational force of a body due to the presence of the Earth, measured when the body is at rest relative to the Earth at this place (and this holds also within GR, where this "force" is well defined together with the specific frame of reference defined to be at rest relative to Earth). That's why "weight" cannot be a base unit in any modern system of units, where you want utmost precision in the definition of the base units. The weight of an object not only depends on the place on Earth where you measure it but also on time since the Earth is not a fixed distribution of mass (or within GR energy, momentum and stress) and thus the gravitational field of the Earth (within GR the curvature of spacetime when you use the geometrodynamic interpretation of the gravitational field) depends on time.

• dextercioby
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Oops, . . . ## 1\;\text{N}\, = 1 \text{ kg}\,\text{m/s}^2## . . .

cmb
Any system of units has its specific choice of "base units". All other quantities are then measured by "derived units", which are defined in terms of products of powers of the base units.

Which units you choose as base units is arbitrary, but the SI has as an intrinsic constraint that the powers in the derived units should be integer. This is the reason, why in the SI we have so "unnatural" units for electromagnetism, i.e., that's why we introduce a base unit for electric charge with an additional fundamental constant fixed. In the new SI of 2019 that's the elementary charge, i.e., the charge of a proton, which has since then a fixed value when measured in the base unit unit Coulomb, C; for historical reasons in fact in the SI the unit of electrical current, Ampere (A), is the base unit and then ##1\text{C}=1 \text{A} \, \text{s}##.

The unit of force is a derived unit in the SI. For convenience one gives it a name, Newton, by defining ##1\text{N}=1 \text{kg}/(\text{m} \, \text{s}^2)##.

A weight is a force, namely the gravitational force of a body due to the presence of the Earth, measured when the body is at rest relative to the Earth at this place (and this holds also within GR, where this "force" is well defined together with the specific frame of reference defined to be at rest relative to Earth). That's why "weight" cannot be a base unit in any modern system of units, where you want utmost precision in the definition of the base units. The weight of an object not only depends on the place on Earth where you measure it but also on time since the Earth is not a fixed distribution of mass (or within GR energy, momentum and stress) and thus the gravitational field of the Earth (within GR the curvature of spacetime when you use the geometrodynamic interpretation of the gravitational field) depends on time.
Of course, but the lb isn't defined in SI, so not sure of your point, vis a vis my reference to the 1959 agreement between US/UK/CA/AUS/NZ which does. If you go to that agreement to see the definition of lb (which legally defines lb in those countries) then we might all be slightly clearer.

cmb
Everyone here seems to be stuck on kilograms ALWAYS meaning mass. I understand that in the scientific world.
This is a forum of science in 'the scientific world', hence by your own logic we might be a bit stuck on it!?

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There's nothing to discuss: The kg is a unit for mass and nothing else! If there is one merit of the SI it's that it provides very accurate and logically consistent units. For all practical purposes they are most simply to use and most appropriate to communicate about quantitative descriptions of Nature (Natural Sciences) and their applications (Engineering).

• weirdoguy
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Of course, but the lb isn't defined in SI, so not sure of your point, vis a vis my reference to the 1959 agreement between US/UK/CA/AUS/NZ which does. If you go to that agreement to see the definition of lb (which legally defines lb in those countries) then we might all be slightly clearer.
My point is that mass is mass and weight is a force due to the gravitational field of the Earth. According to Wikipedia, citing the said 1959 agreement also the pound (lb) is a unit of mass and "defined as exactly 0.45359237 kg." Case closed.

• weirdoguy
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This just seems ferociously silly. If you are a purist you can always substitute the phrase "This can weighs the same as that 1kg mass" for the phrase "this can weighs a kilogram". Problem solved.
I think I will not lose sleep over this.

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It is very frustrating to not be able to get past what is "correct". I know what is correct. Even in the dark ages we learned what was called "canceling terms" or what you refer to as "dimensional analysis". What I am trying to get help with is dealing with what is "incorrect" and learning how to differentiate.

Everyone here seems to be stuck on kilograms ALWAYS meaning mass. I understand that in the scientific world. It is apparently not true in the day to day world. If 1 lb of weight is the same as 1 lbm, then why add the "m"? I thought I just learned that "lb" by itself is meaningless in the scientific world.
A kilogram always refers to mass in the everyday world too*.

