Grams vs. Newtons: Why Do I See Weights Measured in Grams?

[Psyrus]

Ok so I've asked my physics teacher and a statics teacher as well and I couldn't get a straight answer from either. So here's my questions...

Correct me if I'm wrong, but isn't the gram a unit of mass? Not weight? I thought that for mass to become a unit of weight, it has to have to acceleration of gravity applied to it. And the unit we use for weight after gravity is applied to the mass of an object is then called the Newton, right?

So why do I see weights at the gym that are measured in kilograms and not in Newtons? Or even on kitchen scales that measure in grams instead of Newtons?

What am I missing here?

Is it a just misnomer when companies use grams for gym weights or other products use that measure using grams? Or is there a misunderstanding on my part?

Thanks!

 

[symbolipoint]

You are conceptually correct. MASS is not WEIGHT. Mass is amount of matter. Weight is a force. One of the measurement units for mass is the gram. One of the measurement units for force is the Newton.

 

[Bandersnatch]

No, you're right. Weight is, technically, measured in Newtons.
But that's not in the common usage - where mass is used synonymously with weight. This is an alright thing to do, since for all common purposes, any weight will be measured at the same strength of the gravitational field. So weighing a mass of e.g. 5 kg will always nett 49.05 N. I.e., seeing a 5 kg dumbbell you know it always weighs 'as much as a 5 kg mass'.
One could look at the reading of scales etc. as saying just that: 'I weight as much as X kg mass on Earth's surface'.

 

[Psyrus]

No, you're right. Weight is, technically, measured in Newtons.
But that's not in the common usage - where mass is used synonymously with weight. This is an alright thing to do, since for all common purposes, any weight will be measured at the same strength of the gravitational field. So weighing a mass of e.g. 5 kg will always nett 49.05 N. I.e., seeing a 5 kg dumbbell you know it always weighs 'as much as a 5 kg mass'.
One could look at the reading of scales etc. as saying just that: 'I weight as much as X kg mass on Earth's surface'.

Cool. So you may or may not know the answer to this next one but... I used to work at a pharmaceutical company and we would often "weigh out" raw materials or large tanks full of product. The scales used grams as the unit of measure whether it was grams, kilograms, micrograms, milligrams, etc., and we would document them as such. So do those types of scales, or any regular household scale for that matter, actually account for gravity to display the objects true mass? In other words, when I step on a scale and it displays 70kg, is it actually displaying my mass? Not weight?

And this actually brings up more questions. Like is lbs truly a unit of mass or weight?
I remember in my statics class whenever we were given an objects mass in kg, we would always have to find the weight of it by multiplying by 9.81m/s^2. But whenever it was given to use in lbs we could just go on to answer the question from there. So does that mean that lbs is actually a unit of weight that has already been multiplied by the acceleration of gravity?

Hope all of that made sense...

 

[Bandersnatch]

In other words, when I step on a scale and it displays 70kg, is it actually displaying my mass? Not weight?

If you think about the mechanics of it, what a typical bathroom scale measures is neither mass nor gravity, but the compression of a spring. The scale display is calibrated so as to translate it to units of mass.
So, to be painfully technical, when a scale says you weigh 70 kg, it actually says: 'the spring was compressed as if under a force equal to the weigh of a 70 kg mass accelerated by Earth's gravitational field at its surface'. The calibration must then account both for the gravity, and the particulars of the mechanical assembly of the scale.
This becomes kind of obvious once you e.g. jump on the scale, or push it with your finger. After all, neither the weight nor the mass changes as you do so, even though the display shows some new numbers.

And this actually brings up more questions. Like is lbs truly a unit of mass or weight?
I remember in my statics class whenever we were given an objects mass in kg, we would always have to find the weight of it by multiplying by 9.81m/s^2. But whenever it was given to use in lbs we could just go on to answer the question from there. So does that mean that lbs is actually a unit of weight that has already been multiplied by the acceleration of gravity?

I'm not too familiar with the Imperial system, but from what I gather, pound-mass (lbs, aka just 'pound') is a unit of mass, while pound-force (lbf) is a unit of force. Because of how the pound-force is defined, they have the same numerical value. I.e., 1 pound-force is how much a 1 pound-mass weighs at Earth's surface.

Remember that it's just a unit. We can define any new unit at any moment, to suit our needs. E.g., we know that 1 kg mass weighs approx. 9.81 N in standard gravitational field. I could just now define 1 kilogram-force as the force exerted by 1 kg of mass in standard gravitational field. It would be equal to 9.81 N.
If I weighed a 5 kg mass, the result would be 5 kg-force, and as long as everyone was in on my system they'd know exactly how to translate it into Newtons, if needed.
And in fact, going back to the previous point, this is just about exactly what the scale display does.

