# Mass vs Mass as a Force (Weight)

LT72884
Been thinking about mass today and came up with a question. Why is that objects on this Earth describe its weight in Kg, g, mg, Mg? IE 2.2Lbs is 1Kg. So why do we name the 1Kg to be mass, but the 2.2Lbs we call weight. Both have to be a unit of force if there is a conversion factor between the two numbers. if 1Kg IS 2.2 lbs, then 1Kg is also considered weight because a 1.3Kg jar of honey is NOT 1.3Kg on the moon or anywhere else.

we know mass to be what we are made of, atoms, etc. so when and how decided it to be a unit of force?

so how do we know what really is. How do i know what my mass really is? Some say my mass is 104Kg, but that is purely based on a gravitational constant of 9.81.

so how do we really measure mass?

thanks

• Digcoal

LT72884
also, who decided that a 1Kg block on Earth is indeed 1Kg of atoms? and who decided that 1Kg is to weigh 2.2Lbs. In the uk, mass IS weight. you ask anyone how much they weigh, they will tell you it in Kg.

i take a 1Kg block to the moon, it won't weight 1Kg. the mass will stay the same but the 1Kg they labeled on the weight or block is based off of Earth's 9.81... My food scale is in grams at home.

• Digcoal
Homework Helper
Hi,

Good questions! I suppose you googled a little as well ?

Easiest approach is Newton: ## F = m\, a\ ##. Mass is same here and on the moon and in between as well. Weight differs, because the gravitational acceleration differs. Basically the attracting force is $$F = {G\,Mm\over R^2}$$ with G Newton's (again!) constant.

Who decides is the SI committee -- but that's very technical.

##\ ##

LT72884
Hi,

Good questions! I suppose you googled a little as well ?

Easiest approach is Newton: ## F = m\, a\ ##. Mass is same here and on the moon and in between as well. Weight differs, because the gravitational acceleration differs. Basically the attracting force is $$F = {G\,Mm\over R^2}$$ with G Newton's (again!) constant.

Who decides is the SI committee -- but that's very technical.

##\ ##
yes, i googled a lot haha. I am in my upper division physics classes for my aerospace degree, but i tend to ask really deep questions that boggle my mind.

For example, the weights in my physics lab that we use to solve problems, are labeled 50g, 1Kg etc. If i put those on a scale, they are indeed 50g, and 1Kg, but a scale uses gravity to give us the weight back.

so the 1Kg weight is still a weight, not a mass? that 1Kg weight does not have 1Kg of atoms?

thanks

• Digcoal
LT72884
ohhh, balance scales vs spring scales is an interesting topic

Homework Helper
No, the 1 kg thingies are 1 kg mass. The scales measure forces and are calibrated for a particular value of ##g##, mostly 9.81 m/s2 .

So that $$F = {G\,Mm\over R^2} = {G\,M\over R^2} m = mg$$where R and M are radius and mass of the earth

(and ## g = {G\,M\over R^2}##)
##\ ##

• sophiecentaur and LT72884
LT72884
school of thought:

If we take a balance scale, here on earth, add 1 cubic cm of water to one side, then rice to the other and let it balance out. THEN take it to the moon, will it still be in balance? if so, and i add more rice, will it go out of balance?

thanks

• Digcoal
Homework Helper
so the 1Kg weight is still a weight, not a mass?
A 1 kg "weight" is normally constructed to be 1 kg in mass.

The apparent force of gravity on this weight may or may not be approximately 9.81 Newtons depending on the location where that force is measured.

In commerce we normally want the buyer and seller to agree on the amount of goods that are bought or sold. In particular, we do not want disputes to arise if the gravitational down-force on a box of Cheerios changes between the factory where it is made and the grocery store where it is purchased. For this reason, the folks who engage in commerce use mass measurements to do their business. They may use load cells to perform the measurements, but those load cells are calibrated to deliver accurate figures for mass. They may call the quantity that they measure "weight", but the equipment they use and the manner in which they use it conforms to an operational definition of mass.

