Converting lbm & lbf: Help with Newton's 2nd Law

[zzinfinity]

I'm a little confused about the conversion between lbm and lbf (mass pounds and force pounds).

I'm doing a problem where I'm using Newton's 2nd law to calculate mass flow rate.

F= Δ((Mass flow rate)*Velocity)

I know my force is 400 lbf and velocity is 40 ft/s so mass flow rate is

10 lbf/(ft/s)

Is the the same as 10 lbm/s? Or do I need to divide by g or something?

Thanks!

 

[Travis_King]

Take a look at this. Slugs are confusing sometimes.

 

[D H]

I know my force is 400 lbf and velocity is 40 ft/s so mass flow rate is

10 lbf/(ft/s)

Is the the same as 10 lbm/s? Or do I need to divide by g or something?

Thanks!

It's the same as 10 slug/s. To get lbm/s you need to multiply by 32.17404855643.

 

[jim hardy]

English system confuses a lot of people because word "pound" can refer to either a force(like weight) or a mass. It takes some mental exercise to get accustomed to the difference between force and mass.


a one pound mass happens to weigh a pound on Earth at standard latitude, which is someplace around Boston.
A spring scale and a balance scale using weights would agree in Boston.
If you carry the whole apparatus to Miami, the one pound mass will weigh less by about 0.17% because of increased centrifugal force near the equator opposing gravity..

A spring scale taken to Miami would have to be recalibrated for local gravity if it is to report mass,
and a balance scale using weights would have to be recalibrated if it is to report force..

In my power plant we bought special weights for our deadweight pressure calibrators because pressure is lbf/in^2.

There's another old English unit, the poundal.. one pound of mass weighs 32.174 poundals in standard gravity... sort of the flip side of the 'slug'.

Some old Mercedes Benz shop manuals gave torque specifications in Kg-meter
which ought to have driven purists crazy. So don't take your Mercedes to a repair shop on the moon, everything will be set too loose.

Please excuse my silly exaggerations - but taking things to extreme sometimes helps cement a cocept. Afterward you don't have to admit you ever stooped to it.

old jim

 

[OldEngr63]

It is a serious mistake to use lbf and lbm in the same calculation.

If you have lbf and other units such as ft (or in) and sec, then you such use slugs (or lb-s^2/in) for mass.

If you have lbm and other units such as ft and sec, then you should use poundals for force.

They really do not mix well at all, and they can lead to gross confusion and major errors.

 

[D H]

It is a serious mistake to use lbf and lbm in the same calculation.

No, it's not. It's just clumsy. Newton's second law is F=kma, not F=ma. It was rewritten as F=ma 100 years after Newton's time.

 

[OldEngr63]

I stand by what I said. It is a serious mistake to use lbf and lbm in the same calculation. It has led to countless mistakes.

The idea that F = kma is nonsense. There is no k in there. Newton's second law is F = m a with nothing more, provided consistent units are used. The use of inconsistent units (such as lbf and lbm) is dangerous foolishness and a very bad, unprofessional practice.

 

[OldEngr63]

IBF = ?
IBM = ?
What are these quantities? I don't recognize either one, unless the second one makes computers.

 

[gmax137]

IBF = ?
IBM = ?
What are these quantities? I don't recognize either one, unless the second one makes computers.

lb_{f} is pounds force
lb_{m} is pounds mass

I know you hate to see them together on the same page, but there it is...

 

[D H]

I stand by what I said. It is a serious mistake to use lbf and lbm in the same calculation. It has led to countless mistakes.

If you're careless and use F=ma. So don't be careless.

The idea that F = kma is nonsense. There is no k in there.

Lex II. Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
In English, "The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed."
In math, F\propto \Delta p

Note well: Proportional to, not equal to. Of course there is a k in there. That proportionality constant can be made to be equal to 1, which is what the metric system handily does.

Newton's second law is F = m a with nothing more, provided consistent units are used. The use of inconsistent units (such as lbf and lbm) is dangerous foolishness and a very bad, unprofessional practice.

What about the Planck constant, the Boltzmann constant, the universal gravitational constant, or the speed of light? These, too, can be made to vanish with the "right" choice of units. Physicists oftentimes do just that. Does this make systems of units such as the metric system that don't have ħ, k_B, G, and c identically 1 "wrong"? Of course not. You just have to be careful when you are using metric units.

I much prefer to work in (and almost always do work in) metric units. That proportionality constant k pops up in a number of places, and I'd much rather avoid it. Sometimes I'm forced to work in English units, and that constant of proportionality pops up in a variety of places. There's nothing wrong with it. It's just clumsy.

 

[gmax137]

It is a serious mistake to use lbf and lbm in the same calculation...

No, it's not. It's just clumsy...

OK, I just can't let this go.

1) I have a 1 pound mass and I put it on my bathroom scale. What does the scale read?
Answer: "one pound"

2) I carry a 10 pound mass up a flight of stairs that is 12 feet high. How much work did I do on the mass?
Answer: "120 ft-pounds"

What's wrong or clumsy here?
Answer: It assumes you are answering from the surface of the earth.

Seems like a good trade-off, since so far I am on the surface of the earth.

 

[jim hardy]

"Answer: It assumes you are answering from the surface of the earth.

Seems like a good trade-off, since so far I am on the surface of the earth."


What's wrong or clumsy here?
Actually your pound mass weighs a pound only if you are someplace on surface of Earth where local gravity is same as "standard".
Not that one is likely to notice, but in Miami it'd weigh about 0.9983 pounds.

 

[gmax137]

Yeah, but you have the same problem if you're using metric units (is g 9.8 m/s or is it 9.799 here?).

I guess the 'English' units may mask that issue; allow an inexperienced person to miss it if it is important. And in fairness to OldEngr63, that's not a bad point.

 

[OldEngr63]

As was observed above, Newton said that
F \propto Δp
and so to write this in equation form requires the introduction of only a single constant,
F = m a,
not the double constant form
F = k m a

The only MKS and CGS systems (that preceded SI) were often used with many inconsistencies, such as the bastard forms kilogram-force (kgf) before the Newton was established by SI, gram-force in stead of a dyne, which present exactly the same problem of the pound-mass. One of the big thrusts of the SI system was to sort that mess out, at least in the metric world, so that kg are used for mass, Newtons are used for force and people think that the world was created this way. It took a careful effort to get that right, but it was worth it, and the same thing can and should be done with US Customary units.

If someone asked you to look at a calculation you made seven years ago, and tell them, is that a pound-mass or a pound-force, could you quickly tell them? I could, because I always use consistent units. I never, ever, under any circumstances use inconsistent units. It is a fatal error. Suit yourself.

 

[jim hardy]

i travel in a mostly unscientific circle and get this question all the time, "just how much is a Newton?"

I usually respond "approximately the weight of a McDonald's Quarter Pounder" because they'll remember that word picture.


@ oldengineer - thanks for remembering Poundals.

old jim