Newton's law of gravitation
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Mass and weight clarification
In this video, I want to clarify two ideas that we talk about on a regular basis, but are really muddled up in our popular language. And these are the ideas of mass and weight. And first, I'll tell you what they are. And then, we'll talk about how they are muddled up. So mass is literally-- there's a couple of ways to view mass. One way to view mass is-- and this is not a technical definition, but it will give you a sense of it-- is how much the stuff there is. So this is similar to saying matter. So if I have more molecules of a given mass, I will have a total of more mass. Or if I have more atoms, I will have more mass. So how much stuff there is of something. And I want to be careful with this definition right here, because there are other things that aren't what we would traditionally associate with matter, once we start going into more fancy physics, that still will exhibit mass. So another way to define mass is, how does something react to a specific force? And we already learned from Newton's second law that if you have a given force and you have more mass, you'll accelerate less. If you have less mass, you'll accelerate more. So how something responds to a given force. Something with lower mass will accelerate more for a given force. Something with higher mass will accelerate less. Now weight is the force of gravity on a mass, or on an object. So this is the force of gravity on an object. And just to think about the difference here, let's think about, I guess, myself sitting on Earth. So if I'm on Earth, my mass is 70 kilograms. My mass-- let me do this in a new color-- so my mass is 70 kilograms. There's 70 kilograms of stuff that constitute Sal. But my weight is not 70 kilograms. I mean, you'll often hear people say, I weighs 70 kilograms. And that's all right in just conversational usage, but that is not technically correct. Because weight is the force that Earth is pulling down-- or I should say-- the force of gravity on my mass. And so my weight-- let me think about the weight for a second-- the weight is going to be equal to the gravitational field at Earth. Hopefully you've watched the video on gravity. Or if you haven't, feel free to watch it. But the gravitational attraction between two objects, so the force of gravity between two objects is going to big G, the universal gravitational constant, times the mass of the first object-- let me actually-- times the mass of the second object, divided by the distance that separates the two objects squared. And if you're on the Earth, and if you take all of this stuff right over here combined-- so if you say that this right here is the mass of Earth. If you say this, right here, is the distance from the center to the surface of Earth, because that's where I'm sitting right now. So distance from center to surface of Earth. Then all of this stuff over here simplifies to what's sometimes called as lower case g. And lower case g is-- and I'm just rounding it here-- 9.8 meters per second squared. So the force of gravity for something near the surface of the Earth is going to be this quantity right over here times the mass. So my weight on the surface of the Earth is this 9.8 meters per second squared times my mass, times 70 kilograms. And so this is going to be-- I won't do, well, I could get my calculator out. Why don't I just get my calculator out and do the math? I was going to round it to 10 and say it's about 700, but let's just actually calculate it. So we have 9.8 times 70 kilograms. So we have 686. So this gives me 686. And then the units are kilogram meters per second squared. And these units, kilogram meters per second squared, are the same thing as a newton. So my weight-- and you'll never hear people say this-- but my weight on the surface of the Earth is 686 newtons. And notice, I just said that is my weight on the surface of the Earth. Because as you could imagine, weight is the force due to gravity on an object, on a mass. So if I go someplace else, if I go to the moon, for example, my weight will change. But my mass will not. So let's write this. This is the weight on Earth. If I were to take my weight on the moon-- and I haven't looked this up before the video. And you can verify this for me if you like. But I've been told that the gravitational force on the moon, or the gravitational attraction at the surface of the moon, is about 1/6 that of the surface of the Earth. So my weight on the moon will be roughly 1/6 of my weight on the Earth. Times 686 newtons. So that gives me a little bit over-- what is that-- 114 maybe? I'll just get the calculator out. My brain operates a little bit slower while I'm recording videos. Yeah. I got it right. 114. So that gets us 114, approximately 114 newtons. So this is the thing I really want to emphasize then. Weight is a force due to gravity on an object. Your weight changes from planet to planet you go on. Your weight would actually even change if you went to a very high altitude because you're getting slightly further-- it would be immeasurably small-- but you're getting slightly further from the center of the Earth. Your weight would change an imperceptible amount. In fact, because the Earth is not a perfect sphere-- it's often referred to as an oblique spheroid-- your weight is actually slightly different on different parts of the Earth. If you went to the poles verses the equator, you would have a slightly different weight. Your mass does not change. It doesn't matter where you go, assuming that you don't have some type of nuclear reaction going on inside of you. Your mass does not change. So your mass does not change depending on where you are. Now, you might be saying, hey, look, I don't deal with kilograms, and newtons, and all of this. I operate in America. And in America, we talk about pounds. Is pounds appropriate? And yes, pounds is a unit of weight. So if I say that I weigh 160 pounds, this is indeed weight. I'm saying that the force of gravity on me is 160 pounds. But then you might say, well, what is mass then if you're talking about the English system or sometimes called the imperial system? And here, I will introduce you to a concept that very few people know. It's kind of a good trivial concept. The unit of mass-- so let's just be clear here-- the unit of mass in the imperial system, mass is called the slug. So if you wanted to figure out how many slugs you are, so your weight-- the force of gravity on you is 160 pounds. This is going to be equal to-- if you were to calculate all of this stuff-- the force of gravity on the surface of Earth. But if you were to do it in imperial units, instead of getting 9.8 meters per second squared, you would get 32 feet per second squared, which is also the acceleration near the surface of the Earth due to gravity in feet and seconds, as opposed to meters and seconds. And then, this is times your mass in slugs. So to figure it out, you divide both sides by 32 feet per second squared. So let's do that. Let's divide both sides by 32 feet per second squared. It cancels out. And then let me get my calculator out. So I have 160 pounds divided by 32 feet per second squared. And I get exactly 5. I should have been able to do that in my head. So I get 5. And the units here-- in the numerator, I have pounds. And then I'm dividing by feet per second squared. That's the same thing as multiplying by second squared per feet. And these units, 5 pounds second squareds over feet, this is the same thing as a slug. So if I weigh 160 pounds, my mass is going to be equal to 5 slugs. If my mass is 70 kilograms, my weight is 686 newtons. So hopefully that clarifies things a little bit.