Actually, this is a tough question... but in fact, even on the earth mass and weight are not the same. The earth spins, so if you are at the equator, you are traveling at over a thousand miles an hour to the east. At the equator, your mass is essentially the same, while your weight is a few pounds (or kg) less than at either pole.

For low velocities and accelerations, mass is the constant of proportionality between an applied force and the resulting acceleration. Mass is related to weight (gravitational acceleration) because gravity creates an acceleration for which, for you to remain at rest on the earth's surface, you need to apply an opposing force through your feet. Since the acceleration from the force of your feet exactly balances that due to gravity, (or you wouldn't stay motionless) the force you measure on a balance or bathroom scale (the weight) is also proportional to your mass.
F(total)= m * a -F(on your feet) ,
here a is from gravity and the F(feet) is what you feel as weight. (Since the earth is a spinning platform you are actually accelerating when you think you are at rest -- and this causes the deviation from equator to pole).

The notion of mass independent of material is due to Galileo, the laws of inertia (F = m a) was worked out buy Newton, and the notion of mass causing a true acceleration (not a force) is from Einstein.

Mass is an absolute quantity (I will explain what that means) but weight (on earth) is really the force with which you are pulled towards the center of the earth. Weight is what the bathroom scale measures. There is a spring in the scale. When you stand on it, the spring is pushed down because of the force with which the earth pulls you. How much the spring is pushed is what is measured.

Mass on the other hand is what would be measured using a comparative balance, by hanging two objects on the ends of a beam, and then seeing by how much one side is pulled down. Masses are measured by comparing an unknown mass against a known one.

While on most parts of the earth, the weight and mass turn out to be the same, there can be small changes in the weight, if for example, you take your scales to the top of a very high mountain and weigh yourself. If you compared yourself with a standard mass, this would not change, whether you are on the earth or the moon.

That's a good question. It can get confusing because some words that have very specific meanings in science have much more general meanings outside of science. When you learned in science that mass is a measure of the amount of matter in a body and that weight has to do with gravity it was right, but outside of science the terms are often treated like they both have the same meaning.

If your mass is 49 kg, that means your weight is 480 kilogram-meters-per-second-squared or 480 Newtons. Both of those terms are a bit awkward to say, and most people outside of science don't have a clear concept of what they mean physically. As you pointed out, most people only plan on hanging out on earth, so they only care about what weight results from their mass due to the gravity on earth. Instead of telling people that they weigh 480 Newtons, then, and instead of saying "I have a mass of 49 kg", people started treating the words "weight" and "mass" as the same in daily speech despite the fact that the meanings are still very different in science.

Whether your bathroom scale is measuring your weight or your mass actually depends on the type of scale you have. Old-fashioned scales involving small metal masses that you slide across a bar (like the kind you would usually see at a doctor's office) measures your MASS by balancing the mass on the pad you're standing on with the masses you move on the bar. Newer scales, though, like digital and spring scales, measure the FORCE your body exerts on the pad you're standing on, which is your WEIGHT. The scale then divides your weight by gravity to give you your mass.

So if you have a digital scale at home, your scale measures your weight(480 Newtons), then divides it by gravity to show you your mass (49 kg),and then everyone goes ahead and calls that "mass" your "weight". It's a little bit crazy, but it's the way the world works... ;-)

That is a very good question! For practical purposes of your daily life,you are correct. You understand that mass is the amount of matter contained in your body, and that if you were to go up in the international space station, you would be in a state of free fall, and feel weightless, but you would still have the same mass. However on earth, we use the gravitational field of the earth to measure our mass by how much the earth and our bodies attract each other.

Technically, we say that one kilogram weighs 9.8 NEWTONS on earth, because w = mg, and g = 9.8 meters/second² . On the moon, for example, where g is only 1.6 meters/second², one kilogram of mass would weigh 1.6 Newtons, not 9.8 Newtons, and you could not use the kilogram to stand for the same unit of mass and weight - you'd have to either invent a new unit of weight, or simply use the common unit of Newtons, which is a unit of force, that we use on earth.

Now you understand that weight is really a FORCE, and force and mass are related to each other by a ratio:
Force/mass = acceleration.

Now I'll show you why we use the convention that our mass = our weight on earth.

On earth, the acceleration of gravity we call "1 g", and its average value is 9.8 meters/second².
So, here's how we get 1 kilogram of mass = 1 kilogram of weight on earth:
Since Force/mass = acceleration, we DEFINE the unit of gravitational acceleration ONLY FOR REGIONS CLOSE TO THE SURFACE OF THE EARTH to be 1 g.

So, in these units, Force/mass = 1, therefor force = mass. Since weight is the force that the earth exerts on you when the acceleration IS 1 g, then we can say your weight on earth = your mass.

So, you are quite right, that if you only want to restrict yourself to the earth, then you can say your mass = your weight. But now you know that this definition is ONLY true if you are on or very close to the surface of the earth, and it is not true anywhere else in the universe.

