Transcripts
1. Introduction - Newton's Universal Law of Gravitation: welcome to this class, where we will explore together Newton's universal law of gravitation. Newton discovered the school by realizing that the force on an apple that force on the ground is all the same nature than the one that keeps planets turning around the sun. Pretty strict thought for the end of the 17th century. Then do you think the first video presents a universal law of gravitation and explores this rule by presenting as told example, the two videos that follow contained four exercises for you to train on? I tried to make these exercises interesting. For example. In one of them are result. We show why you a moon of Jupiter, has a strong volcanic activity. This class is part of the global course named Gravity. The Basics. You can see this class as an introduction to the course himself. Yeah, in the foreign glasses, off course, when we dive deeper, we will realize that the universal law of gravitation emerges from the description of gravity as gravitational fields. The level of this glasses around and of high school, so it is a great tool for high school students taking physics and preparing exams. It is also well suited for any person that wishes to revive the knowledge concerning the universal law of gravitation said. Now jump to the next video on Enjoy.
2. Discovering the Universal Law of Gravitation: You probably know the story where Sir Isaac Newton received enough on his head and that's discovered gravity. I'm pretty sure that the story is a little bit woman stop. But I can easily imagine Newton observing an apple falling from a tree and then start to wonder why the upper affair Streets of Ground. There was clearly an acceleration associated with that apple. He had recently divide his famous law linking force to acceleration, an object subject in and balance fools experiences an acceleration which is proportional to that force. The proportionality constant is a mass of the object. F equals I'm a. Consequently, they must have been a force involved with that apple. His straight of genius was to consider that the force on the apple was the same force that governed emotional celestial bodies like planets, the force of gravity. In 16 87 Newton published his gravitational theory in a book called Fillers Off. Not you're released. Principia Mathematica. The gravitational force between two point masses is proportional to the product of their masses and basically proportional to the square of the distance between them. Mathematically, you might like this the gravitational force between two masses is proportional to the product of the two masses and inversely proportional to square the distance between them. The two masses. I'm killer whales. You can see them like that. The charge that triggers the gravity right? When there's mass triggers gravity, the distance is expressing meters. What distance are we talking about? We are talking about the distance between the two Center of mass is off the bodies. These two math is actually point masses. Mathematical points with carry a property which is their mass causing the two planets, for example, planet off Mass and one on a planet off Mass. And to the distance considered here is no the distance between surface. Now it's a district between their centers. The center of the sphere is the center of mass of the school. What about G? G? Is a universal gravitational constant. We know that the forces in neutral can you figure out its unit pulls a video figure out the unit of G. That's express this equation was units. So you got new terms which is equivalent to the unit were looking for X kilograms square que going by here, meters squared. The students were you Tones is no s i unit is reconstructed. We know that ethical zehr So Newtown's is also kilograms meters second minus two. So here put kilograms meters second minus two. I can cancel one of the kilograms and now we arrange to get me too Cubes second men's too. And he had kilogram because underneath kilogram minus one. So that would be the unit off value for G is 6.67 by 10 to the minus 11. Meet a few seconds to Cuba. Let's now do an exercise together will appear on the screen the text of the exercise. Pause the video and figure it out. This exercise we had to I asked him who is which. Actually, big walks in space one has a mass of 500 Tom's theater, 150 tons on the distance between their center of nice testicular meters. We want to find out what is a force of gravity between them. It's just about liking the numbers in the universal law of gravitation. So let's do that. 6.67. My tenders of miles 11. 40 that applied by the project of the masses said 500 tops up. We can these stars. We need to use kilograms. So 500 tongs is 500,000. Gil around 500,000 is five by 10 to the five. So five by 10 to the five multiply by this one, which is 1.5 10 to the five and divided by the square of the distance between them, the square of the distance between them, the distant Winfrey kilometers. We need to be in media's self 3000 meters squared. Now let's like this into our calculator. I found a force of gravity between the two walks off 5.56. I tend to demand a seven YouTube. Is this what you found? That was cushioned? A question being that shouldn't be related to the acceleration of each of these walks. So we know that the explanation is given by F equals where f will hear me. The force of gravity. The force of gravity will be the same for the two months. Same magnitude, just opposite direction. Because they are attractive for the first walk, F is going to be cool to m one a one. And for the 2nd 1 F is going to be cool to him too. a to F being for the same for the two by the masses being different, you realize that the accelerations will be different. So that's carefully. A one F one. So 5.56 by 10 to the minus seven, divided by 500 Tom So 5 10 to the five kilograms. And for a two same story, half of them two equals 5.56 by 10 to the minus seven, divided by 1.5 by 10 to the five Kittleman's now like the numbers in find one point 11 10 to the minus 12 meters per second. Squared off 1st 1 and for the 2nd 1 3.71 by 10 to the minus 12 meters per second squared. So, yes, the accelerations are different, the smaller world will accelerate more. You can easily imagine the small work moving towards the bigger work and the big walk toward a small walk different is that the smaller world will have its velocity increased faster and faster. It's going to do something like this. I encourage you to check the next deal. In the next video, which is a training video I will present to you if you exercises, I prepared for you where you can train yourself in using the universal law of gravitation. Plugging numbers is trivial, right? But here you see that the numbers are pretty big, so it can be difficult to talk from the calculator in my career way. So see the next deals, that training for using your calculator and gaining confidence and the result it gives you .
