# Why can lb's be considered a mass and a force?

1. Nov 12, 2011

### nod32

For example from one of my textbooks
So the car has a mass of 3000lb, but then they measure the force applied also in pounds.
Unlike SI units where forces are always measured in N and mass in kg.

2. Nov 13, 2011

### JeffKoch

Pounds is a unit of force, not mass. A 3000-lb car puts 3000 pounds of force down on the ground.

3. Nov 13, 2011

### nod32

So is it incorrect to say 1 lb = 0.454 kg?

4. Nov 13, 2011

### JHamm

From this wiki article: http://en.wikipedia.org/wiki/Pound_(force [Broken])
It appears that a pound is a unit of mass however a pound of force is defined as a pound multiplied by the Earth's gravitational constant. So a pound may refer to the unit of mass or the unit of force however these are different and should be inferred from context.

Last edited by a moderator: May 5, 2017
5. Nov 13, 2011

### D H

Staff Emeritus
The pound is
• A unit of mass. Multiple units of mass, in fact. There's the avoirdupois pound, which is what is typically meant when the term "pound" is used without any qualifier. Other pounds include the troy pound, tower pound, merchant pound, etc. The pound as a unit of mass is rather old.
• A unit of force. In modern parlance, a pound-force is the weight of one avoirdupois pound. However, legally and colloquially, "weight" is a unit of mass rather than force in the English system. So, better said, a pound force is the force needed to make a one pound mass accelerate at exactly 9.80665 meters per second squared. Mixed units? You bet. The US has been using the metric system for a long time. You just don't know it.
• A unit of money. At one point, the pound sterling was exactly one tower pound of sterling silver. Inflation has changed the exchange ratio just a bit, but the term pound sterling has stuck.

6. Nov 13, 2011

### Phrak

Even better, "1 kg = 1000 grams" is either false, or should be understood as shorthand notation.

The value 1000 represents the tranformation from a one dimensional gram space to a one dimensional kilogram space. But the conversion factor itself has associated units.

Correctly stated, the conversion is: 1[kilogram] = 1000[kilograms/gram] 1[gram].

Otherwise we are equating apples to oranges. Physicists should pay far better attention to units than has become customary.

Last edited: Nov 13, 2011
7. Nov 13, 2011

### nod32

Well that's confusing
So the mass in the example is really 3000lb/32.17ft/s^s

I'm glad I dont have to use imperial units for my thermodynamics class!

8. Nov 13, 2011

### JeffKoch

It's shorthand for, a mass of 0.454 kg produces a downward force at the Earth's surface of 1 pound. You can get yourself confused with conversions if you don't keep this in mind - for instance with torque wrenches, that usually read in both N-m and Ft-lbs. "Slugs" are sometimes referred to as an imperial unit of mass (http://en.wikipedia.org/wiki/Slug_(mass [Broken])), but I personally have never, ever used such a thing - if you just keep in mind that pounds are really weight, not mass, it's not difficult to deal with them if you have to.

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9. Nov 13, 2011

### I like Serena

Hmm, I don't get this.

The SI prefix "kilo" literally means 1000 and is unit-less.

As far as I know:
$$1 \textrm{ kg} = 1 \cdot \textrm{ kilogram} = 1 \cdot (1000 \cdot \textrm{ gram}) = 1000 \cdot \textrm{ gram} = 1000 \textrm{ gram}$$

10. Nov 13, 2011

### D H

Staff Emeritus
The mass in the example is 3000 lb, or 3000 lbm if you want to use a non-standard abbreviation for pounds (mass). To convert pounds mass to kilograms, multiply by 0.45359237. This is an exact number; the pound is defined to be exactly 0.45359237 kg.

One nice thing about English units is that (ignoring variations in Earth's gravity) the force in lbf due to gravity on some object is numerically equal to its mass in lb. Thus the force due to gravity on the car in the example is 3000 lbf.

One not so nice thing about English units is that you have to use F=kma (k=1/32.1740486) instead of F=ma.

Wrong. Pounds are a unit of mass and a unit of force. Read NIST Special Publication 811. Here are the conversion factors: http://physics.nist.gov/Pubs/SP811/appenB8.html. Note the conversion factors for pounds are to kilograms, not newtons (there are two conversion factors, one for avoirdupois pounds, the other for troy pounds). When talking about pounds as a unit of force it is better to say pounds-force.

