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Old 12-03-2018, 11:52 PM
A Dodgy Dude A Dodgy Dude is offline
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What exactly is mass?

The Science Channel is airing a show about black holes and all the experts talk about the holes have "x times the mass of the sun."

I can't figure out what they are talking about exactly. Is mass
  • weight
  • size/volume
  • density

If you had a one-pound ball of feathers and a one-pound ball of lead, which one has the most mass?
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Old 12-04-2018, 12:16 AM
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Here in everyday life on earth, weight and mass are equivalent. That should answer your question.

More technically though, "mass" is the fundamental characteristic of the object, and "weight" refers to the force of gravity on it. You weigh less on the Moon than on the Earth, but your mass is the same in both locations.
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Old 12-04-2018, 12:18 AM
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A good intuitive feel for mass is, how hard do you have to push on the object to get it moving? If you shove a boulder with the same force as a pebble, it will not go as fast. It is related to the amount and type of matter present.

So mass is none of the things you listed above: not weight, density, or volume.

Though it is related: Newton said F = m a, so your one-pound balls have the same mass, assuming you weigh both on Earth.

Volume is how much space an object takes up (how much it takes to fill it). If you divide the mass of the object by its volume, that defines its density; feathers are less dense than lead.
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Old 12-04-2018, 12:19 AM
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Mass is a measure of mass/energy. Two one pound bags of anything at all have exactly the same mass--a one pound bag of helium has the same mass as a one pound bag of lead. Weight is how that mass is effected by gravity--a one pound mass weighs one pound on the Earth's surface (within a small margin depending on where on the Earth's surface) but would weigh more or less on another planet, asteroid, neutron star, whatever. A one pound mass of feathers on a neutron star would be pretty weighty (but not sure how much without doing the math--maybe the weight of a carrier battle group? A small city?)
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Old 12-04-2018, 12:24 AM
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Fun fact: a black hole is not necessarily very dense at all, once it gets super massive.
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Old 12-04-2018, 12:34 AM
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Okay, a one pound mass of feathers on a neutron star would weigh around a dozen Great Pyramid of Gizas.
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Old 12-04-2018, 01:23 AM
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Originally Posted by A Dodgy Dude View Post
p
If you had a one-pound ball of feathers and a one-pound ball of lead, which one has the most mass?
If the above measurement is carried out on earth, in its atmosphere, the ball of feathers has more mass due to buoyancy in air.

If the measurement is done is vacuum, then both have the same mass.
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Old 12-04-2018, 02:43 AM
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If the above measurement is carried out on earth, in its atmosphere, the ball of feathers has more mass due to buoyancy in air.

If the measurement is done is vacuum, then both have the same mass.

No.
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Old 12-04-2018, 07:04 AM
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Mass is a measure of a body's resistance to a change in state of motion, i.e. the larger a body's mass, the greater the force that needs to be applied to produce some acceleration. The gravitational force acting on a body in a gravitational field is directly proportional to its mass; at the Earth's surface the gravitational field has approximately constant magnitude and the magnitude of the gravitational force acting on an object is often called its weight, which is why mass and weight are often treated as synonymous.
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Old 12-04-2018, 07:53 AM
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If the above measurement is carried out on earth, in its atmosphere, the ball of feathers has more mass due to buoyancy in air.

If the measurement is done is vacuum, then both have the same mass.
This is absolutely, completely, 100% wrong.

If you had a one pound bag of feathers and a one pound bag of lead, their weight ON EARTH is the same... One pound. That indicates their mass is the same, since we usually determine mass by weighing something. Their density is very different. The bag of feathers has far less density than the bag of lead.

Mass is not weight. Mass is confused with weight because we often use an object’s weight to determine its mass. However, they are NOT the same thing.

If I took a bowling ball on Earth, I could measure its weight as a method of determining its mass. Then if I flew to the moon and measured it, the weight would be significantly less because the pull of gravity is weaker on the moon. But as long as I knew the force of gravity on the moon, I could still calculate the mass correctly. The mass of an object never changes unless you physically break the object into smaller pieces.

If we were orbiting in a space ship it is very difficult to measure weight because we are in free-fall. If the ship is orbiting without any propulsion, the object would not rest on the scale and so we would not be able to measure its weight. However, mass still functions. If I am floating in space and I touch an object that is smaller (less massive) than me, I can accelerate the object away from me and I will move very little. If I touched an object more massive than me, even though we are in zero gravity, I would be pushed away from it and the more massive object would move very little.

