 This is part one of the lecture series on the physics that's going to be needed in astronomy. Well, even then it's a small part. So this is in this particular lecture, which is quite longer than many others, so I'll try to be brief. Motion, force, energy, and gravity. And then after that the next one we'll look at. Energy, orbital motion, angular momentum, linear momentum. I think this is a great idea to review what the Greeks thought. And let's start with what the Greeks thought about motion. Remember, the Greeks used deductive reasoning. And that means they start with things that they would assume to be obvious. There's no debating about it. For example, what if I drop two objects? Well, the heavier one falls faster. That's what the Greeks said. And they thought that was obvious enough that they didn't need to test it or do anything. But you can ask yourself, what do you think would happen if you drop a bowling ball and a basketball? Many people would say the answer that they've heard before, but very few people really either believe that or understand why that is. But that's where the Greeks started. Aristotle did a lot of this work. And this is what Aristotle says about motion. He said that there are first two kinds of motions. Well, three really. Natural motions are when objects move on their own without anyone having to do anything. And they do this motion because they try to seek their place. So if I take a rock and I let go of it, then it falls. It wants to get to the rest of the rocks. It tries to get to rocks where rocks belong at the center of the earth or something like that. I'm not sure exactly. And if you take fire, fire belongs in the sky so it rises. So these things don't require you to do anything. They just happen on their own. The next kind of motion he would say is a violent motion. These are motions that require some type of interaction. And when you stop that interaction, they stop. So if I push a cart, I'm making it do something that is not natural to that cart. The cart wants to be at rest. And when I let go, the cart stops because it returns to its natural motion, which is to be at rest. That's really the key thing that everyone has trouble with. And then Aristotle said, well, the moon and the sun, they move and they don't stop. So they're not bound by the same rules. They're in the heavens and they apply their own little rules. So they're exempt from these normal natural and violent motions. Okay, so I already went through this. What happens when you stop pushing a cart? It stops. And here's Aristotle didn't say force. One, because he spoke Greek. But even then. So Aristotle says, if you have no force, that means you have no motion. And this is an idea that most people, vast majority of people will accept today. When you stop exerting force, it stops. And it's easy to see why. Because if you go push a cart and you let go, it stops. So here's a little question. Actually, there's several set of questions in here. So you can ask yourself, what would Aristotle say would happen to a ball if you kick it after you kick it? There's force slowing it down. That's just what balls do. Or there's no force to keep it going. Aristotle would say, that's the nature of balls. They slow down because they want to be stopped. But that's not the correct answer. So really, the next major person to talk about force, not the only person to talk about force, but the one that summarized things really well and that we want to look at next was Galileo. And what Galileo did, and probably not the first one to do this, was to challenge Aristotle's assumptions that he based all his findings off of. If the assumptions aren't true, then the things that come logically afterwards aren't true either. So does a heavier ball fall faster than a lighter ball? The common story is he dropped these off the leaning tower of pizza, but probably he didn't, but I don't really know. So but you can ask yourself some questions. What about a rock and a feather? Which would fall faster? Or would they fall the same? I think everyone would agree the rock would fall faster. What about a pebble and a pillow? You have a big pillow and a little pebble. The pillow is heavier, but the rock, the little pebble would fall faster. So right there you see that there's something wrong with this idea that heavier things fall faster. So Galileo's experiment was not just to take things and drop them. He wanted to do it quantitatively. He wanted to have some numerical values to it. And he wanted to do it in a nice controlled manner. So if you just drop things, you can't time that, especially with the timing devices that Galileo had. It happens too fast. So in order to make the motion slower, he put it on a track and he let a ball roll down a track. And he kind of got the idea that this would lead to falling. If it turned, the steeper it got, the closer it got to falling. If it vertical, it would be falling. So it's okay to study this motion in this slowed down sense. And he did some other things too. He would change the angle, but not change the mass. And then he would change the mass, but not change the angle. So he did some controlled experiments about what he found made the thing go down there. And there I tried to animate the ball rolling down the track as it goes down. And that's what he found. That it did speed up as it went down. And Aristotle said that it would travel at a constant speed. So right there, he found a problem with Aristotle's assumption. So this is what he found. Things speed up as they fall. He found they speed up as they roll, but he inferred that meant they also speed up as they roll at fall. And the distance something goes is related to its time that's rolling squared. So he did get a quantitative relationship between those. It does not depend on the mass of the object. You have different mass balls and they still go the same. And Galileo came to the idea, especially by having a level track, if there's no force, it doesn't stop. It keeps going. And the way he did this was, well, if I have a very slightly inclined track, I can make the ball travel at a constant speed. And so he idealized the situation to say, well, maybe I could get to a case where there's no force, nothing resisting it, and it would just keep going on forever. So it