11. Nov 13, 2011

### Staff: Mentor

I think you mean
1[kilogram] = .001[kilograms/gram] 1000[gram]

12. Nov 13, 2011

### JeffKoch

:rofl: I can't believe you said this, presumably with a straight face. You can use "pound-force", or "pound-mass", to avoid confusion, but historically and generally "pound" without clarifiers is a unit of force (weight). I think I even learned that in middle school.

13. Nov 13, 2011

### D H

Staff Emeritus
Apparently you had some teachers who didn't know their lb from their lbf. Your teachers were wrong. Teachers are not the keepers of standards or nomenclature. In the US, that job belongs to the National Institute of Standards and Technology.

One pound without a qualifier means either "avoirdupois pounds" or "pounds sterling". There isn't much room for confusion between mass and money now that a pound of silver is worth a tad more than a pound sterling. Without a qualifier, the shorthand notation "lb" means pounds (mass), not pounds-force. If you mean force when you say or write pounds it is best to use the term pounds-force, or lbf for short. That is the official nomenclature, after all.

Given that a lot of teachers don't know their lb from their lbf and propagate the incorrect terminology, it is of course best to be explicit and use pounds (mass) (or lbm for short) rather than expecting that the reader will know the correct terminology.

Last edited: Nov 13, 2011
14. Nov 13, 2011

### I like Serena

I decided to look this up on wikipedia, just to see what's written there (although of course this is no guarantee).
It turns out there are 2 separate pages, one for mass, and one for force.

On the first page it says:
"The pound or pound-mass (abbreviations: lb, lbm, lbm, ℔[1] ) is a unit of mass used in the imperial, United States customary and other systems of measurement. "

On the other page it says:
"The Pound force (symbol: lb, lbf, lbf) is a unit of force in some systems of measurement; including, English Engineering units and British Gravitational units.[1]"

If I interpret this correctly, the unqualified use of pound refers to mass!
I checked a number of other wiki pages and each time the unqualified pound referred to mass, and otherwise the word pound-force was used.

Is it possible there is still a difference between e.g. US and UK?
Note that where I live the pound refers to the metric pound which is 500 grams.

15. Nov 13, 2011

### JeffKoch

O.K., you can put a bag over your head and redirect to NIST, but consider that the word "pound" derives from the Roman libra unit, which obviously long predates Newton, F=ma, and the concept of mass as opposed to weight, which is a force. Or consider that your torque wrench is written in ft-lbs, not ft-lbs-force.

Or not.

16. Nov 13, 2011

### I like Serena

You are right of course, but I believe the use of the word pound changed (slowly) when it was linked to the kilogram in 1901.
Before then it didn't matter much.
Note that the abbreviation "lb" is still ambiguous (looking at the wiki articles).

17. Nov 13, 2011

### D H

Staff Emeritus
That bag is on your head, not mine. We in the technical community often lament when the lay world hijacks one of our terms. Prime example: "theory". Here it is the other way around. "Weight" meant "mass" long before it meant "force". This newer meaning is an abuse of long-standing terminology by the technical community. In this case, we are the ones guilty of convoluting the language, not the lay community.

You mentioned the Roman libra. Romans measured quantity of matter with a balance, not a spring scale. (The spring scales that we use measure what we now call "weight" are a fairly recent invention, dating to about 240 years ago.) The libra was a unit of mass, not force. Look to the sky. The symbol for the constellation Libra is a balance, not a spring scale. Balances measure mass, not what we now call "weight".

Perhaps you should consider that NIST strongly notes that the correct term for this unit is ft-lbf. In this case, there is little ambiguity, so calling it ft-lb does not raise a lot of heartburn.

18. Nov 13, 2011

### Staff: Mentor

What textbook is this? In most introductory books that I've seen that use the "British" system, the 3000lbs would be the car's weight (so really it should be 3000 pound-force).

I'd say it would be rather criminal to use 'lb' in two different senses within the same paragraph in a textbook!
Yes, in slugs.

19. Nov 13, 2011

### Staff: Mentor

Personally, while I think it is good to know what the official definition is, I don't think it is important. I have never once been in a situation where it wasn't clear from context whether the pound in question was a mass or a force (or money).

20. Nov 13, 2011

### D H

Staff Emeritus
You are assuming that the OP gave a fair rendition. I'm not saying that it isn't a fair rendition, but you have to admit that that is a big assumption. That said, some US engineering texts that use customary units are a bit loose with terminology.