Somebody said they are different because of gravity.
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It looks like others have already answered this question – this subject can be difficult to understand at first for the 95% of the world that uses the metric system due to the measurement of one’s mass by using weight instead of displaying the weight itself.
For example: I weigh 145 lbs. I *am* 65 kg. On the moon, i only weigh 24 pounds, but i am still 65 kg. I have 65 kg worth of “stuff” that makes up my body.
Weight is a pulling or pushing sensation. It’s a force. You WEIGH on something. If I stand on a platform, then I weigh on that platform. It has to suffer my weight. Like a thought can psychologically weigh on your mind. Physical objects physically weigh on other objects.
Mass is (on a large scale) a measure of how much of something there is. It also describes how greatly an object is affected by gravity.
Since we spend all of our time in the same gravity well (earth), our mass always results in the same amount of weight. If you are 70kg, then you will weigh about 700N of force. If you went to the moon, you would weigh less than on earth, but you would still have the same mass.
You don’t shrink when you get to the moon. You just push less aggressively.
Mass means how much “stuff” a thing contains. Weight is the force this stuff exerts due to gravity, which can change depending on where the stuff is (Moon, Mars, Earth, etc.).
If you use a balance beam to “weigh” your sample. That means you put it on one side of a fulcrum and you put a known mass on the other side until it balances. Example, your sample is 7 grams. On the other side of the balance you put a calibrated 5 g and 2 g mass. The balance looks even.
If you bring your balance to the moon and try again, your 7 g mass weighs less because gravity pulls on it less. However, the 5 and 2 g masses also weigh less by the same factor, so your balance will still remain balanced and you will get the same answer of 7 g. This works because the force pushing down on the calibrated side changes with gravity.
A scale, on the other hand, uses a spring. The more you compress a spring, the harder it pushes back. Or more appropriately for this example, the harder you push a spring the more it compresses. The scale basically measures how much that spring compresses (in inches or millimeters or whatever) and does math to convert that to weight. (Sometimes, it will tell you kilograms or grams which is mass, but that ONLY works on Earth under Earth’s gravity).
If you take this scale to the moon and put the same sample on it that you did on earth, the sample is under less gravity, so it puts less force on the spring, so the spring compresses less, so the scale reads a lower number. If you’re reading in pounds or Newtons, these are measures of force (well, there’s pound-mass and pound-force because imperial is awful, but you get the idea), which means the answer is correct. That is the force your sample is putting on the scale. If it’s reading out grams or kilograms, the answer is incorrect because the scale is calibrated to tell you what mass object would produce that force *IF* it were on Earth.
So weight is a force. If you apply a force to a mass, it will accelerate. The higher the mass, the harder it is to accelerate, so the same force will result in less acceleration. This is what is meant by an object in motion tends to stay in motion and an object at rest tends to stay at rest, or inertia. The exact relation between force, mass, and acceleration is Newton’s second law F=m*a and this makes sense because if you jump out of a plane, your weight (force) begins accelerating your mass towards the Earth.
To “complicate” things a little…. we can measure mass, most of the time, in two ways: via the gravitational pull, or via the inertia.
If we apply a given specific force over an object (discounting all other forces) the more mass the object has, the less t will accelerate. So, by seeing how the object moves we can calculate its mass, if we know the forces in place. This is, for example, the mass that we calculate when we hang the object from a string and make it oscilate like a pendulum.
That’s the inertial mass.
Then, there is the gravitational mass, which is the one you will get, for example, by using a balance.
Both happen to have the same value. And you may use any of those methods in any place of the surface of the earth, and get “errors” in calculating the mass of an object, because the force of gravity is not the same in every place over the Earth. It can vary depending on the local density of the Earth, altitude, or how far you are from the equator line.
But that part of the error is just because of using a wrong value of the gravity acceleration.
So, you can go with a pendulum, with an object whose mass you already know, and go around and measure the gravitational acceleration in different parts of your city or town, and verify that it can be different.
Weight is a result of gravity. If you are on earth, things with mass also have a specific weight because of Earth’s gravity pulling on them. But if you were on Jupiter, they’d have the same mass but a much higher weight (because Jupiter pulls more strongly than earth does). If you’re in freefall (e.g. orbit) in space there’s no apparent gravity, and objects seem to have no weight at all.