With regard to OP... When some says a black hole has “X times the mass of the sun” they are saying that the sum total if matter composing it is X times bigger than our sun. Imagine I have a sphere made of lead. Then I make another sphere composed of twice as much lead. All other factors being equal, the larger sphere will be twice as massive, and twice as heavy, because it has twice as many lead atoms composing it. I know this because the density of the two spheres would be the same, because it is really, really hard to compress atoms together.

But let’s say I was Superman, and I used my incredible strength to physically shove the atoms together and - using an unbelievable amount of force - I compressed the larger lead sphere into a smaller space. Now they have the same size, but the second sphere still has twice the mass and twice the weight, because I have not changed the total number of atoms in the sphere. However, it is also now twice as dense, because I have not changed the total number of atoms... I just compressed them into a smaller space.

It would take an absolutely insane amount of force to compress atoms in this way. But that’s what is happening in a black hole. The total amount of matter is X times our sun, but that matter has been compressed into a (relatively) tiny and exceedingly dense little ball.

Last edited by JB99; 12-04-2018 at 07:56 AM.
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Old 12-04-2018, 08:05 AM
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You do absolutely need to make a correction for air buoyancy when weighing masses, because air is dense. If you do not, your mass calculation will be off by a few to hundreds or even more parts per million.
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Old 12-04-2018, 08:13 AM
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This is absolutely, completely, 100% wrong.
What I said is ďabsolutely, completely, 100% ď correct. Donít make Archimedes squirm in his grave.
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Old 12-04-2018, 08:19 AM
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You said “the ball of feathers has more mass due to buoyancy in air.” There’s no way this is true. You have not changed the MASS of the feathers, which remains invariant. You’ve changed the MEASUREMENT.

Last edited by JB99; 12-04-2018 at 08:21 AM.
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Old 12-04-2018, 08:29 AM
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What I said is ďabsolutely, completely, 100% ď correct. Donít make Archimedes squirm in his grave.
You are confusing Mass and Density.
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Old 12-04-2018, 08:36 AM
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If you had a one-pound ball of feathers and a one-pound ball of lead, which one has the most mass?
They have the same mass. Don't confuse mass with density.
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Old 12-04-2018, 09:25 AM
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Urm, am77494 is quite correct. In the limiting case, weigh one cubic metre of air at STP. The mass is pretty close to 1kg. If you ignore the weight of the balloon holding your 1m3 of air, you will get a weight of zero.
The buoyancy of objects being weighed in air matters, and is accounted for when accurate measurement is required. It isn't confusing mass and density, it is allowing for the density of the object relative to the density of air perturbing measurement of the force seen due to gravity acting on the object's mass. This is a common correction that is required to be made in accurate work.

Last edited by Francis Vaughan; 12-04-2018 at 09:26 AM.
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Old 12-04-2018, 09:26 AM
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Your total mass is the sum total of the mass of all the proton, neutrons and electrons in your body. Since an electron weighs only 1/1800 of the others then, essentially, it is the protons and neutrons of your atoms that constitute the majority of the mass of your body. When you step on the scale, that is what your are weighing. More massive objects have more of these things and less massive objects have less.
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Old 12-04-2018, 09:39 AM
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Okay, a one pound mass of feathers on a neutron star would weigh around a dozen Great Pyramid of Gizas.
"... on Earth" - important caveat.

And on a nitpicky note, I'm sure it's Great Pyramids of Giza

Last edited by MrDibble; 12-04-2018 at 09:41 AM.
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Old 12-04-2018, 09:48 AM
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Maybe everyone needs the feathers thing explained more clearly. Hopefully I have this right.

You have two scales that measure WEIGHT in front of you. You pour lead shot onto one until is says 1 lb. You move to the second scale and pour feathers onto it until it says 1 lb. They both have the same WEIGHT.

Which one has the greater mass? Well, buoyancy is acting on both and buoyancy is proportional to the weight of the displaced fluid (air). The feathers, being less dense, displace more air, so they will experience more buoyancy. Because of this there must be more MASS of feathers on my scale to make it say 1 lb of WEIGHT.
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Old 12-04-2018, 09:50 AM
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Urm, am77494 is quite correct.
He said two objects that have the same mass in a vacuum have different mass in Earth's atmosphere. Are you saying that is correct or are you interpreting what he said differently?