3. Training Exercises 1 and 2: in the previous video we've learned about U turns universal law of gravitation. In this video, we will carry out some training exercises using this law and exercise appears on the screen , force a video and work on the question. When you are ready, resumes the video on view the collection this exercise requires from us to calculate the force of gravitation between the earth and the sun. So for this, we can use Nugent's universal law of gravitation. Yes, because we have the masses and we have the distance between the two bodies. So we just plight f equals G and M Over the squared. You plug in the numbers 6.67 by 10 to the minus 11 but glide by the mass of the sun in kilograms with applied by the mass of the earth in kilograms on, divided by the distance between them distant. That needs to be in meters. So here we have one, also 150 million meters, so we have 150. I tend to the six kilometers that's tend to the nine meters. If I plug in the numbers in my calculator, I find 3.53 I tend to the 22 noodles. In this exercise, we have enough pull up a tree and it falls due to gravity. The force of gravity is the force between two objects. Two bodies would have a such mess. That's what we learned. Where's the universal law of gravitation? The other body is actually the earth. So if we tried to calculate this force, we just apply the universal law of gravitation. Just like in the numbers, the mass of the earth is 5.98 by 10 to 24 kilograms. On the mass off the apple is 0.3 kilograms. We need to stay in kilograms and then you divide this by the distance between the two centers of mass. Well, four meters compared to 6000 kilometers is negligible. So we can just put the radius of the earth in meters bitter plowed back into the three. I find that the force on the uproar would be 2.95 Newtons. That was questioning that's the question. Be determining the acceleration of the apple, The net force on the Apple Answer Gravitational force. It's the only force there is on the apple, so we can write down that the force of gravitation of the apple is just go to m a. Rearranging this, we find a equals force of gravitation on the apple. If I device math so 2.95 divided by 0.3 kilograms and I find 9.83 meters per second squared . Maybe you can ask the number. The force of gravitation is between the airport near the earth also should be attracted by the apple. So the earth also should feel an acceleration due to the apple. If calculated, the acceleration of the earth due to the apple should be a force of gravity invited by the Knights of the Earth. So they have began. 2.95 did I did by 5.98 by 10 to the 24. That's about 2.5 seed by my sticks, my 10 to the minus 24 meters per second squared. So yes, the earth is attracted by the apple has an acceleration due to the apple. But when you look at its magnitude, where we realize that the earth is not going to gain a lot of speed due to the apple question, see how long would the app will take to reach the ground? We have the acceleration him so we can feel without its emotion Problem So let me We weren't hearing a little bit of space questions. See, we tried to find how long it takes with the apple to fall to the ground. So first of all, is the exploration constant? Yes. So can you suit up second Different axis Positive downloads. Same direction as the initial motion Step number three Filling the data So see that s would be four meters You the initial velocity zero meters per second Be the final velocity. We don't really care because we have the acceleration which is positively so downwards Because he chose positive downwards 9.83 meters per second squared and we're looking for the time. So which equation from the equations of motions doesn't have V It's s equals ut plus 1/2 a T squared u is zero so we can kill it and we get s equals 1/2 a t. If I rearrange this find T equals two s of a square bit so two by four divide by 9.83 on our found 0.90 seconds
4. Training Exercises 3 and 4: an exercise appears on the screen, pulls a video and work on the question. When you are ready this use the video on view the collection. So here we have a satellite which is in orbit around the earth at the height from surface equal to the radius of you. So the distance between the satellite and the center of massive year either center of the earth is to radius is two ready? Then we move the satellite at a distance from the surface, which is seven maybe therefore eight. Radio from the center of the earth. So we are basically moving a satellite from a distance off to Brady 28 waiting for most until you. So we want to know how well the force of gravitation change for the satellite. So this is a universal law off gravitation. There are two ways to solve this one super fast and one added longer but safer. So let's take the safer food first. I consider the first case case number one. Therefore, my force of gravity will be G and end over the first distance and concentrate take case to have to. It will not be the same force because of distance changed G and M over deep to square when asked how the force had changed so basically amounts to find a ratio f to F one. So I realized that if I plug in performing us, all these trends go away and up with D one squared of D two squared that we write f two ef one. Do you want squared? Well, the first cases to radio says to eighties Quit Andi two squared its aid. Ready said a radius squared. If I developed the square, I got full r squared and 64 r squared. So the are square can be canceled, leaving me with full over 64 which is 1/16. It's also deep the fast way if you consider that