• nasu and Delta2
Homework Helper
school of thought:

If we take a balance scale, here on earth, add 1 cubic cm of water to one side, then rice to the other and let it balance out. THEN take it to the moon, will it still be in balance?
Yes

if so, and i add more rice, will it go out of balance?
Yes

##\ ##

Homework Helper
With a balance scale you compare forces. The 9.81 m/s2 calibration doesn't come into it.

##\ ##

• jbriggs444
LT72884
A 1 kg "weight" is normally constructed to be 1 kg in mass.

The apparent force of gravity on this weight may or may not be approximately 9.81 Newtons depending on the location where that force is measured.

In commerce we normally want the buyer and seller to agree on the amount of goods that are bought or sold. In particular, we do not want disputes to arise if the gravitational down-force on a box of Cheerios changes between the factory where it is made and the grocery store where it is purchased. For this reason, the folks who engage in commerce use mass measurements to do their business. They may use load cells to perform the measurements, but those load cells are calibrated to deliver accurate figures for mass. They may call the quantity that they measure "weight", but the equipment they use and the manner in which they use it conforms to an operational definition of mass.
But how do we KNOW what the mass is to even calibrate machines? it is still based off of Earth's gravity? is it not? 1Kg of mass from what i have been taught is 1000 grams of matter. so what is a gram then? how many atoms are in a Kg? in the Uk, i am 104Kg, but that is not mass, that is still weight

maybe the commerce scales are balance scales vs force scales? never thought of that.

Homework Helper
yes, i googled a lot haha.
Any questions left over after having read e.g. the ones I referred to ? It seems to me not all of it has landed the way it should have ...

Your mass is 104 kg. In SI countries your feet exert a force of 104 kilogramforce on the floor, or 104 * 9.81 Newton (again !)

##\ ##

• LT72884
Gold Member
2022 Award
school of thought:

If we take a balance scale, here on earth, add 1 cubic cm of water to one side, then rice to the other and let it balance out. THEN take it to the moon, will it still be in balance? if so, and i add more rice, will it go out of balance?
A balance scale is just for comparison. "Weight" is measured on the surface of the Earth with a, for example, bathroom scale, based on G and calibrated so that 1Kg "weighs" 2.2lbs.

BUT ... if you take that same bathroom scale to the moon, it will AGAIN measure "weight" (NOT mass, because it never really was measuring mass) and it will be a lot less that 2.2lbs for 1 Kg of mass.

You're making this all much more complicated than it needs to be.

Gold Member
The pound used in the USA is officially defined as 0.453 592 37 kg. As such, it is a unit of mass.

Weight is defined as a force in physics but for purposes of commerce and in medicine the word weight refers to what a physicist calls mass.

These things are decided by the BIPM. You can find more information at bipm.org.

Most textbooks present this in a confusing way. They usually define the pound as a unit of force even though there is no such officially-sanctioned definition. This doesn't stop people from using the pound as a unit of force. NASA is an example.

I used to tell my students that to keep it all straight remember that if it's measured in kilograms it's a mass and if it's measured in Newtons it's a force. The meanings of the words weight and pound have to be inferred from the context.

In physics class I have a mass of 110 kg but at the doctor's office I have a weight of 110 kg.

• Digcoal, Astronuc, russ_watters and 2 others
italicus
Put a bathroom scale on the floor of a lift, which rests at a given position in a skyscraper. The scale is well secured to the floor. Then put a body of mass m on the scale: you will read its weight.
Then , cut the rope of the lift, so that it falls freely. Then the “apparent” weight of the body becomes zero, for all bodies fall locally with the same g ( suppose the gravitational field constant within the small volume of the lift). The body doesn’t weight wrt the lift. Have you ever seen astronauts floating within the ISS ?
The ISS and bodies inside are in free fall, orbiting around the Earth , at a mean distance of 400 km from its surface.
But this doesn’t mean that they have a zero mass! And they have a weight too, wrt to the Earth, which you can determine using the law of universal gravitation , set forth by Newton.