But, though all of this, the mass hasn’t changed! It’s an inherent property of the object. And mass has consequences other than weight. On earth we often conflate the effects of mass with the effects of gravity, but this is incorrect. We know that heavy objects are hard to move, but they’re actually hard to move for two reasons: one is that gravity creates friction with the ground, which creates drag. The other is that more massive objects require more energy to accelerate.
Imagine for a moment that you have a perfectly frictionless skating rink and two ten foot cubes, one made of lead and one made of styrofoam. If you push them on the frictionless surface, both will move (it’s frictionless, so any force will cause some velocity) but they won’t move at the same *speed*. A good hard shove will send the styrofoam rocketing across the floor, but the same shove on the lead brick will barely start it moving. Likewise, for slowing down. If you get the styrofoam block moving at 20 miles per hour and you get stuck between it and the wall, it’ll hurt a bit, but you won’t be seriously injured. If you do the same thing with the lead block, it’ll kill you. Again, we’ve taken out friction here, and thus the part of “hard to move” that’s caused by gravity. This is all a consequence of mass. Likewise, very massive objects are still hard to move in space, even though gravity isn’t a factor.
**Mass**
An object’s mass is what you get when you add up the “heaviness” of all the atoms in the object. We could call that the “atomic mass” and measure it in “atomic mass units” or amu’s.
A water (H2O) molecule, for example, contains 2 Hydrogen atoms and 1 Oxygen atom, and the “heaviness” of all the bits and bobs in that water molecule will be the same all over the universe. Of course it’d be the same! The number of amu’s hasn’t changed, has it?! Nope, because there’s still 2 hydrogens and 1 oxygen whether you’re on Jupiter, in your garage, or in the dead of space.
Obviously amu’s are pretty tiny, so for human-relevant things, we prefer to measure the mass in kilograms instead. Kg.
**Speed**
As you know, if you drop a water balloon either on Earth or on the moon it won’t just fall at a constant speed, instead it will accelerate towards the ground, getting faster and faster as it goes.
Just like the “miles per hour” you know and love, speed can be formatted as “meters per second” or “m/s”. (And this can also be written as “ms^(-1)”.)
**Acceleration**
Now, since the object is getting faster and faster and faster as it falls, it’s gaining some extra speed “per second” that it’s falling.
You might even ask “How many meters-per-second is it gaining *per second*?” And that would be you asking for it’s acceleration.
On Earth, as things fall, they get 10m/s faster *per second* that they’re falling. (“10 meters per second *per second*”). Whereas on the moon, the acceleration of Gravity is only 1.6 meters per second *per second.*
“Meters per second *per second*” can be written as “ms^(-2)”.
**Weight**
So, since the same object will accelerate downwards more slowly on the moon than on the Earth (ie. the “gravity” is different), the combinations of Mass and Acceleration are different.
In other words, the same mass (kg) will be affected by the different accelerations/gravities (ms^(-2)) depending on where it is. Ie. the “kg” x “ms^(-2)” will be different.
kg ms^(-2)
And these “kg ms^(-2)” are your units of “weight”. You can call them “Newtons” or “N” for short.
So weight is actually a “force”. When you hold that 1kg object in your hand, you’re not so much feeling its mass (in kg), you’re feeling it *force*fully pressing down into your hand because of gravity sucking it into your flesh (in Newtons).
If there was no gravity, it wouldn’t “force” itself down onto your hand… and you might even say it was “weightless”… despite it still having a “mass”.
So, “Weight” is the vertical force exerted by a “mass” as a result of gravity.
**Summary**
So, the long story short is that “Mass” is the “heaviness” of all the atoms, no matter what those atoms are doing, where they are or where they’re going.
And it’s measured in kg. Or kilograms.
Whereas the “Weight” is the force of those atoms pressing into your kitchen scales when they’re being sucked down onto those scales by your chosen gravity.
And it’s measured in kg ms^(-2). Or kilogram meters per second *per second*. Or Newtons.
My chemistry teacher always said “if you have the mass and you want the weight, multiply by 9.8!” Sigh. But I also remember it.
Mass is how much stuff a thing has in it. (How much matter is used to make the thing)
Weight is how tightly the planet is holding on to said thing. (Gravity pulling everything to the planets center)
Mass is how much stuff a thing has (or is).
The stuff in things pulls at other things’ stuff.
Weight is how much pull a really big thing (like the Earth) has on a smaller thing on it (like you).
Mass doesn’t change, but the smaller thing’s weight changes if you change the bigger thing (like go to the Moon).
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