If what he meant to say is that when the measurement is performed in Earth's atmosphere the ball of feathers would seem to have more mass (due to the scales' measurements) because of buoyancy, then he has it backwards. The ball of feathers would seem to have less mass, i.e., the ball of feathers would exert less pressure on its scale then the ball of lead would.

Last edited by x-ray vision; 12-04-2018 at 09:54 AM.
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Old 12-04-2018, 10:13 AM
Francis Vaughan Francis Vaughan is offline
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No, it is subtle. In order to get the weight the same, you would need to add a few more feathers to overcome their buoyancy. So for the same weight, in the atmosphere, the feathers require more mass than the lump of lead. Whereas in a vacuum, you don't need the extra feathers.

Last edited by Francis Vaughan; 12-04-2018 at 10:14 AM.
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Old 12-04-2018, 10:22 AM
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Okay, I see what he's saying now. Yes, he's correct.
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Old 12-04-2018, 10:33 AM
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Originally Posted by MrDibble View Post
"... on Earth" - important caveat.

And on a nitpicky note, I'm sure it's Great Pyramids of Giza
Actually, no. They are the Pyramids of Giza. The Great Pyramid of Giza (or Cheops or Khufu) is the largest and oldest of the three.

Hey, look at me contributing to a sciency-type thread!
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Old 12-04-2018, 11:17 AM
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An extreme example of weight and mass not being proportional in Earth's atmosphere is a hot-air balloon.

As you add heat to an inflated balloon, mass decreases slightly (fuel is burned; the air in the envelope grows hotter and thus less dense). But weight - what a scale under the balloon would indicate - decreases significantly. Eventually, it becomes zero and even negative - the balloon rises.

The result is an object with a great deal of mass (in the case of a largeish balloon, it could easily exceed 10 tonnes) and no weight.
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Old 12-04-2018, 03:33 PM
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This topic will have the same problem all of these discussions do, random use of inconsistant definitions.

In the "metric" system the word weight has a specific defined meaning that most people ignore, and as a low precision measurement is just invalid in the cases of a large amount of buoyancy as mentioned above..

https://www1.bipm.org/en/CGPM/db/3/2/
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The word "weight" denotes a quantity of the same nature as a "force": the weight of a body is the product of its mass and the acceleration due to gravity; in particular, the standard weight of a body is the product of its mass and the standard acceleration due to gravity;
If you choose another definition for weight no comparisons will hold except for those that choose the same definition you.

The same problem presents itself with mass.

If you use the definition of "mass" that is used by modern science you will be talking about "inertial mass" which is a measurement of a closed systems resistance to changes in momentum. Or phrased slightly differently the property that is the inertial resistance to acceleration of a body when responding to all types of force.

If you choose another definition for mass your results will vary.

In low precision uses you can use "mass" as a quantity, like cooking with divisions of the kilogram. But that is a low precision measurement that ignores that added energy like heat or changes in configuration (density) will impact the inertial properties if you have accurate enough instruments.

Stick with the Metric definition of weight and the rest mass or inertial mass and you will be OK.

Otherwise this problem will have no answers or may lead to false understanding of fundamental physics.

Last edited by rat avatar; 12-04-2018 at 03:33 PM.
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Old 12-04-2018, 05:25 PM
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I worked in weights and metrology and have had to explain the difference between weight and mass many times. Here's what gets most folks over the speedbump:

Weight is a special name for the force that results from gravity's influence on mass.
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Old 12-04-2018, 06:57 PM
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Buoyancy is irrelevant to both mass and weight. The only relevance of buoyancy to the feathers-and-lead example is that most typical scales will be slightly inaccurate at measuring the feathers' weight (actually they'll be slightly inaccurate for the lead, too, but more so for the feathers).

For comparison, suppose that you're weighing yourself on your bathroom scale, but while you're doing so, you lean against the sink. That'll make the scale show a lower number. Does that mean that, by leaning against the sink, you've lost weight? No, it just means that the scale isn't measuring all of your weight, because part of your weight is supported by the sink instead of by the scale. Buoyancy is the same deal, except there you're leaning against the air.
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Old 12-04-2018, 07:09 PM
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A one kilogram mass weighs 2.205 pounds on earth.

On the moon it now weighs about 6 ounces, but the mass is still one kilogram.