The confusion does not arise because in the day to day world 'people' use kilograms as a measure of weight, the confusion arises because because in the everyday world 'people' use the word weight when they actually mean mass.

When the doctor says 'you need to reduce your weight' he doesn't expect you to achieve this by taking the elevator/lift down a few floors or taking up space flight. When you buy 5 pounds of potatoes you make sure the shopkeeper waits for the scales to settle after tossing the potatoes in, rather than accepting the greater weight of the potatoes as they decelerate in the pan.

* Edit: I can think of one example where this is not the case: ropes and other lifting equipment are almost always specified in kg (or tonnes): there is obviously a safety issue here: it would be easy to think that a 1000N sling was 10 times as strong as it actually is.

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• Digcoal
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the greater weight of the potatoes as they decelerate in the pan.
There is another layer of complexity lurking beneath this remark. Does the "weight" of the potatoes refer to the downward force of gravity on those potatoes, to the support force required to keep them at rest in the grocery store frame or to the support force currently provided by the pan?

Personally, I usually go for the "support force required to keep them at rest in the lab frame" and sometimes qualify "weight" as the local apparent force of gravity.

* Edit: I can think of one example where this is not the case: ropes and other lifting equipment are almost always specified in kg (or tonnes): there is obviously a safety issue here: it would be easy to think that a 1000N sling was 10 times as strong as it actually is.
When it comes to elevator safety margins (typically about a factor of 11), a discrepancy of plus or minus 0.5 percent for the delta between local g and standard g is probably down in the noise. I agree that familiar units (e.g. the kilogram) are preferable to unfamiliar ones (e.g. the Newton) in such a case.

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Ironically, even if basic physics knowledge of mechanics, electricity and thermodynamics was needed to enter a medical school (in my native country, but perhaps in other countries as well), all forms and medical parlance use the word "weight" in the documents to be completed by the general public. That is because there is probably a law/regulation somewhere which states that people need to provide their known weight in kilograms/pounds, because the general public is assumed to be too uneducated to recognize that the weight is really a force (measured in Newtons or lbf), while kilograms/pounds could only refer to a mass (rest mass, but that's taking it to extremely pedantic).

So all of this apparent or real confusion, and threads such as these here, and other places on the internet, because people are assumed not to have studied basic physics and pre-High school or HS. Assumption of ignorance.

I am deeply passionate about linguistics in general, and etymology and grammar, in particular. Also in this domain, it is said that the less educated dictate how a language is developing. This saddens me, really.

• Digcoal
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##\ ##

• Digcoal
Digcoal
Ironically, even if basic physics knowledge of mechanics, electricity and thermodynamics was needed to enter a medical school (in my native country, but perhaps in other countries as well), all forms and medical parlance use the word "weight" in the documents to be completed by the general public. That is because there is probably a law/regulation somewhere which states that people need to provide their known weight in kilograms/pounds, because the general public is assumed to be too uneducated to recognize that the weight is really a force (measured in Newtons or lbf), while kilograms/pounds could only refer to a mass (rest mass, but that's taking it to extremely pedantic).

So all of this apparent or real confusion, and threads such as these here, and other places on the internet, because people are assumed not to have studied basic physics and pre-High school or HS. Assumption of ignorance.

I am deeply passionate about linguistics in general, and etymology and grammar, in particular. Also in this domain, it is said that the less educated dictate how a language is developing. This saddens me, really.
My thoughts exactly.

Langauge has a single purpose, and that is to convey an idea from one mind to another. Without agreement, we are left to constantly learn how each individual defines a particular word which bogs down communications and progress.

Mathematics is a language.

Digcoal
A kilogram always refers to mass in the everyday world too*.

The confusion does not arise because in the day to day world 'people' use kilograms as a measure of weight, the confusion arises because because in the everyday world 'people' use the word weight when they actually mean mass.

When the doctor says 'you need to reduce your weight' he doesn't expect you to achieve this by taking the elevator/lift down a few floors or taking up space flight. When you buy 5 pounds of potatoes you make sure the shopkeeper waits for the scales to settle after tossing the potatoes in, rather than accepting the greater weight of the potatoes as they decelerate in the pan.

