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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>But… mass is determined by weighing an object on a scale.
This is where you’re wrong. Yes, in the presence of a known gravitational field (i.e., on Earth), you can weigh an object on a properly calibrated scale to figure out its mass. But what if you were in outer space? A scale would tell you that you’ve got zero mass, which isn’t true. Or what if you were on Pluto, and you didn’t know Pluto’s gravitational force offhand, and you were fresh out of Pluto-calibrated scales? An Earth-calibrated scale would be useless to figuring out your mass here.
Instead, think of mass as a measure of how hard it is to move something, or change something’s momentum. If I’m standing (floating) still in a spaceship in outer space and you throw a 7 kg bowling ball at me and I catch it, I’m going to start moving backwards at a particular speed. That speed will be slower if I have a high mass, and faster if I have a slow mass. Even though a scale is useless here, I could still calculate my mass using this kind of method (and many other methods). But a scale would show that my weight is zero.
F = m•a
m = F/a
If I apply a force of 100 N on an object, and as a result it accelerates at 5 m/s^2, then I know it’s mass is 20 kg.
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