Last edited by bizerta; 12-04-2018 at 07:11 PM.
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Old 12-04-2018, 07:27 PM
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Buoyancy is irrelevant to both mass and weight. The only relevance of buoyancy to the feathers-and-lead example is that most typical scales will be slightly inaccurate at measuring the feathers' weight (actually they'll be slightly inaccurate for the lead, too, but more so for the feathers).

For comparison, suppose that you're weighing yourself on your bathroom scale, but while you're doing so, you lean against the sink. That'll make the scale show a lower number. Does that mean that, by leaning against the sink, you've lost weight? No, it just means that the scale isn't measuring all of your weight, because part of your weight is supported by the sink instead of by the scale. Buoyancy is the same deal, except there you're leaning against the air.
That's a fantastic explanation. It also makes the point that your true weight isn't what shows on a scale -- which might not matter in everyday life but does in science.
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Old 12-04-2018, 07:44 PM
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Buoyancy is irrelevant to both mass and weight.
I'd say you can't have weight without weighing (the act of determining weight) and, since buoyancy plays a role in weighing, it's not quite right to say irrelevant.

It's like that old saying 'Falls from height never killed anyone, it's the landing.' I argue that the landing is part of the fall, just as weighing is the only way to determine weight and buoyancy must be considered.
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Old 12-04-2018, 08:01 PM
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I'd say you can't have weight without weighing (the act of determining weight) and, since buoyancy plays a role in weighing, it's not quite right to say irrelevant.

It's like that old saying 'Falls from height never killed anyone, it's the landing.' I argue that the landing is part of the fall, just as weighing is the only way to determine weight and buoyancy must be considered.
What you are mentioning is the operational definition of weight or the force measured by the operation of weighing it, which is the force it exerts on its support.

As the operational definition does not explicitly exclude the effects of buoyancy and it counter to the gravitational definition and will also have to take centrifugal force into account when working with scales.

So remember to discard this version when you try to use scientific formula. As example, an object in free, e.g. an astronaut does not lose "gravitational weight" during free-fall but would under the operational model.

Really this is only a pain because Newtonian and Galilean Mechanics uses a space that looks simple yet ends up being an ℝ3 bundle over ℝ1 with an inability to invert matrix that is degenerate. Note that technically under the operational definition weight needs to be a vector too.

IMHO taking the official Metric definition stand for low precision measurements and ignoring the entire concept is probably the best. As these threads show it is impossible to get people to stick to one definition for 'weight', mostly because people seem to want gravitational and inertial acceleration to be from separate fundamental properties when they are not, because we historically lie to students and tell them this is.

Last edited by rat avatar; 12-04-2018 at 08:03 PM.
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Old 12-04-2018, 09:17 PM
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...so your one-pound balls have the same mass...
So why do they droop unequally?


mmm
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Old 12-05-2018, 05:11 AM
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Actually, no. They are the Pyramids of Giza. The Great Pyramid of Giza (or Cheops or Khufu) is the largest and oldest of the three.

Hey, look at me contributing to a sciency-type thread!
Err, hate to break it to you, but no, the referent here is to the Great Pyramid, alone, as a unit of measure.
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Old 12-05-2018, 08:30 AM
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Err, hate to break it to you, but no, the referent here is to the Great Pyramid, alone, as a unit of measure.
Darren Garrison said "Great Pyramid of Gizas." You corrected him and said "Great Pyramids of Giza." Chefguy in turn corrected you. There are the Pyramids of Giza and the Great Pyramid of Giza.
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Old 12-05-2018, 09:37 AM
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Sure, a typical scale will not account for buoyancy, when measuring weight. But that's easy enough to fix: Just put the scale (and whatever you're weighing on it) in a vacuum chamber. If only all sources of inaccuracy in measuring instruments were so easily fixed.
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Old 12-05-2018, 09:49 AM
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Darren Garrison said "Great Pyramid of Gizas." You corrected him and said "Great Pyramids of Giza." Chefguy in turn corrected you. There are the Pyramids of Giza and the Great Pyramid of Giza.
But using the Great Pyramid as a unit of measure, results in multiples of it. Something with 5 times the mass of the Great Pyramid of Giza is equal to "5 Great Pyramids of Giza" not "5 Great Pyramid of Gizas". We're nitpicking grammar here, not math or geography.

