Conceptually I understand that mass is a measure of the amount of stuff present in an object, while weight is a measure of the force of gravity applied to that object. An object of a given mass will have a bigger weight on Earth than on the moon because Earth’s gravity is stronger. But… mass is determined by weighing an object on a scale. And there is a simple mathematical conversion between grams (mass) and pounds (weight), implying that they’re just different units for the same concept. So what gives? (Also this is a question that applies to so many fields, I had no idea which flair to apply.)
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Mass is how much matter there is. It won’t change unless you add or take away matter. A 1 kg mass will be measured with a mass of 1kg everywhere in the universe, no exceptions.
If we push it with 1N of force, it will accelerate at 1m/s^2
If we put it on a triple beam balance, it will always result in 1kg even if we are on the moon.
Weight depends on the gravitational field you’re in. That 1kg weight weight 9.8N here on Earth but only weighs 1.6N on the surface of the moon. On the surface of Jupiter, it would weigh 24.8N. It’s still 1kg, but its weight is how strong of a force gravity exerts on it.
>mass is determined by weighing an object on a scale.
This isn’t entirely true. It doesn’t use a scale as you know it. It uses a balance, which compares one side to another. Modern scales measure your gravitational force directly without the need for a comparison.
The way these balances work is by using the equation Force (F) =Mass (m) × Acceleration (a) (F=ma). Older balances would have you put the object on one side and then slowly add standardized weights on the other side until the balance was balanced.
Modern balances (ones made specifically to measure mass), however, work on a slightly different concept. You still have the plate to put your object on one side, but the other side has 3 long bars with sidable weights on each one. You don’t add to the mass of this side, you change the force. Balances are a type of lever and levers have this property where the further away you are from the pivot, a constant amount of mass will have a bigger force. An experiment you can do to see this is try pushing a door right next to the hinges, then compare that to puching the door as far away from the hinge that you can get.
The object your “weighing” is applying a constant force on the balance so you slide the weights to change their force until it’s balanced. Using F=ma, a being constant for all object on the balance, it tells you the mass. If that balance were to magically teleport to the moon, the only thing that changes directly is the acceleration, so the force of both sides changes by the exact same amount remaining balanced so the reading will remain the same. A scale in this situation would start displaying a lower value.
Some scales do display in kg, but it’s not actually measuring your mass. It’s measuring your weight and does the F=ma conversion, but it assumes that “a” is the gravitational acceleration of Earth and thus doesn’t change so if you were to take that scale to the moon, it will tell you that your mass is less than what it actually is; those scales only work on Earth.
As for there being a conversion; there actually isn’t a true conversion. For it to be a TRUE conversion, the conversion factor would be a constant, meaning that it remains the same regardless of the situation. The 1 kg = 2.2 lbs is NOT constant. There’s a hidden acceleration term in there that assumes the gravitational acceleration of Earth. On the moon, 1kg = 0.36 lbs. The conversion factor is not constant. An example of 2 units that have a true conversion are lbs and Newtons (both are forces). 1 lb = 4.45 N, regardless of where you are or what you’re weighing. That 4.45 is constant.
You get the same mass measurement from a scale everywhere because while the force of the mass being weighed goes up or down so to does the balancing mass on the other side of the scale.
So your mass is your mass. How much stuff is in something.
Weight is more like mass * gravity. It changes depending on what planet/moon/whatever you are standing on.
Mass scales typically have a counter balance, so they would still work, still measure whatever object accurately if you take them anywhere. (0 gravity may be a prob tho)
Digital mass scales wont work if you take them off earth, they are just doing math based on expecting earth’s gravity.
Edit: I re-read your question. Really it sounds like what you are asking is how do mass scales work. You have an object, and you say, this is 100 grams. then you put that on one side of the perfectly balanced scale. then you put an object you are trying to discover the mass of on the other side, if it balances, you know the object you are “weighing” is 100g too. But if you took that scale off world, both the left and right had side of that scale are still 100g, and the scale would still balance.
Also, conversion between grams and pounds equations you find assume you mean you are still on earth, and would need to be different on different celestial bodies.
Mass is a measurement of “amount of stuff”, and is calculated with a balance because there’s a “known mass” on the other side against which you are comparing. On earth or elsewhere, the force of gravity scales proportionally, so 1 kg mass here will balance against 1kg in whatever gravity field you’re measuring in.
Weight is a measurement of *force*, and is about how hard the objects are attracted to one another. The “standard conversion” between mass and weight only applies in standard Earth gravity. 1kg has a standard number of pounds (or Newtons), but only here. On the moon, 1kg is pulled weaker, and therefor has a lower weight. Two 1kg masses both have reduced weight on the moon, so would still balance against each other.
Mass is how much stuff. Weight is *how hard is it pulling*.
Edit: Bonus ELI2 version
Gravity pushes against stuff. Objects with more mass have more stuff for gravity to push against. Weight is a measurement of how hard gravity is pushing against a given amount of stuff. Without gravity to do the pushing, there is no weight; but the stuff (mass) is still there.
TL;DR: Mass refers to how much “stuff” is in a given object. Weight refers to how hard that object pushes against another object (like a planet) due to its mass and gravity. More mass = more stuff being pushed by gravity = more weight.
Long version:
Let’s say you have two bricks; one is made of lead, and the other is made of foam. They are solid and identical in size, but the lead brick has more mass.
In the presence of an equal gravitational field (say, sitting next to one another on two identical scales in your kitchen) gravity pushes both bricks “down” against the scales. The objects’ *weights* are a function of the strength of the field and the *mass* of each object. So, the object with more mass pushes harder on the scale, which displays an accordingly larger number.
In the *absence* of a gravitational field (say, in deep space) neither one would have any weight. However, they still have mass. If you were to hypothetically try to push each object (and assuming you had something to brace yourself against) it would be much harder to get the lead brick moving compared to the foam one, because of its greater mass. It would also be much harder to stop.
Regarding your observation about weights being convertible, you’re correct–because scales actually display mass, not weight. They are generally calibrated to the gravitational field of Earth, and do a little math (or are mechanically designed) to factor out local (Earth) gravity and display only the mass.
If you’re interested, the math would basically be…
Mass = (push strength) ÷ (gravity²)
Mass is the amount of stuff something is made up of, weight is how much gravity pulls on something.
Something will weigh more if gravity is more.
Something will weigh more if mass is increased.
But something’s mass, the amount of stuff it is made up of, will not be more if only gravity is more.
Mass is determined by measuring the pull of gravity on something _compared_ to something with a known/set mass in the same gravity.
Think about if you and your friend who weighs the exact same get on a see-saw. Gravity pulls on you both equally and if you push off the ground carefully you can balance and not tip one way or the other. It would work the same on Earth or the moon. That’s mass.
Now imagine on the moon you stood on a soda can. You probably wouldn’t crush it, but on Earth you probably will. That’s weight.
Mass is your value of total stuff.
Weight is the rate other stuff that has mass pulls you at.
Weight is a force and the English system uses a force unit to measure it; technically the English system measure of mass is the “slug.” Common metric system just used th e mass unit as also for weight. Force units in metric are basically used by scientists and engineers and the mks and cgs variant systems use compeltley differnet units for force. It’s really just a convention on both sides.
Image you’re at a gym on Mars: It’s a lot harder to fall on the floor and hurt yourself, because your **weight** is less. But if you were to run into a brick wall full speed, it’d knock the shit out of you, because your **mass** is the same.
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