* Edit: I can think of one example where this is not the case: ropes and other lifting equipment are almost always specified in kg (or tonnes): there is obviously a safety issue here: it would be easy to think that a 1000N sling was 10 times as strong as it actually is.
When you "weigh" something down, that requires mass and gravitational acceleration. This implies a force, not an amount of matter.

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When you "weigh" something down, that requires mass and gravitational acceleration. This implies a force, not an amount of matter.
I come down pretty strongly on the descriptivist view of language rather than the prescriptivist point of view.

The operational definition of "weight" in commerce is mass. That is not an implication. That is a fact.

• Astronuc and pbuk
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I come down pretty strongly on the descriptivist view of language rather than the prescriptivist point of view.

The operational definition of "weight" in commerce and medicine is mass. That is not an implication. That is a fact.
Then being “weightless” in space means being “massless”?

• pbuk
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Then being “weightless” in space means being “massless”?
Words mean different things in different contexts. That too is a fact. One which we may bemoan or celebrate, certainly. But one with which we must live.

We do not do much weighing of goods in space, so the commercial definition of weight is currently irrelevant in orbit. If we were engage in commerce in space, one suspects that the relevant measurements would be of quantity of matter rather than force exerted on deck plates.

Digcoal
Words mean different things in different contexts. That too is a fact.
Which is the point. The nomenclature is convoluted creating plenty of instances for conflation and confusion.

Hence this post.

And we have a term that is never ambiguous and is invariant to the context for “an amount of matter”: mass.

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Which is the point. The nomenclature is convoluted creating plenty of instances for conflation and confusion.

Hence this post.

And we have a term that is never ambiguous for “an amount of matter”: mass.
Indeed we do. We, as members of the physics community are certainly free to use that word. And we do.

The English-speaking merchants of the world are equally free to continue to use the word "weight" in the way they have historically done -- a way that amounts to an operational definition of mass. And they do.

Digcoal
Indeed we do. We, as members of the physics community are certainly free to use that word. And we do.

The English-speaking merchants of the world are equally free to continue to use the word "weight" in the way they have historically done -- a way that amounts to an operational definition of mass. And they do.
Nobody is making a freedom/tyranny point.

This is strictly a matter of logic.

cmb
* Edit: I can think of one example where this is not the case: ropes and other lifting equipment are almost always specified in kg (or tonnes): there is obviously a safety issue here: it would be easy to think that a 1000N sling was 10 times as strong as it actually is.
FWIW, all the new straps and slings I have seen recently in the last few years are now given in daN .. decaNewtons.

It's one of those 'adapt-a-SI-unit' type that brings a compound SI unit into harmony with existing usage.

Hence, "100 daN" is the 'weight force' of 100 kg.

• pbuk and jbriggs444
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Nobody is making a freedom/tyranny point.

This is strictly a matter of logic.
Langauge choice is dictated by history and convenience, not by logic.

Digcoal
Langauge choice is dictated by history and convenience, not logic.
And just as synaptic pruning is a natural process for removing extraneous synapses, society also has a natural tendency for such efficiency.

Stating that something irrational is so because of “history” seems quite antithetical to the scientific method.

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And just as synaptic pruning is a natural process for removing extraneous synapses, society also has a natural tendency for such efficiency.

Stating that something irrational is so because of “history” seems quite antithetical to the scientific method.
Words are used as they are used. We do not get to pick how speakers use them.

Saying that a word does not mean what it is used to mean and what it is understood to mean is the height of irrationality.

Again, I am a descriptivist, not a prescriptivist.

Digcoal
Words are used as they are used. We do not get to pick how speakers use them.

Saying that a word does not mean what it is used to mean and what it is understood to mean is the height of irrationality. Your stance here appears irrational.
Again, who said anything about “picking how speakers use them?”

Perhaps my stance seems irrational to you because you keep responding to things nobody has said?

• weirdoguy
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Words are used as they are used. We do not get to pick how speakers use them.

Saying that a word does not mean what it is used to mean and what it is understood to mean is the height of irrationality.

Again, I am a descriptivist, not a prescriptivist.
Be whatever you want, and enjoy explaining irrational use of words.