Mentor
The pound used in the USA is officially defined as 0.453 592 37 kg. As such, it is a unit of mass.
Just wanted to “second” this. The pound is defined by the NIST. It is defined as the above specific fraction of a kilogram, so it is a mass not a force.

A mass can be measured using either a balance scale or a spring scale. If you use a spring scale then you must calibrate it to account for local differences in g. If you took it to the moon then you would need to recalibrate it. Once you did then the spring scale would still measure kilograms.

• Astronuc and LT72884
Staff Emeritus
The mass of the Sun is 1.9885×1030 kg or 330,000 times the mass of the Earth.
How do you suppose we know that?
Here's another hint. Google mass spectrometer.

• LT72884
LT72884
Any questions left over after having read e.g. the ones I referred to ? It seems to me not all of it has landed the way it should have ...

Your mass is 104 kg. In SI countries your feet exert a force of 104 kilogramforce on the floor, or 104 * 9.81 Newton (again !)

##\ ##

A balance scale is just for comparison. "Weight" is measured on the surface of the Earth with a, for example, bathroom scale, based on G and calibrated so that 1Kg "weighs" 2.2lbs.

BUT ... if you take that same bathroom scale to the moon, it will AGAIN measure "weight" (NOT mass, because it never really was measuring mass) and it will be a lot less that 2.2lbs for 1 Kg of mass.

You're making this all much more complicated than it needs to be.
Then i don't think I am explaining my question well enough. How do we know that 1Kg of mass IS indeed 1Kg of atoms? mass is matter, atoms, material, what we are made of. When we see the 1Kg mass "weights" in lab, its a mass of 1Kg, but what does the actually mean? is there a specific number of atoms that fit in a 1Kg "weight"? thanks

Last edited:
LT72884
The mass of the Sun is 1.9885×1030 kg or 330,000 times the mass of the Earth.
How do you suppose we know that?
Here's another hint. Google mass spectrometer.
thats what I am trying to figure out. I am 104Kg but what does that mean? 1Kg is 1000g yes, but again, what does that actually mean. How many atoms is in 1Kg of me, or something? Do all objects that have a mass of 1Kg have the same number of atoms? if not, then how can 1Kg be constant? IE, 1Kg of water have same amount of atoms of 1Kg sand?

Mentor
Do all objects that have a mass of 1Kg have the same number of atoms?
It makes a difference whether the atoms are hydrogen, or oxygen, or iron, or lead, or uranium, or...

• Delta2
Gold Member
Summary:: understanding mass and mass as a force(weight)

Been thinking about mass today and came up with a question. Why is that objects on this Earth describe its weight in Kg, g, mg, Mg? IE 2.2Lbs is 1Kg. So why do we name the 1Kg to be mass, but the 2.2Lbs we call weight. Both have to be a unit of force if there is a conversion factor between the two numbers. if 1Kg IS 2.2 lbs, then 1Kg is also considered weight because a 1.3Kg jar of honey is NOT 1.3Kg on the moon or anywhere else.

we know mass to be what we are made of, atoms, etc. so when and how decided it to be a unit of force?

so how do we know what really is. How do i know what my mass really is? Some say my mass is 104Kg, but that is purely based on a gravitational constant of 9.81.

so how do we really measure mass?

thanks
When I was at school the absolute unit of force for the Imperial System was the Poundal. And the acceleration of gravity was 32 feet/second /second, so a Poundal was a Pound/32. The Pound was used as a practical unit of force as well as mass.

Do all objects that have a mass of 1Kg have the same number of atoms?
If it's the same type of atoms, yes.

• Delta2
Gold Member
Just wanted to “second” this. The pound is defined by the NIST. It is defined as the above specific fraction of a kilogram, so it is a mass not a force.
But it is all a bit of a mess. Since we (UK and most of the rest of us) went Metric, and in particular SI, we have different sounding units for Mass and Force (Weight) Kilograms and Newtons are not easily confused. But in the 50's, we used the fps system in school and had to use (strictly) Poundals for forces. Our knuckles were frequently rapped for misuse of the word Pound for weight in Physics classes but everywhere else we were confused by Pounds used as force.
At least, in SI Engineering, we use Newton metres for torque. IN imperial you have pound-feet and foot-pounds. How crazy is that?