 

[Psyrus]

If you think about the mechanics of it, what a typical bathroom scale measures is neither mass nor gravity, but the compression of a spring. The scale display is calibrated so as to translate it to units of mass.
So, to be painfully technical, when a scale says you weigh 70 kg, it actually says: 'the spring was compressed as if under a force equal to the weigh of a 70 kg mass accelerated by Earth's gravitational field at its surface'. The calibration must then account both for the gravity, and the particulars of the mechanical assembly of the scale.
This becomes kind of obvious once you e.g. jump on the scale, or push it with your finger. After all, neither the weight nor the mass changes as you do so, even though the display shows some new numbers.I'm not too familiar with the Imperial system, but from what I gather, pound-mass (lbs, aka just 'pound') is a unit of mass, while pound-force (lbf) is a unit of force. Because of how the pound-force is defined, they have the same numerical value. I.e., 1 pound-force is how much a 1 pound-mass weighs at Earth's surface.

Remember that it's just a unit. We can define any new unit at any moment, to suit our needs. E.g., we know that 1 kg mass weighs approx. 9.81 N in standard gravitational field. I could just now define 1 kilogram-force as the force exerted by 1 kg of mass in standard gravitational field. It would be equal to 9.81 N.
If I weighed a 5 kg mass, the result would be 5 kg-force, and as long as everyone was in on my system they'd know exactly how to translate it into Newtons, if needed.
And in fact, going back to the previous point, this is just about exactly what the scale display does.

I think i get it now. Thanks.

 

[256bits]

Or is there a misunderstanding on my part?

Not really a misunderstanding as much as you might not be aware that each country sets by law what units can be used legally for trade and commerce, with some international flavor thrown in also, so that everyone is on the same page. You won't see "chunks' of tomatoes, or "flabs' of salt, but there is nothing stopping any country or international agreement from adopting such units to the consternation of trading individuals and companies.
You see board-feet for wood, barrels of oil ( DO you know how much oil is in a barrel - the ones doing the trading do ), carats( not carrots) for precious gems and metals as jewelry, etc. . You can find many more odd units if you look around. A dozen of eggs is one common packaging and selling item for the public.

For amount of substance, mass and lb_m ( ound mass ) are two of the usual units used and seen by the public, and the scales represent that factor. Whether you want to discuss with some one that they are trading or buying by weight, or by mass is irrelevant, as long as each individual involved in the transaction understands that the price per pound or price per gram is a fair price to do an exchange.

For the physical sciences, mass and weight are distinct, with weight depending upon the gravitational field you are within at the time of measurement. A scale would be calibrated to take that into account, such as a scale on Earth vs one on the moon. And same so for trading on the moon and earth.

 

[sophiecentaur]

Like is lbs truly a unit of mass or weight?

History is to blame for all this stuff. It was a brave attempt at sorting it all out when the cgi - mks - - SI systems were developed and I think they at least achieved some consistency amongst the Scientists and Engineers. But the words Mass and Weight are too ingrained in general language to put things totally right.

 

[anorlunda]

Not really a misunderstanding as much as you might not be aware that each country sets by law what units can be used legally for trade and commerce,

How true. You remind me of an shameful example from the 1970s. There was a minor crisis when gasoline prices in the USA exceeded $1 per gallon for the first time. Tens of thousands of mechanical gas pumps could only use two digits for the price. Should they have to throw away all of the old pumps overnight?

Some clever people suggested that we should simply switch to selling gasoline by the liter. After all, in each of the previous 200 years of American history, Congress had declared "This is the year we're switching to the metric system."

But law makers in New York State thought that was fraud. The feared that gas stations would change the price from $0.99 per gallon to $0.99 per liter (a 3700% increase in price). So they passed a law making it illegal to sell liquids by the liter in New York. I'm not sure, but that law may still be in force.

 

[Dale]

The scales used grams as the unit of measure whether it was grams, kilograms, micrograms, milligrams, etc., and we would document them as such. So do those types of scales, or any regular household scale for that matter, actually account for gravity to display the objects true mass?

Yes. Scales that are legal for trade have been calibrated so that they actually display mass. The local value of g varies slightly over the earth, so such scales factor that in and give the correct mass.

 

[CWatters]

This is where scientific and common usage diverge.

In the scientific world mass is measured in Kg and weight in Newton's

In common usage weight is in Kg.

