# Why is 1 lbm considered equal 1 lbf?

• B
• vSpeedy
In summary: Many agree that the US should get in step with the rest of the world and convert to SI. But the fact is that is not the case now, and units of pounds and feet will be around for decades to come.As for the Imperial system, when I visited England I found the only remainder were some distances quoted in miles. They sell coffee by grams and milk by liters. Perhaps the name should be changed to US system.Many agree that the US should get in step with the rest of the world and convert to SI. But the fact is that is not the case now, and units of pounds and feet will be around for decades to come.
vSpeedy
My understanding is that 1lbm = l lbf/32.174 ft/s^2 = 3.1081*10^-2 (lb*s^2)/ft (slug)

My textbook suddenly claims that 1 lbf is equal to 1 lbm. This doesn't fundamentally make sense to me because one unit is mass and the other is force (which has an acceleration constant).

Thanks for helping me understand

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They aren't the same; one is a mass and the other a force.
Unfortunately, the same confusion showed up with the kilogram: we have the mass kilogram and the force kilogram (now largely replaced with the Newton as the unit of force).
The quantities differ in the gravity acceleration, that's why you invent the slug in a way that when you apply a force of one pound you get an acceleration of 1ft/s2. A slug is a big chunk of mass.Conversely, when a one force pounds acts on a mass pound we obtain an acceleration equal to g (32.2 ft/s2)
When a was a teenager I spent long hours memorizing the different conversion factors. Now I hardly remember them and I use SI units.

vSpeedy said:
My understanding is that 1lbm = l lbf/32.174 ft/s^2 = 3.1081*10^-2 (lb*s^2)/ft (slug)

My textbook suddenly claims that 1 lbf is equal to 1 lbm. This doesn't fundamentally make sense to me because one unit is mass and the other is force (which has an acceleration constant).

Thanks for helping me understand
Textbook is wrong if it is worded that way. 1 lbm has a weight of 1 lbf on planet Earth. It's mass is as you state , in slugs. Always use slugs as the mass unit in calculations involving mass. The pound-mass is seldom used,

Gordianus said:
we have the mass kilogram and the force kilogram (now largely replaced with the Newton as the unit of force).

I have never heard of a "force kilogram". And I come from a metric country.

PhanthomJay said:
Always use slugs as the mass unit in calculations involving mass.

*groans*

I would say, never use slugs for anything.

sophiecentaur
W
rumborak said:
*groans*

I would say, never use slugs for anything.
well I guess you don't come from the USA. If imperial units of force and length (poinds and feet) are used, which is the norm in many engineering disciplines, then youust use slugs as the mass unit. Usually we talk force units of pounfds,and must divide it by 32 to get the proper mass unit in problems involving mass such as when calculating accelerations in ft/sec^2, or for frequency or seismic calculations.

I know that that's what's happening, but I would hope you agree that it shouldn't be that way. The moment derived units come into play, anything but SI is a waste of time. Reality is, you aren't hireable for an internationally operating engineering company if you can't do SI.

davenn
rumborak said:
I know that that's what's happening, but I would hope you agree that it shouldn't be that way. The moment derived units come into play, anything but SI is a waste of time. Reality is, you aren't hireable for an internationally operating engineering company if you can't do SI.
Many agree that the US should get in step with the rest of the world and convert to SI. But the fact is that is not the case now, and units of pounds and feet will be around for decades to come. So here, if you apply a force of ten pounds to a mass of one slug, its acc is 10 ft/sec^2. But would be a waste of time to convert to kilos and Newtons and get results in meters per sec squared and then convert back again to ft per sec squared. If you want to get a job here you need to know customary US units.

rumborak said:
I have never heard of a "force kilogram". And I come from a metric country.

When I was a teenager, the Newton hadn´'t won "the battle of forces" yet and we had the force kilogram (the weight of the famous cylinder) and the mass kilogram (the mass of said cylinder). As a result, we had a unit of mass conceptually similar to the slug. A big mess I don´t miss.
As for the Imperial system, when I visited England I found the only remainder were some distances quoted in miles. They sell coffee by grams and milk by liters. Perhaps the name should be changed to US system.

Gordianus said:
When I was a teenager, the Newton hadn´'t won "the battle of forces" yet and we had the force kilogram (the weight of the famous cylinder) and the mass kilogram (the mass of said cylinder).
Which decade was that? (and where?) I started at School (UK, 1950s) with ft,lbs and poundals (yuk), then moved on to cgs (dynes, ergs etc). Finally ended up (1960s) with mks, which became regularised as SI. I never remember anyone talking of a force kilogram. What a ghastly idea.

nasu said:
I think he means "kilogram-force". And it was used in many parts of the world, if not in the UK. Maybe is still used somewhere.
https://en.wikipedia.org/wiki/Kilogram-force
I guess that Mr Scales my Physics master and hero (and possibly the Oxford and Cambridge Joint Examination Board to) decided to avoid such a horrible unit. My physics education was never aimed in the direction of Engineering.