I think what your teacher was trying to get across is that mass is a fundamental property. If you had a loaf of Wonder bread and you sat on it or otherwise squished it into a ball, it will be smaller but it will have the same mass. If you took the loaf of bread to the moon, it will weightless but will have the same mass. An object's size, density and weight are all ways to describe it, but they can change. An object's mass cannot change. If you ate a couple slices of the bread, the bread loaf is now smaller and weighs less because it is missing a few slices, but the slices you ate have the same mass inside your body that they would have had when they were part of the loaf of bread. The slices are just in a different form: they get mushed up in your mouth and liquefied in your stomach and are then absorbed by your body and converted into tissue or are removed as waste. Mass can not be created or destroyed. If you left the loaf of bread on the counter for years and years and years, it would slowly change form but would still have the same mass, if you could track the molecules. (This would be pretty hard to do since some will be carried away by ants and other bugs, some will be converted to mold spores and waft away in the air, etc.) The universe has the same mass(the same number of atoms) now as it did when dinosaurs walked the earth. It's just that the mass - the atoms - keep shifting into different molecules and take different forms. If you consider the life of your loaf of bread only on earth, then yes, mass and weight are sort of the same thing. That is, the relationship between the loaf of bread's mass and its weight will not change. Assuming you could track all the molecules of bread in your body as you ate the slices, and could retrieve those molecules a few days later and weight them, the weight would not have changed. But just beware that weight is a descriptive term for mass , and that the relationship between mass and weight is not constant if the force of gravity changes.

By the way, you weigh 49 kilograms. Your bathroom scale is telling you your weight. Your mass would be the number of atoms in your body. As the number of atoms in your body changes, you weight will change. So here's a question: when loose weight, where you think those atoms go, if they are not destroyed?

Let me answer your middle question first: a very careful scientist would say that you "mass" 49 kg because the kg is a unit of mass. Of course, most folks would just say that you "weigh" 49 kg. This is ok because most folks are talking about how much you weigh on Earth and since the conversion factor between weight and mass on Earth is always the same for everybody (well, *almost* the same), you can always convert one to the other. Your bathroom scale is probably giving your weight in pounds, however, and pounds is actually a unit of force - so it is measuring your weight. It may also give you your "weight" in kg, but this number assumes you are on the Earth.

If you lived on Mars, you would have to get a new scale. On Mars gravity is different, and the scale would read a smaller number of pounds when you stepped on it. This number of pounds *correctly* measures the force you are exerting on the scale. On the other hand, your mass has not changed - so the same scale on Mars would tell you your mass was smaller than it was.

Confused yet?

Well, that is sort of the point. If we tried to keep track of weight in science, it would become very confusing very quickly because, to different people, it would mean different things. That is the beauty of mass - everybody has the same mass no matter where they are or what they are doing. This is especially important because the mathematical laws of physics don't care where you are or what you are doing either - the laws of physics are always the same for everyone. I guess this is an assumption scientists make and there is no proof, but it has never, ever failed before. So if the laws of physics are the same everywhere, they should depend only on things that are also the same everywhere. This is why the important number in science is the mass, not the weight.

When you study collisions in a physics class, for example, the weight of an object is completely unimportant. It is the mass (and a few other things), that tell you what happens after they collide. That is the real reason why you have to learn about mass - it comes up again and again in all sorts of places in science.

Of course, if you know the weight and you know you are on Earth, you can always work out the mass. So in most situations, you can safely interchange

Your mass is 49 kg. Your weight on Earth is: 2.2 lb/kg x 49 kg = 108 lb.

kg is a metric measure of mass. When you stand on a scale on Earth, gravity is pulling on you, so you exert a force on the scale, which is measured in Newtons (or in dynes, being a dyne a derived unit of force specified in the centimetre–gram–second (CGS) system of units). But you will always use the scale on earth (probably !) so it can give you mass readings that are accurate on Earth.

The pound is an English measure of weight, which is a force, so it gives you the force you exert on the scale when you stand on it.

Both scales will say you are lighter on the moon, because they're both actually measuring force; but they're only designed to use in earth's gravity.

You and your friend could sit on a see-saw and be exactly balanced, if whoever was heavier would sit a little farther from the end of the see saw. You could sit in those same places on the see-saw if it was on the moon or anywhere, and it would still be balanced. That happens because your mass is the same everywhere.

The same thing happens if you put 2 identical weights (= 2 identical masses) in the 2 pans of a pan balance. The 2 pans will be balanced on earth or the moon, because the masses are the same everywhere.

As long as you're on Earth, and as long as you're not talking to a physicist, you can basically think of your weight as a measurement of your mass. (I say basically, because, believe it or not, you really do weigh lightly different amounts at sea level or on the top of mount Everest).

To be totally accurate, though, here's the difference: Mass is a measurement of how much matter is in an object, and weight is a measurement of the force applied to that object by gravity.

The connection between mass and weight is that the amount of force that gravity applies to an object is directly related to how much mass that object has. More mass = more force applied by gravity = greater weight. What you heard about weight being related to gravity is thus true.

The reason why most people confuse the two, and why the difference doesn't matter to most of us, is that most of us never leave Earth. If you went to the Moon (which you may someday!), your mass would be the same, but you would weigh a lot less because the Moon exerts less gravitational pull on objects. (Incidentally, the reason why it exerts less gravitational force than the earth does is that it's smaller than the earth--it has less mass!)So, stay on Earth and your mass and weight will be essentially the same. You will "weigh" 49 kg, which is the same as saying you "have a mass of" 49 kg.

I hope that helps. Keep asking such great questions!