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.
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.
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?)
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.
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.
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.
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.
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 1m[sup]3[/sup] 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.
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.
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.
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.