I actually have to somewhat revise my initial statement about the kilogram-force. In the country I grew up in it had the name "kilopond', and yes, I have heard that name before. It has a distinct "twirly moustache" feeling to it though.

Last night on YouTube I saw a video from 1972 on how America would soon be a metric country.

sophiecentaur
rumborak said:
I have never heard of a "force kilogram". And I come from a metric country.

sophiecentaur said:
... I never remember anyone talking of a force kilogram. What a ghastly idea.

I have asked this before but I don't remember getting an answer: When someone asks your weight, do you answer "70 kilos" or "685 Newtons" ?

gmax137 said:
I have asked this before but I don't remember getting an answer: When someone asks your weight, do you answer "70 kilos" or "685 Newtons" ?
The question "how much do you weigh" is reasonably interpreted as "what is the mass of your body". That is the quantity that is of importance to most physicians (other than orthopedists dealing with ankle, knee and hip problems). It is also the quantity that is measured in a doctor's office on the balance scales there. It is the quantity that is nominally measured by your bathroom scales, even though the displayed value is typically determined through the use of a force proxy. In the grocery store, calibration is done so that the displayed quantity is not just nominally equal to the mass of the object being weighted, it is actually equal to the mass of that object despite the use of a force proxy.

Despite what most first year physics textbooks teach (or taught in my day), in the U.S. the "pound" is legally standardized as a unit of mass and "net weight" is legally standardized as an assertion about mass. In the grocery store, "weight" is mass. In the physics classroom, "weight" is force.

Dale
So, your answer is "xx kilos"?

I understand all the rest of your post and I don't disagree with any of it.

gmax137 said:
I have asked this before but I don't remember getting an answer: When someone asks your weight, do you answer "70 kilos" or "685 Newtons" ?
Yes. And if you went into a greengrocer's shop and asked for 20N of potatoes he/she would give you a funny look. But there is a difference between a Scientific discussion and a system of proper units and the way those units are used by the general public. I could give you an almost endless list of how Science is mis-used by non-Scientists. We just have to grit out teeth and avoid being that naughty amongst ourselves.

gmax137 said:
So, your answer is "xx kilos"?
Yes. At least that would be my answer if I lived and worked in a country whose customary system of units and measures included kilograms and Newtons.

Where I actually live, I would give the answer as [too many] pounds and not worry about the fractional percentage point of ambiguity in the answer.

OK thanks you guys. My curiosity is not about "scientific discussions" I was really interested in what terms are in "everyday" use in SI countries. I half expected the answer to be "11 stone."

gmax137 said:
I half expected the answer to be "11 stone."
Whilst teaching 14 year olds about Work (mechanical type) and Power I got them to run up stairs, timing themselves. They were more than happy for their mass in kg to be written down but I avoided telling them what that made their 'weight' in stones and pounds. They just didn't associate the two things at all. Personally, I haven't used stones for a long time and I don't actually know my 'weight' in those units. The only way to cope is to make a clean break.
Now I'm off for a pint.

DrClaude, gmax137 and Dale
vSpeedy said:
My textbook suddenly claims that 1 lbf is equal to 1 lbm.
Which textbook is it? Is it a high-school or university-level book?

Yeah, kilograms and meters are used for bodily measurements in metric countries. There *is* a "pound" in German (Pfund), but it's just shorthand for exactly 500g, and only used for groceries below a kilogram.

## 1. What is the difference between lbm and lbf?

Lbm stands for pound mass, which is a unit of mass based on the international avoirdupois pound. Lbf stands for pound force, which is a unit of force based on the gravitational force of one pound acting on a mass of one pound. In simpler terms, lbm measures the amount of matter in an object, while lbf measures the force exerted on an object due to gravity.

## 2. Why is 1 lbm considered equal to 1 lbf?

This is because the avoirdupois pound, used to measure both lbm and lbf, was originally defined as the mass of one cubic inch of water at its maximum density. This means that under standard gravity, the weight of one pound mass is equal to the force of one pound force.

## 3. Is this relationship between lbm and lbf always true?

No, this relationship is only true under standard gravity. If the force of gravity changes, for example on another planet, the relationship between lbm and lbf will also change.

## 4. Can lbm and lbf be converted into other units?

Yes, both lbm and lbf can be converted into other units of mass and force, respectively. However, it is important to note that the conversion factor will vary depending on the specific unit being converted to.

## 5. Why is it important to distinguish between lbm and lbf?

It is important to distinguish between lbm and lbf in order to accurately measure and calculate forces and masses in scientific experiments and engineering applications. Using the wrong unit can lead to errors and inaccuracies in calculations.

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