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Old 12-05-2018, 09:57 AM
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But using the Great Pyramid as a unit of measure, results in multiples of it. Something with 5 times the mass of the Great Pyramid of Giza is equal to "5 Great Pyramids of Giza" not "5 Great Pyramid of Gizas". We're nitpicking grammar here, not math or geography.
Doh! That's twice now I've misinterpreted a poster in this thread.
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Old 12-05-2018, 10:00 AM
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After I build an even more impressive pyramid in Giza, there is going to be a lot of confusion in the literature. I understand something of this nature occurred when the old prototype kilogram lost mass, even though at the time by definition it couldn't.
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Old 12-05-2018, 10:16 AM
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Sure, a typical scale will not account for buoyancy, when measuring weight. But that's easy enough to fix: Just put the scale (and whatever you're weighing on it) in a vacuum chamber. If only all sources of inaccuracy in measuring instruments were so easily fixed.
The question of whether a balance can be used under vacuum would come up from time to time. Few of the off the shelf instruments can be used in a vacuum, mostly because of the liquid crystal or vacuum florescent displays as well as the electrolytic capacitors. Heat dissipation was also cited. It's possible to separate the mechanical portion of the balance from the electronics but that requires either major surgery on the scale or a very expensive specialty device and most people found another way around it.
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Old 12-05-2018, 10:22 AM
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A tangent question:

Isn't mass, fundamentally, a function of the number of neutrons + protons (and if there's enough of them, electrons?) in a given hunk of something? I guess that just pushes the question back a step, though -- what is mass at the level of a subatomic particle?
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Old 12-05-2018, 11:04 AM
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For anything we deal with on a day-to-day basis, mass will be pretty close to being proportional (within about 1%) to the total number of neutrons + protons. But that's not inherently what mass is, for a few reasons. First, neutrons and protons have slightly different masses (the neutron is a little bit heavier). Second, there's also binding energy, which differs from one nucleus to another, and which also accounts for some mass (this is the difference in mass that nuclear energy generation, controlled or in weapons, is based on). Third, not all matter is made up of protons and neutrons, and in fact, most of the mass in the Universe is made out of something else (though we don't yet know what).

jnglmassiv, my off-the-shelf bathroom scale would work just fine in a vacuum. It contains no LCDs, no capacitors, nor anything electronic at all: It's just a spring connected mechanically to a moving dial. Of course, I'm sure that it has other inaccuracies which dwarf those caused by buoyancy, but if you care about that much accuracy, you're going to have to go with some sort of specialized instrument anyway. And the fact that there are easier ways to deal with the buoyancy problem (like assuming a density and calibrating the scale based on that) doesn't change the fact that there's also a way of dealing with it that is conceptually quite simple, and in practice still not all that hard.
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Old 12-05-2018, 11:27 AM
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Buoyancy is irrelevant to both mass and weight. The only relevance of buoyancy to the feathers-and-lead example is that most typical scales will be slightly inaccurate at measuring the feathers' weight (actually they'll be slightly inaccurate for the lead, too, but more so for the feathers).
The error due to buoyancy of feathers is less than one might think. For the purposes of assessing buoyancy, what is the density of feathers? Pretty high, actually. Feathers have a very loose structure which confers a lot of aerodynamic drag compared to their weight, but the gaps between feather elements are filled with air, which has a net zero effect on buoyancy.

So what is the density of the actual material from which feathers are made? Feathers are modified hairs; both are made of keratin. Couldn't quickly find a direct reference for the density of keratin, but according to this PDF, wool fibers have a density of 1.3 grams per cc, which is probably a good estimate for the keratin from which feathers are made. Compare with lead at 11.34 g/cc, and sea-level air at 0.001225 g/cc.

So if we're using a scale to measure the weight of a 1000-pound mass of lead in open sea-level atmosphere, buoyancy will cause the scale to indicate 999.89 pounds. If we're using a scale to measure the weight of a 1000-pound mass of feathers, the scale will show 999.06 pounds.
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Old 12-05-2018, 11:41 AM
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To compensate for buoyancy: Put the object to be weighed in a sealed container and weigh. Take the object out of the sealed container and weigh the sealed (but now empty) container. Subtract the second measurement from the first and the result is the actual weight of the object (within the limits of accuracy and repeatability of your measuring system). No need to consider the volume or density of the object, and it even works for lighter-than-air objects!
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Old 12-05-2018, 11:55 AM
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Originally Posted by Bear_Nenno View Post
But using the Great Pyramid as a unit of measure, results in multiples of it. Something with 5 times the mass of the Great Pyramid of Giza is equal to "5 Great Pyramids of Giza" not "5 Great Pyramid of Gizas". We're nitpicking grammar here, not math or geography.