Homework Helper
But how do we KNOW what the mass is to even calibrate machines? it is still based off of Earth's gravity? is it not? 1Kg of mass from what i have been taught is 1000 grams of matter. so what is a gram then? how many atoms are in a Kg? in the Uk, i am 104Kg, but that is not mass, that is still weight
If we go back as long as there was a thing called a kilogram, you come to the year 1795. Someone had the idea to standardize on a unit of mass equal to the mass of one cubic centimeter of pure water at normal atmospheric pressure and its temperature of maximum density.

The narrative that I like is that in the wake of their revolution, the French were trying to cast off all things from the prior regime and start fresh. The old system of units just had to go.

It turns out that water is a finicky thing to measure precisely. It evaporates. It reacts with things. It sticks to things. Atmospheric buoyancy is a bit of a problem. After years of work, a metal mass was finally fabricated that approximated 1000 of these grams as closely as could be arranged.

The kilogram was then defined to be the mass of this particular hunk of metal. A gram, naturally is defined as 1/1000 of that mass.

If you buy a 1 kilogram mass from a scientific supply company, you get a hunk of metal that has been compared against a copy (of a copy...) of that prototype.

Skip forward a bit more than 200 years [and skip some details] and the kilogram was showing its age. We'd made copies of the prototype kilogram. Comparisons showed that the copies were changing mass slightly over time. A better standard definition was wanted.

One proposal was to redefine the new kilogram in terms of a sphere containing a carefully counted number of atoms of a pure isotope. That proposal was not selected.

A competing proposal was rather more esoteric and involved Plank's constant and a device known as a Kibble Balance. That is the proposal that was selected.

How many atoms are in a kilogram? You either measure out a kilogram of them and count. Or you look it up. If you look at the Periodic Table of the Elements, you will see listed with each atom an "atomic weight". This "atomic weight" is the mass, in grams, of 6.02 x 1023 (Avogadro's number) atoms of that pure element. Avogadro's number has been defined (and redefined slightly) to give Carbon-12 an atomic weight of very close to or even exactly 12.

• Richard R Richard, Limebat and sophiecentaur
Mentor
At least, in SI Engineering, we use Newton metres for torque. IN imperial you have pound-feet and foot-pounds. How crazy is that?
Yes, I agree. The mistaken belief that the pound is a unit of force comes directly from the engineering community. I have even had engineering textbooks that incorrectly asserted that as fact. I don’t know how a simple mistake in the engineering literature turned into the common view held by non-engineers.

Homework Helper
Yes, I agree. The mistaken belief that the pound is a unit of force comes directly from the engineering community. I have even had engineering textbooks that incorrectly asserted that as fact. I don’t know how a simple mistake in the engineering literature turned into the common view held by non-engineers.
When I was in school in the 70's in the U.S., it was common for physics textbooks to preach that the pound was unequivocally a unit of force. I believe that Halliday and Resnick clung to this practice religiously at least into the 90's. However, I have no references to offer in support of this claim.

I think this was a conscious choice in the name of pedagogy. The goal was to hammer in a clear distinction between force and mass and to motivate the use of SI ("the metric system").

• vanhees71 and Dale
Gold Member
I don’t know how a simple mistake in the engineering literature turned into the common view held by non-engineers
That's not hard to explain. The only force that non-Engineers experience in a quantitative sense is actually Weight. Every weighing machine they see shows kg or lbs. Ergo . . . . .
Plus the fact that everyone laughs at the iconic Physics Teacher character, saying that "Weight is not Mass" and shooting himself in the foot each time he is correct and further confirming their misconception.
Also, I have to say that Engineers can be incredibly sloppy about their terminology, despite usually ending up with the right answer and a working system. (I speak as an Engineer here.)

