pound of lead

[rbos]

I don't understand the joke in today's strip. Since a pound is a unit of weight, not mass, measurements taken under identical conditions should always be the same by definition. The force that a certain mass of feathers would exert on a scale (assuming as Danny does identical conditions) would take into account buoyancy and thus, a pound of feathers and a pound of lead are by definition exerting the same amount of force on a scale.

Unless I'm misunderstanding US measurements, and a pound isn't a force measurement. A pound according to wikipedia is the amount of force exerted by 7000 "grains" (a mass measurement, about 65 milligrams) at sea level, notwithstanding local gravitational variations.

So a "pound" of feathers could be the amount of force exerted by 7000 "grains" of feathers, or 7000 "grains" of lead, under Earth-normal sea level conditions.

Taken that way, a "pound" could vary from negative values (7000 grains of helium) all the way up to the upper limit.

For today's strip's joke to work, then, the entire concept of "pound" as a stable unit of weight is gone and is entirely materials and conditions-dependent.

[Javelin]

Though I hesitate to question the Great and Powerful Wikipedia, I seem to recall seeing somewhere (and I'm wanting to say it was an ANSI standards publication) that somewhere along the line, "pound" (abbrev. "lb") was actually (re-?)defined as a unit of mass, and that "pound-force" (abbrev. "lbf") is the corresponding unit of force. This was many years ago, and I'm too lazy atm to attempt to look it up, so I'm really not sure. But if so, the joke works.

Update: okay, shamed myself into looking it up; asked Wikipedia about "pound force" -- http://en.m.wikipedia.org/wiki/Pound_force

Seems my memory was at least close, but it's actually a bit more confusing. From the section on "foot-pound-second systems of units":

In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf*s^2/ft. In other contexts, the unit "pound" refers to a unit of mass. In circumstances where there may otherwise be ambiguity, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish.

[rbos]

Makes my head hurt a little. I empathize with the need for tradition and using the system you grew up with, but I wish the US would just switch to metric already.

[rbos]

I think the joke still fails. "What weighs more, a pound of feathers or a pound of lead". The use of "weighs" implies force-pounds, or newtons, not mass-pounds, or grams. So if we assume consistency of units, then Danny's nitpicking is wrong, he's using a different definition of pound than the joke-teller.

Still funny, thought-provoking, and educational, but I think Danny was wrong to raise that objection.

[sylver]

He explains the issue: buoyancy in air.

The assumption here is that the weight of the feathers and of the lead is measured in a vacuum, and of course once measured in air, a "pound" of lead is now slightly less than a pound, while a pound of feather is now considerably lighter than a pound.

[Gav]

That's correct, more or less. The "joke" extends the previous panel's point about assumptions (and also pokes fun at english units, which I despise as much as any non-american). One might "assume" if one is talking about how much a pound "weighs," one is talking about pounds-force. But that's just an assumption... the same kind of seemingly-logical "speed travels at the speed of light" assumption.

In fact, one cannot refer to "a pound of lead" in such a question and mean pounds-force. One could only say "an amount of lead which exerts a pound of force under certain gravitational and atmospheric conditions." If one says "a pound of lead," one must be talking about pounds-mass.

In other words: "A pound-force of lead" doesn't uniquely describe any one object. "A pound-mass of lead" does. So for the question to have a unique answer (which it must if one asks it, thus expecting an answer), it must imply pound-mass.

It would be like saying "What has more paper, a book or a magazine?" versus "What has more paper, this book or this magazine?"

So now that we've established the units must be pounds-mass, the larger volume of feathers displaces more air than the lead and just as a ping pong ball weighs less than an equal-mass BB under water, the lead weighs slightly less than the lead on a scale in air. Eureka.

Although, I wouldn't guess the feathers would be "considerably lighter." Probably more like 0.999 pounds. Someone want to figure it out?

[Javelin]

Although, I wouldn't guess the feathers would be "considerably lighter." Probably more like 0.999 pounds. Someone want to figure it out?

Sure! How tightly packed are the feathers?

[Gav]

Sure! How tightly packed are the feathers?

Heh. Way to not make assumptions!

It seems to me there are two logical arrangements. One would be if the feathers were packed as tightly as possible so as to remove all intervening air. You'd have to wrap it in plastic and vacuum out all the air and then subtract the weight of the plastic. This then becomes an incredibly academic example, but we went there a long time ago. In this case, I'd just make the assumption that feathers are about 1 g/cc. The second example would be feathers "naturally stacked."

In fact, I think there isn't a difference in weight in either case. The "buoyancy" is caused by the total displacement of air, and adding air doesn't displace any more air. Like, if you had a bunch of ping pong balls in water, their total buoyancy wouldn't be affected by if they were closely packed and glued together in one big hunk, or in BCC form, or into a huge hollow (water-filled) sphere.

So I think all you need is the feathers' density without air. Am I thinking about this right?

Darren

[MaxJenius]

Sure! How tightly packed are the feathers?

In fact, I think there isn't a difference in weight in either case. The "buoyancy" is caused by the total displacement of air, and adding air doesn't displace any more air. Like, if you had a bunch of ping pong balls in water, their total buoyancy wouldn't be affected by if they were closely packed and glued together in one big hunk, or in BCC form, or into a huge hollow (water-filled) sphere.

So I think all you need is the feathers' density without air. Am I thinking about this right?

Darren

Well considering air itself has a bit of weight, technically unpacked feathers actually weigh more than packed feathers, so if you consider things volume wise feathers weigh more with air as air would be included within the volume.