Mass vs Mass as a Force (Weight)

[jbriggs444]

kg is a unit of mass.

lb is a unit of weight

lbf is a unit of force

"lb" is ambiguous. It could denote a pound force. It could denote a pound mass. One needs to use context to decide which. Saying that it means "weight" does not help since "weight" is ambiguous in ordinary language as well.

3. If you take the same 1kg lab test mass and the same scales, it'll read about '0.17kg' for your 1kg test mass on the Moon.

It will read '1 kg' because you will have re-calibrated your scale at its place of use.

If you do not recalibrate, the result will depend on the technology used in the scale.

4. If you take the same lb lab test weight and the same scales that has a lb readout, then it'll read about '0.17lb' for your 1lb test weight on the Moon.

Ambiguous. Since the scale has a 'lb' readout, you won't know whether to recalibrate to correctly read in pounds force or pounds mass.

 

[cmb]

"lb" is ambiguous. It could denote a pound force.

Only in misuse. lbf is a pound force. lb is a weight.

It will read '1 kg' because you will have re-calibrated your scale at its place of use.

If you do not recalibrate, the result will depend on the technology used in the scale.

I guess you are correct. 'Scales' might be, pedantically, argued to be explicitly the type of device where one measures a weight-to-be-tested against a calibrated weight (like 'scales-of-justice' type statues, and the type grandma used to use, both being wholly inaccurate! ;/)

In that case, you have a point, testing a lb weight against an lb test mass.

In general 'scales' these days measure a downward force. I was trying to provide a representative illustration of the difference between weight and mass for the OP.

Ambiguous. Since the scale has a 'lb' readout, you won't know whether to recalibrate to correctly read in pounds force or pounds mass.

I said, use the same scales, implies no recalibration. Again it was illustrative.

 

[Quester]

It is because scales measure opposing forces (Newtons) and are calibrated to report calculated masses (kg). The confusion is further exacerbated by common parlance involving asking for the WEIGHT of something and providing the calculated MASS given by a scale.

Kilograms is a measurement of mass. Newtons is a measurement of force, gravitational or otherwise.

I was in the same boat as you, at one point, so do not feel alone in this.

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.

 

[jbriggs444]

In general 'scales' these days measure a downward force.

Normal scales these days use load cells, yes. The result that they present reflects the force that is applied, yes.

However, this ignores the fact that most scales accurate enough for the distinction to matter are calibrated to produce accurate mass readings at the place of their use. They are not calibrated to produce accurate force readings.

 

[jbriggs444]

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 1 kg is certainly mass. The kg is a unit of mass.

How much force you need will depend on how long you are allowed to apply that much force.

 

[Quester]

The 1 kg is certainly mass. The kg is a unit of mass.

How would I know that?

How much force you need will depend on how long you are allowed to apply that much force.

I see that. I used a poor example, obscuring my intent. I should have stated a problem that asked something like:

How much force would be required to accelerate 1kg at a rate of 3 m/sec^2

 

[Quester]

I failed to include "legal for commerce" with science as specific instances where kg is used for mass and not weight.

A bathroom scale is used to answer what question that people ask in everyday conversation?

"How much do you weigh?"

When you ship a package, what is asked?

"What is the weight of the package?"

The reason commerce uses mass is because it is the direct measurement used to calculate fuel costs for shipping. However, everyday usage is predominately weight. This is why the original question was asked, and why it took me a while to understand it myself. Mass and Weight are conflated because we have the same symbolic representation for two entirely different concepts.

It is the same as calling cats "cats" and birds "cats." Distinction without distinct terms leads to unnecessary confusion.

Exactly! That is my problem and why the original post caught my attention!

 

[cmb]

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.

 

[jbriggs444]

How would I know that?

How would you know that a "1 kilogram object" is an object whose mass is one kilogram?
How would you know that the kilogram is a unit of mass?

One might google "kilogram unit" and find something like this.

Kilogram (kg), basic unit of mass in the metric system. A kilogram is very nearly equal (it was originally intended to be exactly equal) to the mass of 1,000 cubic cm of water. The pound is defined as equal to 0.45359237 kg, exactly.

 

[Quester]

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.

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?"

 

[jbriggs444]

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]

 

[Digcoal]

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.

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

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.

 

[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.

 

[jbriggs444]

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

 

[jbriggs444]

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.

 

[vanhees71]

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.

 

[BvU]

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!?

 

[vanhees71]

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).

 

[vanhees71]

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.

 

[hutchphd]

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.

 

[pbuk]

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.

 

[jbriggs444]

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.

 

[dextercioby]

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.