• Digcoal, vanhees71 and Dale
Mentor
The imperial system uses lbs to describe two types of units, lbs mass and lbs force. 1lb force is the force exerted by gravity on 1 lb mass. Unfortunately, the lb mass is not the correct unit to use in applying Newton's 2nd law, so that, F is not equal to ma, if m is in lbs mass and F is in lbs force. If one uses lb mass and lb force in Newton's 2nd law, to get the right answer, one must write $$F=\frac{ma}{g_c}$$ where $$g_c=32.2 \frac{lb_f\ ft}{lb_m\ sec^2}$$

• Digcoal and Dale
Staff Emeritus
In the case of pressure, PSI pounds per square inch, pounds must mean force not mass.

It is a historical accident where words for force and mass have been used interchangeably by the public for centuries. The SI system does not eliminate the problem. SI spring scales are labeled in kg, not Newtons. The precision of science can never overcome the evolution of natural language, with one exception.

The exception is when we coin a word that is meaningless in any natural language. For example entropy. When Standard Oil of New Jersey wanted a new name, they methodically tested candidate names against every known language. They found a word that had no preexisting meaning, no innuendo, no suggestiveness, in any language --- Exxon.

Unlike Exxon, science is haphazard choosing names. Sometimes, the result is horrible. Thanks to English astronomer Fred Hoyle, we are stuck with the term "Big Bang". It stuck, and forevermore we are saddled with the burden of undoing the false impressions that phrase creates in the minds of the public. Similarly regrettable example is the word "observable" in quantum mechanics. It means Hermitian operator in physics, but to the public it means something very different.

• Digcoal, russ_watters, sophiecentaur and 1 other person
Mentor
thats what I am trying to figure out. I am 104Kg but what does that mean? 1Kg is 1000g yes, but again, what does that actually mean.
To find out what something means, you simply check the definition. The definitions of all of the SI units are published and maintained by the BIPM. According to their definitions $$1 \text{ kg} =1.60511 \ 10^{30} \ \frac{h \Delta \nu_{Cs}}{c^2}$$ Since anyone with the right equipment can measure ##h##, ##\Delta \nu_{Cs}##, and ##c## the ##\text{kg}## can be replicated anywhere.

Note that the constant I wrote as ##1.60511 \ 10^{30}## is actually exactly $$\frac{3668388484640072000000000000000000000000000000000000000}{2285439203704853426737563}$$

• • Digcoal, Motore and BvU
Mentor
SI spring scales are labeled in kg, not Newtons.
Yes, but this one is correct, if the spring scale is properly calibrated at its location.

• • Digcoal, Mister T, jbriggs444 and 1 other person
The Fez
Yes, I agree. The mistaken belief that the pound is a unit of force comes directly from the engineering community. I have even had engineering textbooks that incorrectly asserted that as fact. I don’t know how a simple mistake in the engineering literature turned into the common view held by non-engineers.
It is not a mistake at all. In engineering, we distinguish between a pound force (lbf) and a pound mass (lbm). Confusing, maybe. But not a mistake.

• Digcoal
Mentor
It is not a mistake at all. In engineering, we distinguish between a pound force (lbf) and a pound mass (lbm). Confusing, maybe. But not a mistake.
It is not a mistake to use lbf as a unit of force and lbm as a unit of mass. It is a mistake to use lb as a unit of force.

• Digcoal
Mentor
When I was in school in the 70's in the U.S., it was common for physics textbooks to preach that the pound was unequivocally a unit of force. I believe that Halliday and Resnick clung to this practice religiously at least into the 90's. However, I have no references to offer in support of this claim.
In my entire college-student and -teaching career, intro physics courses always used the pound as a unit of force. I don't have a copy of H&R handy, but I do have Serway & Vuille's College Physics (8th edition, 2009). In section 1.1, "Standards of Length, Mass and Time", it mentions the
[...]U.S. customary system, in which the units of length, mass and time are the foot, slug, and second.
In section 4.3, "Newton's Second Law", it states:
In the U.S. customary system, the unit of force is the pound.
Then follows a table of SI and U.S. customary units of mass, acceleration and force, which lists the slug as the U.S. customary unit of mass. These may be the only two places in the book that mention the slug. It doesn't even appear in the index.

• Digcoal
• 