# Lbf, lb and lbm, SI units

1. Dec 17, 2014

### Redoctober

Ok i am too confused with these american units. I have a couple of questions about them

Q1) Is lbf a force. Is lbm a mass. If yh does it mean 1 lbm = 32.174 lbf.

Q2) Is lb equal to lbm or lbf.

Q3) Is lbs equal to lb or lbm or lbf.

Q4) Lets say 1 lbm = 32.174 lbf. and from many sources i found that 1 lbf = 4.44822 N and 1 lbm = 0.45359 Kg.

So lets try this.

1 lbm ---> 0.45359 kg

0.45359*g = 0.45359*(9.81) = 4.4497 N

then using conversion 4.4497 N = 1 lbf !!!

Wow we proved 1 lbf = 1 lbm. ??!! Does it mean 1 lbm = 1 lbf and not 1 lbm = 32.174 lbf. ??

What is going on here.Is the mass and force same in the American system.

2. Dec 17, 2014

### Bystander

Yes. Yes. No.
lb. = lbf., the force exerted by 1 lbm. at the earth's surface.
lbs. is plural of lb. which is lbf. or lbm.

Now, try the rest of the exercise again.

3. Dec 17, 2014

### Redoctober

So if I say a car is 1 lbm and is accelerating by 5 ft/s^2.

Then force is 5 lbm ft/s^2..

Is there a label to this unit ? Something that symbolise Force. Then whats the force in lbf .. 0.155 lbf ?

4. Dec 17, 2014

### Bystander

F = ma, yes, had to think about that for a minute. English units are peculiar.
Looks about right for 5/32, I'll trust your math.

5. Dec 17, 2014

### SteamKing

Staff Emeritus
Imperial units may appear strange to the uninformed, but they are no more peculiar than SI units may appear to those similarly ignorant of their meaning.

The pound mass, abbreviated lbm, is a unit of mass which is defined as 0.453 592 37 kilogram.

http://en.wikipedia.org/wiki/Pound_(mass)

The pound force unit, abbreviated lbf or simply lb, is a unit of force equal to that exerted by one pound mass under the gravitational acceleration at the earth's surface.

http://en.wikipedia.org/wiki/Pound_(force)

As such, 1 lbf = 0.453 592 37 kg * 9.80665 m/s2 = 4.44822162 N

There is also a unit of mass called the slug, defined as the mass which exerts a force of 32.174 049 lbs under the gravitational acceleration at the earth's surface.

http://en.wikipedia.org/wiki/Slug_(mass)

Therefore, 1 slug = 32.174 049 lbm

If it isn't already obvious, g = 9.80665 m/s2 = 32.174 049 ft/s2 at the earth's surface

6. Dec 17, 2014

### Staff: Mentor

1 lbm is the unit of mass typically used in american system.

1 lbf is the unit of force employed in american system. 1 lbf is equal to the force exerted by gravity on 1 lbm at the earth's surface.

There is an equation for getting the net force F (lbf) on an object of mass m (lbm) when it experiences an acceleration a (ft/s2). This is the american system version of Newton's second law:

$$F=m \frac{a}{g_c}$$

where gc=32.2 $\frac{lb_f}{lb_m}\frac{ft}{s^2}$

So, if a = 32.2 ft/s2 and m = 1 lbm, F = 1 lbf

7. Dec 17, 2014

### gmax137

Yes the american system can be confusing but it does simplify certain calculatons. For example, if I carry a 20 pound box of nails up a ten foot ladder, I have done ... 200 ft-pounds of work on the box. The assumption, of course, is that I'm doing this in New York or Paris or Shanghai; it doesn't work out if I'm on the Moon or Mars.

I dont know if this helps or not (it helps me): if you push on a one lbm object with a one lbf force, it accelerates at ...32.2 ft/sec/sec

Compare to SI units, where, if you push on one kg mass with one N force, it accelerates at ... 1.0 m/sec/sec

8. Dec 17, 2014

### Danger

I never heard of any of those imperial things like Newtons until joining PF, and I still don't know what they mean. That's odd, because we used imperial units for volume and distance before going metric a few decades back. (Even that gets me once in a while in real life. I have no problem thinking in km/h now, but I still figure gas mileage in miles/gallon rather than l/100km.)

9. Dec 17, 2014

### jbriggs444

The "poundal" is a name for the unit of force equal to 1 pound mass times 1 foot per second per second.

If you don't want a "k" in your f=ma formula, you can use poundals, pounds(mass) and feet per second squared. Or pounds(force), slugs and feet per second squared. If you are willing to tolerate the k then you can use pounds(force), pounds(mass), feet per second squared with a conversion factor for the standard acceleration of gravity.

10. Dec 19, 2014

### Redoctober

In american high schools, The mass is inserted to the F=ma as slugs ???! ... Its cruical because in Aerospace Eng. Variables such as the Dynamic head $\frac{1}{2} \rho V^2$ which is typcally used in non-dimensional analysis in Lift... If in american system, Lift is in lbf which is pretty much like lbm. And if normalized with the dyanimc head which would be poundal/ft^2 and some reference area $\frac{L}{QS_{ref}}$ .. Then if i used lbm in the mass for the dynamic head, it would cause disasters..

So in general is the mass subsituted as slugs in general kinetics equations ??

11. Dec 19, 2014

### jbriggs444

In U.S. high schools, physics is normally taught in meters, kilograms and seconds. Most textbooks talk about the pound only as a unit of force and only as an example of a system of units not to use in the classroom.

In general usage in the U.S. outside the physics classroom, the pound is used interchangeably as a unit of force or of mass. So you can have 20 pound (force) test fishing line and buy a 10 pound (mass) bag of flour.

I have little insight into the units used by practicing U.S. aerospace engineers.

12. Dec 19, 2014

### SteamKing

Staff Emeritus
It depends. A slug is easy to calculate since it is the weight or the force divided by g = 32.2 ft/s2. Most often, slugs show up in things like density (slugs/ft3, for example). In a lot of engineering work, one is more interested in forces (loads on structures typically), so the mass v. force unit problem doesn't arise much.

In other areas of engineering, typically vibrations, thermodynamics, gas dynamics, etc., one encounters the use of mass directly more often, and here, I think, the pound mass gets the nod for convenience, since there is a direct relation between the kilogram and the pound-mass. Thus, quantities like flow rates are given in lbm/s or specific volumes in ft3/lbm.

In my engineering experience, units like poundals are typically not encountered at all.

13. Dec 19, 2014

### Staff: Mentor

In my experience as a Chem eng, gc is used ubiquitously.

14. Dec 19, 2014

### Redoctober

Usage of gc would make sense. actually, but in case if i use it, would it be always set in side with the force, For example $F g_c = ma$ where F is set in lbm and F as lbf..

Can i conclude that the Weight is taken as lbf but mass as lbm. Yet their magnitudes are same. When i substitute to kinetic equation, i should use g_c. Such as $\frac{W g_c}{q S} = C_L$ where the denisty this time uses lbm instead of slugs in calculation of dynamic head so $C_L$ can finally be nondimensional.

15. Dec 20, 2014

### Staff: Mentor

It would usually be $F = \frac{ma}{g_c}$

16. Dec 20, 2014

### Staff: Mentor

You have to be very careful with the context here. In most engineering and materials textbooks and problems it is correct that "lb." means "lbf." However, officially (as defined by NIST) in law and commerce "lb." means "lbm." As a result, I think that the best approach is to always use "lbm." or "lbf." and not "lb.", and if you see "lb." then look carefully at the context to determine which is being used.