really changed from what Aristotle said, which no force means no motion. Galileo says no force means it stays moving. So Aristotle was wrong. But you have to realize that people refer to the ideas of Aristotle for 2,000 years. Well, why was that the case? Well, first Aristotle never did any experiments to validate his deductive logic. And he just started with something that was assumed true, so he wouldn't need to do an experiment. But the problem was that it's very difficult to imagine a case where no force is reacting on an object, because in the case of the cart, you have air resistance and friction. Both are slowing the thing down. In order to see that it keeps moving without... with no force, you'd have to eliminate all those forces. So it's difficult to do. So now we want to talk about force, and we want to talk about motion. So these are some important ideas about motion. First, let's just get some definitions out of the way. Position is where you're at. So if you just had an x-axis, this would be your x-value. You could have an x and y-value. You could actually have what's your x-value and what's your y-value. And the origin is completely arbitrary. So position doesn't have necessarily physical meaning, but change in position would. Okay, speed is what people think about a lot. It's how far you've gone divided by the time it took. Velocity is your change in position divided by the time it took. So the good example of this, a good example would be driving around a track. If you go once around, you went a certain distance and you divide it by the time you get your speed. Your velocity, though, if you go once around your position, you're back to where you were. So your change in position is zero. So your velocity would be zero. Also, I try not to represent it here to make it simpler, but velocity includes direction with it also. So 20 miles an hour east and 20 miles an hour west are not the same thing. And then finally, acceleration is how fast your velocity changes. So the change in velocity divided by time, it also has direction. So velocity is how fast your position changes. Acceleration is how fast your velocity changes. So here I tried to represent this, if you're traveling from position one to position two, then this orange line, this orange arrow would represent your change in position. And if you divide by how long that took, you'd get your velocity, which I'm representing by this green arrow. So it's in the same direction as your change in position. Acceleration is change in velocity. Velocity can do two things. It can change its magnitude, how fast, or it can change its direction. Now, the key thing is, and this is difficult, even though you've just seen this in the previous two slides, acceleration is not velocity. I tell you that now, but people still make this mistake. They say things such as, oh well, if it's at rest, then acceleration has to be zero. That's not true. They're different things. This is a busy looking slide. But I think it can give us some good example. I'm trying to represent a ball that I throw straight up at 20 meters per second. And I want to find out where it goes. It turns out that on the surface of the earth, things naturally fall with an acceleration of about negative 10 meters per second squared. Or what that means is the velocity changes 10 meters per second every second in the downward direction. So in this first ball on the left, you see I throw it up at the speed of 20 meters per second. After one second, it would decrease or change the speed in the downward direction by 10, so that would leave it just going 10 meters per second up. In the next second, it would go from 10 to zero. So I show you the calculation here. To calculate the acceleration, if I did the final speed minus the initial speed divided by the time, I get negative 10 meters per second in all these cases. So at the top, it's going at zero meters per second. But it's still accelerating. Because in the next second, it starts going 10 meters per second down. And I calculate that with the final speed of negative 10 minus the initial zero. That gives me divided by one. That's negative 10. And then finally, I'm going from negative 10 to negative 20. So the final speed is negative 20 minus the initial speed of negative 10. So negative 20 minus negative 10. And so that again gives me negative 10 meters per second squared. I like to say to people at the top of this path, people like to say the acceleration is zero. Well, if that was the case, then the velocity wouldn't change. And if the velocity is zero meters per second and not changing, it's going to stay zero meters per second. So it's just going to float there. Clearly, that doesn't happen. We want to talk about force. One of the really nice things to talk about with force is to use the idea of momentum. Momentum is simply how the velocity of something is applied by its mass. Since velocity has direction, momentum does also. Now this is mass, not weight. Mass is basically, you can use the definition, the operational definition of how many protons, neutrons, electrons, things has. That's a good idea for its mass. It's not perfect, but good enough. It's basically how much stuff is in the thing. So I can change momentum three ways. In this first example on the left, I have a car and it's going from a momentum with the blue vector, the blue arrow at the bottom at one to two. The arrow got smaller, so it slowed down. That's a change in momentum. Another way I can do it is by increasing the momentum, going from one to two. In the next case, my momentum is greater. I change momentum. And then in the final case, my car turned. So the direction of the momentum changed. So again, a change in momentum. So you can think of it as three examples of changing momentum, but they're all change momentum. Change momentum is important because this is essentially what Newton says. Newton calls a force an interaction between two objects. It's always an interaction between two objects. And what do forces do? Forces change the momentum. Forces are not related to the momentum. They're related to the change in momentum. Change is the key word. And so here we have an expression. I wrote it as a vector expression and we don't talk about vectors and I apologize. I couldn't help myself. So the