Weight depends which planet you are on. Common usage assumes it's the Earth.

 

[Chestermiller]

In the Imperial system of units, there are two entities that have units of pounds: pounds mass ($lb_m$) and pounds force ($lb_f$). A pound force is defined as the force that gravity exerts on an object of mass 1 $lb_m$, at a location where the acceleration of gravity is 32.2 ft/s^2. So, in the Imperial system, when we want to use F = ma, we have to write:

$$F=m\frac{a}{g_c}$$ where $g_c=32.2\ \frac{lb_m}{lb_f}\frac{ft}{s^2}$, and where F is in $lb_f$ and m is in $lb_m$. It takes a little getting used to, but not much if you've grown up with it.

The same trick is often done with metric units as well in defining kg force.

 

[sophiecentaur]

Weight depends which planet you are on. Common usage assumes it's the Earth.

Only time will tell how people who spend time living on the Moon or Mars start to talk and think about the weights and masses they deal with. They will look at a massive lump of metal and regard it as easily liftable. That will get into their subconscious feelings about living in those places. I can't imagine a ('local') place where humans might live where weights would be greater.

 

[Jon Richfield]

As the folks said, in common usage we regard grams (lb, kg, tons, tonnes etc) as sufficient to characterise most weights, on the assumption that the context of living on Earth renders any confusion irrelevant. As such measures formally refer technically to mass, we were told in Phys 101 to refer to the weight properly speaking, as grams-weight, pound-weight (or "poundal" (see Wikipedia, which, in those days we did not yet have, but looking it up in dead trees also worked)) etc.

The difference only becomes relevant when there are changes in effective gravity or momentum (such as on alien planets, in free fall, vomit comets etc) or when buoyancy is relevant, such as in weighing a 1 kg He balloon, or weighing a slab of toffee under water.

Compare speaking of weight in terms of mass, with giving pressure in atmospheres or bars, which notionally would vary with local conditions, instead of Pascals, which are independent of what is going on around you. It generally works, and when it doesn't, it isn't hard to work out why, or what to do about it.

 

[jbriggs444]

pound-weight (or "poundal

The pound force and the poundal are different units. The former is the Earth weight of one pound mass. The latter is the force required to give one pound mass an acceleration of one foot per second squared. The two units are in a ratio of about 32 to 1 (one Earth gee expressed in feet per second squared).

 

[zanick]

Cool. So you may or may not know the answer to this next one but... I used to work at a pharmaceutical company and we would often "weigh out" raw materials or large tanks full of product. The scales used grams as the unit of measure whether it was grams, kilograms, micrograms, milligrams, etc., and we would document them as such. So do those types of scales, or any regular household scale for that matter, actually account for gravity to display the objects true mass? In other words, when I step on a scale and it displays 70kg, is it actually displaying my mass? Not weight?

And this actually brings up more questions. Like is lbs truly a unit of mass or weight?
I remember in my statics class whenever we were given an objects mass in kg, we would always have to find the weight of it by multiplying by 9.81m/s^2. But whenever it was given to use in lbs we could just go on to answer the question from there. So does that mean that lbs is actually a unit of weight that has already been multiplied by the acceleration of gravity?

Hope all of that made sense...

I don't know where your "statistics class " was coming from....but , if you have a mass in kg, then its weight will be the same in kg (on earth). If you wanted to have the force in Newtons due to gravity, then you would multiply by 9.81m/s/s.

 

[OmCheeto]

...
Weight depends which planet you are on. Common usage assumes it's the Earth.

Last I heard, only 12 people needed to worry about the difference.

And when was the last time one of them worried about it?
(google google google)

For all mankind

As [Gene] Cernan prepared to climb up the lunar ladder for the last time, he paused and spoke these words:

"As I take man's last step from the surface, back home for some time to come – but we believe not too long into the future – I'd like to just (say) what I believe history will record. That America's challenge of today has forged man's destiny of tomorrow. And, as we leave the Moon at Taurus–Littrow, we leave as we came and, God willing, as we shall return, with peace and hope for all mankind. Godspeed the crew of Apollo 17."​

He and his crewmates returned to Earth on Dec. 19, 1972.​

---

Rounding, as Dec 25th is pretty close to Dec 19th: 2018-1972 = 46 years ago!

ps. This thread brings back happy memories.

 

[anorlunda]

So goes the world of natural language. Crossing correct/incorrect common/uncommon scientific/popular meanings to words.

I think we're going in circles. If anyone has something different to contribute, send me a PM about re-opening this thread.

Thread closed.