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Anderson Video - Mass vs Weight

Professor Anderson
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>> All right, this is probably a great spot to talk about mass versus weight. Okay. Mass is M, written in kilograms, in SI units. Mass is something that is inherent to you as a human. Everything in the universe has mass. Every piece of matter in the universe has mass, there are of course, massless particles, like the photon, but let's talk about things that have mass. Electrons, up quarks, down quarks. Neutrinos, okay? You guys are made up of atoms, which are, of course, electrons, protons and neutrons. We know that protons and neutrons are really up quarks and down quarks, and so you have a mass, and that mass is inherent to that material. So if I have a mass of 65 kilograms, my mass on the earth is 65 kilograms. My mass on the moon is 65 kilograms. It's inherent to the material. It doesn't change based on its surroundings. Okay? Weight is something else. Weight is, in fact, equal to the normal force N. Okay? This is your perceived weight. We'll put it in quotes. Okay? So what do we mean by that? What we really mean is the following. How hard is the scale pushing on you? If you stand on a scale, how hard does it push back on you? That little needle that turns? Or the little weight thing that you have to move over in the gym, you know, and it's really like annoying when you have to move the big weight one -- over one section. It's like the little one is not so offensive, but somehow you're just like, oh, no. Okay? How hard is that scale pushing back on you? Well, that looks like it could just be MG. Right? When we're standing in the elevator and it was not moving anywhere, the normal force was just MG. So if you are at rest, then it is MG. So a lot of people say, oh, well, your weight is just MG. I don't like to say that. I like to say your weight is the normal force N. It's how hard is the thing underneath you pushing up on you. And if that elevator is accelerating upwards, the normal force, in fact, is bigger than MG. It's M times A plus G. And so literally, if you were standing on a scale in the elevator, when that elevator takes off, you'll see the scale increase its number. Instead of 170 pounds, you'd be 175 pounds. Okay? And that is weight in your mind. And that's what you perceive as weight, is how hard is the floor pushing up on you? And at the top of the motion, where the accelerator comes to rest, now A is a negative number and so your weight is, in fact, less than MG. It wouldn't read 175 pounds on the scale. It would read 165 pounds. And then when it all came back to rest, it would read 170 pounds again. Okay? So weight is, in fact, this normal force N. Now, in the case that Anthony was asking about, where we cut the cable and we're just in freefall, what do we call that? When you're in freefall, what do you feel? Yeah? >> Weightless. >> You feel weightless, right? There is no weight. And there's no weight because if I took a scale and I stuck it under my feet, it would read zero, because we're all falling together. You are weightless. And so when the astronauts in outer space put a scale under their feet it says zero. They are weightless. Are they accelerating? Absolutely. They're moving in a circle around the earth. So they are accelerating, but there's nothing pushing back on them. There's no normal force N. Okay? That, of course, will change, depending on the situation, and depending on the gravity. So if you're on the moon, you weigh a lot less than you do on the earth. Even though your mass is the same, your weight is less. The moon doesn't have to push back up on you because gravity is less on the moon.