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 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.
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