force, whatever, and this is the total force acting on an object, is equal to delta p over delta t, where delta p means the change in momentum. And delta t, delta is the Greek triangle sign. And this is the net force. So if this block had a force pushing from the left and the right and they were the same, this would be the exact same thing as no force acting on it. And the momentum wouldn't change for that object. So this is really everything you need to know about. All of Newton's three laws of motion are on this page. I'll go over the rest in detail too, but force is an interaction between two objects and forces change momentum. That's what they do. So on the right I have a map. I have the distance between New Orleans and Chicago. I can't remember the exact distance. Let's say it's 800 miles. I'm guessing. Well, if it's 800 miles from New Orleans to Chicago, how far is it from Chicago to New Orleans? It's 800 miles. New Orleans to Chicago is 800 miles north. Chicago to New Orleans is 800 miles south. So really you can say it's a distance between New Orleans and Chicago is 800 miles. The same thing happens with forces. Since forces are an interaction between two objects, they always have pairs. There's always a force of object A pushing them B and an equal force, but in the opposite direction of B pushing an A. So you most likely have not seen Newton's third law written this way, but this is the way it should be written. For every force there's an equal and opposite force. For forces come in pairs. So on this other picture I have a person and the earth. And so the force of the earth pulling on the person is let's say 200 Newtons down. Well, there's also a force of the earth, of the person pulling on the earth and it would be 200 Newtons up. Really the force between these two things is 200 Newtons and it has two ends. Just like Chicago to New Orleans, New Orleans to Chicago. It turns out there's essentially only four kinds of forces. There's gravity, which we'll talk about a lot. There's electromagnetic force, which we'll talk about later. The weak nuclear, we will talk about this one too. And the strong nuclear. Gravity is the interaction between objects that have mass. The electromagnetic force is the interaction between objects with charge. So here I represent, those are the two most common forces that we're going to see. And you may say, but wait, here's an example of a hand pushing on a block. What kind of force would that be? Well, the one above it, the diagram I drew is a ball falling on the ground. Clearly that's gravity. But what kind of, which of these forces would my hand be exerting on that block? It turns out that this is an electromagnetic force and we'll talk about this in more detail later. But why does a block not pass in my hand? Well, the electric charges in the atoms that make up the block are actually interacting with the electric charges in the atoms in my hand. And that's where that contact force, we call it a contact force. But really, they're not even really touching. But when you get really, really close, you get really strong forces. So you won't see it, a space in between these. But at the atomic level, they don't touch. So I talk about force a lot. And I think this is the most important and common incorrect usage of force. That force is a property of an object. This object has a lot of force. That object moves with a lot of force. It keeps speeding up until its speed is the same as its force. All those are examples that indicate force is attributed as an object, a property of that object. And that's not the case. Force is a property of an interaction between two objects. So that's the first biggest idea, wrong idea people have. And then the second is a problem Aristotle had. No force means no motion. That's not true. No force means no change in momentum. And then people associate the other, no motion implies no force. Again, not true. So really it comes down to people saying force is directly associated with motion. Here's a good example regarding force and motion. There's a big boat on the left. And it's tied up to the dock, but the lines are a little slack. You could stay on that dock and you could put your foot on the boat and push. And you could move that boat. And that's a big boat. You could move it. But you couldn't shake it back and forth. And the reason is you can exert a force and that changes its momentum. But it has such a large mass that it gives it a very small velocity. And then to change the momentum back the other way, it takes some more force. Now take the boat on the right. It's this much smaller boat. Could you shake this one back and forth? Well, it's much easier to move this back and forth and change its momentum because it has much lower mass. But the most important thing is you can move that big boat. You just can't increase its speed like you could the small boat. Wow, this is a long talk. You're probably getting tired of listening to me. Well, go ahead and pause it and take a break if you need to. Too bad I can't pause. Probably can, I just don't know how. Okay, so we talked about objects changing direction would be a type of change of momentum and therefore need a force. Here's an example. Here's a guy swinging a ball around in a circle and the orange arrow represents the momentum of that ball and the pink arrow represents the force acting on that ball. In order to make this move in a circle at a constant speed you have to exert a force on it and the force must be acting towards the center of the circle and that will make its direction. You'll see why this is important when we talk about orbits but the force we want to talk about now is gravity. Newton came up with this idea of universal gravity. Remember Aristotle said the motions of things on earth are different than the motions of things in the sky, in the heavens. Well, Newton says the same interaction that we have between me and the earth is the same interaction between the earth and the moon and the earth and the sun. That's where the universal comes from. And he says that the gravitational force is related to some constant, G, the product of the masses of the two objects and the distance between them. So the more massive they are, or either one of them is, the greater the force, the gravitational force, and