Suffice it to say that it would weigh a great number of kilosgram.
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Old 12-05-2018, 12:24 PM
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Note that gravitation is also different around the earth and based on altitude.

The force calculated would also change based on the local acceleration due to gravity. For anything from about feathers and denser the local variation in gravity will actually exceed that of buoyancy. For stainless steel the local gravitational variance will be around 6-9 time greater than the displacement of air near sea level.

Once again, if you consider mass as the property that is the resistance to changes in movement and weight as the product of mass times the local acceleration of gravity this becomes less of an issue.

As force is a vector the tensor form would allow you to break out most of theses functions into separate elements as buoyancy acts on a different element than gravitational acceleration.

Where you do need to density is if your precision needs are to the point where the fact that gravitationally bound systems, or chemically bound systems have more negative potential energy than the sum of its parts. The definitions of standard gravity, rest mass and metric form of weight help you work with this.

Mass-energy equivalence shows that mass is concentrated energy, and even if you consider the percentage of the mass of the proton that we know
33% quark energy
37% glue field energy
9% u,d, and s quark scalar condensates.
https://arxiv.org/abs/1808.08677

Just consider rest mass as he sum of all energy bound in a system.

You can keep weight simple by just stating it is the product of mass and the acceleration due to gravity or you can complicate it by trying to go with what seems like a simpler definition.

But due to the quirks of Newtonian physics being a 3D bundle over a 1D manifold the energy from Gravity in the Newtonian model won't be conserved in momentum so you will have to resort to tensors anyway if your needs are for this level of accuracy in a dynamical system. You will end up using the rest mass form for one of your vectors anyway.

Rest mass, fundamentally, a function of all energy, of all types contained in a closed system. Rest mass, fundamentally, is a measure of the property of inertia of an object. Adding or removing energy by either re-arranging the components or adding or removing any energy will change this measurement. A compressed spring has more mass than a relaxed one, a warm object has more mass than a cold one, and a group of objects tightly packed have less mass than when they are spread far apart if the "object" you are looking at contains all of those parts.

Don't let superseded theories or non-technical use of the terms confuse this point which does match with our current understanding.

If you care about what mass is fundamentally only use the technical form; Mass is a property of a physical body and a measure of its resistance to acceleration. This property is due to the total energy content of the system.

It is only our assumptions, intuitions and artifacts of our educational system that make this hard to grasp for adults.

The entire concept of "Apparent Weight" is actually quite toxic to our educational efforts.

https://eric.ed.gov/?id=EJ912887

https://link.springer.com/article/10...763-014-9556-7

https://aapt.scitation.org/doi/abs/10.1119/1.880241
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I strongly agree with Richard Morrison that at the end of the twentieth century, the physics teaching community should at least agree on a definition of the word “weight.” That we do not is very strong evidence to me that the word should simply never appear in the literature or textbooks. It should be expunged from our vocabulary—except as a substitute for the word “object” as in “A weight was hanging from a string.”
The operational vs gravitational definitions of weight will never be resolved, as teachers are unwilling to accept the gravitational version as a standard, abandoning the word is the only option.

Last edited by rat avatar; 12-05-2018 at 12:27 PM.
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Old 12-05-2018, 01:26 PM
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Quoth hibernicus:

To compensate for buoyancy: Put the object to be weighed in a sealed container and weigh. Take the object out of the sealed container and weigh the sealed (but now empty) container. Subtract the second measurement from the first and the result is the actual weight of the object (within the limits of accuracy and repeatability of your measuring system). No need to consider the volume or density of the object, and it even works for lighter-than-air objects!
This only works if you always have the same amount of air in the container, with and without the object (I'm guessing you meant none). That does mean that you don't need to put the scale itself in a vacuum chamber, but you do still need a vacuum chamber.

