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Anderson Video - Newton's Third Law

Professor Anderson
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 Hi guys, how is everybody doing today? >> Well. >> Well? Everybody got their caffeine? We're hitting that like 2:00 you know, kind of like post lunch naptime. It's important to get another double espresso. I discovered a secret. When you go to Starbucks, never order a latte on ice. If you're going to do that just order a double espresso on ice and add your own cream. It's costs like half as much. That's a little tip from me to you. Full service institution here. Let's talk a little bit about Newton's Laws. We already went through Newton's First and Newton's Second. What was Newton's first law? Anybody have a thought on that? Do you remember what Newton's First Law is? >> F equals ma, is the Second Law -- >> OK, good. Number two, F equals ma. We like that. What was number one? >> Oh an object will remain in motion unless acted on by an outside force or remain at rest. >> Correct. Objects in motion tend to stay in motion. Good. So those were the first two. Megan, did you have a comment? >> I know the third. >> You know the third already? >> Yes. >> Somebody read ahead in their book. >> For every action there is an equal and opposite reaction. >> OK, that's the action, reaction law. People like to talk about action reaction, every action there's a reaction. When I push on the wall, in fact the wall is pushing back on me. And you might think about this in terms of say linebackers playing football. The linebackers are pushing against each other. If you take one of them away, that person falls down. So action equals reaction, OK? It's in fact much more complicated than that, right? What we want to say about Newton's Third is that no isolated force exists. OK, there is no such thing as an isolated force. So in the case of say me pushing on the wall, not only is the wall pushing back on me but my feet are planted on the ground. And so I'm pushing on the Earth and the Earth is pushing back on me. And everything, in fact, in the universe is connected via gravity and so anytime you have two objects that are just floating around in space, at the very least there is always going to be a force between them due to gravity. Force on one, due to two. Force on two due to one. And those things are always going to be equal and opposite, OK? And the minus sign just takes into account the change in direction. Mass one is being pulled by mass two. Mass two is being pulled by mass one. And this is what we're going to learn later on when we think about Newton's Universal Law of Gravitation. This, in fact ties the whole universe together. Everything is tied to everything else in the Universe. So you could be m1 and the Earth could be m2. And you are being pulled down by the Earth, but you are also pulling up on the Earth. And the Earth is pulling on the Moon but the Moon is pulling on the Earth. Do we notice when the Moon pulls on the Earth? Is there something that happens that we notice? Anybody have a thought about that? Yes Ben, what do you think? Is there something that we notice about the moon pulling on the Earth? >> The tides. >> The tides. Exactly right. The tides are due to the Moon pulling on the Earth. OK, the Earth pulls on the Moon, keeps it in its orbit, but as the Earth goes around it pulls on different parts of the Earth differently and that moves the oceans around, it changes the tides, OK? Good. So there's no such thing as an isolated force, everything comes in pairs and it is always in equal and opposite pairs. So let's take an example of us standing on the Earth. Let's say that you are standing up on top of a building, and now you jump off of the building, OK? You are being pulled down towards the Earth with a force FG. And we know exactly what that is, right? If you're near the surface of the Earth it's just mg. But Newton's Third also tells us that the Earth is being pulled up towards you. And how much is it being pulled up? With the exact same force. Now let's label you m person and the Earth m sub E, so this is really m person times g. The Earth is being pulled up with mE times whatever acceleration is. a of the Earth. And one of them is up and one of them is down so we're put a negative sign on the one that's down. Newton's Third tells us that if this is negative Fg and that's positive Fg that the magnitudes have to be equal. So mpg is equal to mE times a sub E. And now you can solve this for the acceleration of the Earth. How much does the Earth actually move up? How much does it accelerate when you jump off this building? All right, look at this equation right here. We can just divide by m sub E and we get mass of the person, over the mass of the Earth times g. And let's try this for a human being, OK? Let's see how much that acceleration is. So how much is the mass of a human being? I don't know, let's approximate it. A pretty big human being would be 100 kilograms, OK? The Earth is much more massive than that. What's the mass of the Earth? Anybody remember that? Megan what's the mass of the Earth? >> 5.98 times 10 to the 24th kilograms. >> 5.98 times 10 to the 24th kilograms. Is that bigger than 100? >> Yes. >> That's a lot bigger than 100, right? >> Yes. >> That's like 22 orders magnitude bigger than 100, all right? So we suspect that this is going to be a pretty small number. Well, we'll find out. OK, pull out your calculators and run though your calculation and I will approximate it here. This is a 10 to the 2, 9.8 is pretty close to 10, so that's 10 to the 3. And then in the bottom we have 6 times 10 to the 24. So that is 1 over 6 times -- let's see we've got a 10 to the 3 up there and this is a 10 to the 24, so that becomes a 10 to the minus 21. And 0.16 is about -- 1 over 6 is about 1.5. So that should be 1.5 times 10 to the minus 22. And our units are what? Kilograms cancels out, we've got meters per second squared right there. Anybody run in through your calculator and if so what did you get? >> I got 1.6 times 10 to the negative 22nd. >> 1.6 times 10 to the minus 22. All right so our guess was pretty close. Is that a pretty small acceleration? >> Very small. >> Very small. Extremely small. So small we can barely see it on the screen. Can you write bigger professor? That's a very small number right? 10 to the minus 22 where as gravity is 10 to the 1. It's 9.8. So this is a ridiculously small number and this is why you don't usually worry about the Earth accelerating up to -- towards you. Right, you're never going to measure acceleration that big. So, how big would you have to be in order to get something that you can measure? Well, you can do the calculation yourself but I'll tell you what I found out. If you are no longer you, but you are an oil tanker full of oil and you jump off a building that is as tall as the Empire State Building. And you fall in vacuum the whole time, you will fall at a rate that is in fact measurable. Namely if I do that experiment twice I drop an oil tanker and then I follow it up and I drop a marble, I can tell the time difference in those two things when they hit the ground. And it works out to be 10 to the minus 15 seconds, OK? One femtosecond. So that sounds like a little difficult experiment to do. But when you think about physics, I want you to think about these big picture issues, right? When Galileo came a long and he said, Oh if I drop a heavy object and a light object they hit the ground at the same time. That is certainly true, but if I dropped a heavy object first and I time it, and then I drop the light object and I time it, they're not the same time. They're not exactly the same time. The heavy one in fact hits first because the Earth comes up a little bit more when it falls than when the light one falls. And this is a difficult experiment you would have to do the oil tanker versus the marble from the top of the Empire State Building. And as far as I know nobody's done that experiment yet, but it sounds like a lot of fun. I mean the cleanup sounds a little brutal but it sounds like a fun experiment. OK, when you think about Newton's Third Law, always remember that you cannot just have gravity acting on you, you are also acting on something else, OK? Everything has an equal and opposite force. Action equals reaction. Any questions about this one? All right, let's move on.