the greater the distance between them, the less the force. And again, mass is how much stuff is in the object. And here you can see, if I'm standing on the earth, I would be mass one, the earth would be mass two, there would be an interaction between us. What if I wanted to find the force on the earth? Well, if you wanted to, you could switch those two masses around, but that doesn't change the gravitational force. Actually, this is an incomplete equation, so it doesn't tell you the direction. It's just a magnitude. So this is an interesting experiment on how that gravitational constant was determined. It was determined by a guy named Cavendish. I can't remember his first name. I'm sorry. And what he did was he had these two green balls represent some smaller masses on a stick hanging suspended from a wire. And when you turn this wire, it exerts a little bit of force. So what he did was he took two larger objects, the orange balls, and placed them near such that the green balls were attracted. And there is an gravitational attraction between any two objects of mass. And so that pulled it. And by measuring how much it twisted and knowing the mass of the two objects, he could calculate g. And you see here that g is a very small number. 6.67 times 10 to the negative 11th Newton meter squared per kilogram squared. So if I had two objects of both of one kilogram mass, one meter apart, then there would just be 6.67 times 10 to the negative 11th Newtons. Extremely small force. So we don't really notice that. It's really difficult to notice that because there's so many other things acting on it, like friction and air resistance in the gravitational force of the Earth. Okay. So what I want to talk about next is weightlessness and a pair of weight. And here you see a nice picture of some astronauts in the space station and they're floating around in what people would call weightless. But I'm going to show you that there's some problems with this. First, you don't have to follow the calculations. You can just trust me if you want. But what I want to do is calculate the gravitational force on an astronaut, both on the surface of the Earth and in orbit. So if I use the astronaut mass of 70 kilograms and an orbital distance of 360 kilometers above the surface of the Earth, I can plug these values along with the mass of the Earth and the radius of the Earth into Newton's universal law of gravity and calculate the gravitational force. And so what you see here is on the surface, the astronaut is 706 Newtons or 160 pounds. In orbit, he would be 632 Newtons or 142 pounds. So he does have less gravitational force on him, but it's not zero. It's not insignificant either. It's still pretty significant gravitational force. So when people say there's no gravity in space, that's not true. It's called a zero-G environment for different reasons. There definitely is gravity. So why are they floating around then? I think it's useful at this point to look at a model for a person. On the left, I have a model, a model of a person, this is kind of like their spine, where the red dots are masses connected by springs. And in this case, this would be a model of a person just standing in an elevator. So what happens is the bottom springs are compressed a lot more than the top springs because they have to support a lot more mass. And so the yellow arrows indicate the individual forces on all the little masses and then the big blue arrows, the total force, the floor has to push up. And what happens if you add all these up, then the total force is zero until his momentum doesn't change. And I represent that in the elevator picture on the right also. This is something you do every day. You stand there and you feel fine. But what... Okay, let's go on. So now what if the elevator works celebrating up? Well, that would mean his momentum would have to be increasing upwards. You'd have to have a greater force pushing up than down. So when this happens, if I have the blue arrows now much bigger than the little red arrow represents acceleration, then what happens is these masses have to be compressed even more in order to exert the proper amount of force to make him move. So you see, if you compare this model to the previous one, it's much more compressed. And so gravity is not greater, but when you press the up button on an elevator, especially a fast one, you feel heavier because you're more compressed. But gravity is still the same and your weight is still the same. Now what if you accelerate down? Now the opposite happens. Now these springs are not compressed as much. Your gravitational force is still the same. But the springs aren't compressed as much, so you feel lighter. Do gravitational force is the same? What if I was accelerating down at about 10 meters per second squared? Well now there would be no interaction between the masses in the spine model. So you wouldn't feel any compression and you would feel weightless. That's what this sensation feels like. You're not weightless. Gravity is still pulling on you, but you're in an elevator. You may have seen this in a, in amusement park rides like this. They put you in a little chair and the chair drops and you feel weightless. It's the exact same thing. So the final example is what happens if you are away from any large gravitational masses and you accelerate in a certain direction? Well it turns out you can make the model compress exactly like if you were just standing still on earth and you would feel fine. But there's no gravity at all. So what you feel is not gravity. It's really what we call parent weight. It's the total force acting on you. So in this case you could make it feel like there's gravity even when there's not. You can make it feel like there's no gravity even when there is. And this is what they're doing in this apparatus. This is called a plane called a vomit comet. And these astronauts look like they're in space, but they're not. They're in the atmosphere. But the plane is accelerating down such that they have apparent weightlessness. So it's my understanding that the weight, the zero G-scenes in the movie Apollo 13 looks so realistic because they were filmed inside this plane to make it actually weightless. So here's a picture of the plane and what it does is it flies up and then it...