Machine Elf, in practice, the error would be even smaller, and might be in the opposite direction, because the scale was probably calibrated in an atmosphere. If the scale's response is linear, for instance, you could calibrate it by taking all weight off of it, marking the needle's position as "0", then putting a 1000-kg test mass on it, and marking the needle's position as "1000", and then dividing the interval between those two marks into 1000 equal parts. But that test mass that you used would also have some buoyancy. If the test mass happened to be made out of lead (or something with the same density as lead), then the scale would read exactly 1000 kg when it had 1000 kg of lead on it, because that's what it was calibrated to read. And if the test mass used for calibration was less dense than lead, then the lead would actually read slightly more than 1000 kg on the scale's display.
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Old 12-05-2018, 01:30 PM
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While it's nice to understand that there is a small difference between weighing something in a vacuum and weighing it in air, in practice, 99.99999999999% of measurements are made in air. I don't know of anyone who steps onto their bathroom scale in a vacuum.
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Old 12-05-2018, 02:15 PM
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As Chronos pointed out the precision is what matters, the precision you require will dictate the corrections you have to make.

As this thread is about what the properties are and not what convenient ways we have to approximate them, the answer is.
mass=Force/acceleration
Weight = mass * acceleration due to gravity.
The operational definition of weight is problematic because it hides those relations due to assumptions that may hold fine in our daily lives but which do not describe what these fundamental properties are.

Note that the simple forms of Newtonian mechanics only hold in a inertial frame. We simply do not exist in an inertial frame, and the proper way of dealing with this reality is just accepting that and not trying to change those relations to fit our non-inertial existence at the expense of the core concepts.

There is a direct and fundamental relationship between the above forms of both mass and weight. But this is because in this context Weight = mass acceleration due to gravity. It doesn't matter if that same acceleration is provided by a rocket or gravity. That force vector in "F = ma" doesn't depend on committing the act of weighing, and that force exists external of any observers decision to measure that force.

This force as only a measure of the mass times the intensity of acceleration and in some cases this is a gravity field. The fact that people don't get that Weight = mass * acceleration is just Force = mass * acceleration with a named type of acceleration is why the concept is confusing.

The problem is not with the physics, it is merely an artifact of people refusing to accept a common definition.

If you want to account for the buoyancy force you simply need to add another vector defined off of that force. There is no value in co-opting the specially defined force for gravity called weight to try and make it fit in with observations so you can ignore the other components that combine into the overall force.

The strength of acceleration for gravity changes on the earth and on other bodies, but it is not useful as a precision measure of force if you need to account for other forces within a system.

You simply don't change the core ideas to match up with observations in a frame that needs many other forces to be accounted for if the needed level of precision causes those forces to be significant to your answer.


To repeat again, these concepts are not ambiguous, it is only the changing scope that makes them so.
mass=Force/acceleration
Weight = mass * acceleration due to gravity.
Irrespective of some practical uses without high precision requirements, if those relationships aren't concrete in your understanding it is probably best to revisit those concepts. Just remember to ignore your middle school teachers who were lying to you, because they thought you were not as smart as you actually are.

Last edited by rat avatar; 12-05-2018 at 02:19 PM.
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Old 12-05-2018, 03:20 PM
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Originally Posted by beowulff View Post
While it's nice to understand that there is a small difference between weighing something in a vacuum and weighing it in air, in practice, 99.99999999999% of measurements are made in air. I don't know of anyone who steps onto their bathroom scale in a vacuum.
It's not entirely theoretical though. Some years ago I attended a course in flow measurement at NEL's Densitometer Calibration Facility in East Kilbride. When measuring weight, they not only compensated for buoyancy but also local gravity. They had had a man come up from London with an official gravity-measuring device (gravimeter).

The trainer admitted that he had been disappointed with the gravity measurement. He expected some big and elaborate oscillating mechanism that would need to be carefully set up and solemnly observed for a period of time before the result would be announced. Instead, the instrument was taken out of its box, a button was pressed and a small click was heard, and that was that. Very anticlimactic.
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Old 12-05-2018, 04:37 PM
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jnglmassiv, my off-the-shelf bathroom scale would work just fine in a vacuum. It contains no LCDs, no capacitors, nor anything electronic at all: It's just a spring connected mechanically to a moving dial. Of course, I'm sure that it has other inaccuracies which dwarf those caused by buoyancy, but if you care about that much accuracy, you're going to have to go with some sort of specialized instrument anyway.
Your bathroom scale is badly obsolete. I've weighed myself on a scale accurate to 0.1 grams. This is useful for those days when you really want to see how big your lunch was or when you can't remember if you had one aspirin tablet or two.

It actually wasn't all that long ago that mechanical balances were dominant and there are still plenty of them in use. Fascinating contraptions, zilloins of moving parts, complicated mirror and lens projection patterns. Devilish to try to work on, though.
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