the force is inversely proportional to the square of the distance. So if I met, apply my distance by two. That means my force divided by four. Here I need to grab my distance by four. Therefore my force divide by 16 it's council. The second way to solve this problem is much faster, much easier in a way on Kamajor to train yourself to try to think that way on the other hand. If you start getting confused, you know we can go back to the Safeway where you this or two cases and find elation in official exams and the muted choice section of the exam. You often have these kind of questions, but you don't have too much time. No, you have kind off one minute, one minute, half to solve each question. So it's a good idea to train yourself to think the fast way. Okay, let's go and see the next exercise. In the next exercise, we travel through space and pay a little visit to Jupiter. Jupiter has many moves, but there are four big ones. You, you oppa can. He made a Calisto. We will focus our attention on your closest one. It is just 422,000 kilometers from Jupiter. It's radios and its mass are similar to that of the moon. A little less. Maybe the first question asked us not to find the gravitational force between two. By the gravitational force between Jupiter. That's your on one kilogram off matter on the surface off your which is facing Jupiter. If we apply the universal law of gravitation, we have 6.67 by 10 to the miners, 11 g, then the Mass of Jupiter, then one kilogram. This is one kilogram of matter. We concentrate, and for the distance squared, we don't constant of the distance between the two sent off. Masses off the planets found a place on the moon by the distance of center of mass between the scent of Jupiter on the center off the one kilogram block, which is on the surface of you, meaning that the distance is therefore the full distance between the two bodies, minus radius of you and meters. So that's a plus. And if I enter the data in the calculator, I find 0.71 8 Newtons. Now that was questioned. A in question be It's the same question, except that we're looking at the gravitational force on one kilogram off matter, the other side off you compared to Jupiter. So it is the same for me now. I say numbers, but instead we divide by 4.20 to 10 38 plus the majors of you on the force. I find it slightly less. Of course, it's further away. It's point soon, zero six new terms. When we observe our results. We realize that two forces I'm not the same one. Que gran off matter on this side of you is pulled more than one kilogram on the other side . What does it mean? That means that this side of you, the side of your which is facing Jupiter, is pulled more than the other. And that leads us to question. See, why is there volcanism on you? For that? You need to go back a little bit. In the past of the solar system, before even tennis was fooled. You had the sun on around the sandy, had a disc made of dust on the particle, started clamping to each other on the dust particles became looks and the Woakes become bigger works on his works this time. But I would bang into each other, would ban with loss of kinetic energy. I would be skaters. He basically this heat would be used to motor in the works on this goes on and goes on until there's only one big body left that has absorbed everything in its orbit. We say it has gained its orbit. That's actually one of the definitions of a planet, a body that has cleaned its orbit. But with all these collisions, these planets have a huge amount of energy within them. It's still very, very hot, actually, molten blobs off Nana on days. By the way, this is why there's very because it's liquid, so gravity can easily kind off soft in or the edges. And that's why I kind of feel big planets like the Earth and Venus. Well, there have been cooling down since, but they haven't finished. This process is still there you want. If you're going to center. I realize it's very hot. Needs a crust. The surface has cooled down enough to have solid quest. That takes more bodies. They evacuated, their heat much weakened because that's more even. Mars actually is believes that it doesn't have any more volcanic activity. Maybe they're still little bit. We don't know for sure for the moon and for your there shouldn't be any more volcanic activity. The moon is the size of you on the moon has no volcanic activity, but when we observe you, it has tons of it. It's super active, it's vocals anywhere. So how come it implies that you have another source of energy something else that gives it . He'd. So it goes back to our idea here, off differential forces the difference between the forces depending on the position you knew. If you have two walks like this which are feeling a different force, their will sliding into each other, that fiction and if you do this with your hand value has starts to heat up. So the heat comes from the fiction Jew. Two difference off forces between different positions on the moon. This difference is called a tidal force. It's a proximity to Jupiter that creates a title force, which is pretty strong. You providing energy, your friction off its materials. We have also this title force on Earth. It's not snore because it's loon, which attracts more the water, one side and on the other, and therefore we have these types. This closes our view off the universal law of gravitation. But do not worry too much. We will see it again. From now on, we will describe gravitation For another perspective. We will see gravitation described by fields, so the next video, with the definition of what I feel, is on the following videos. We'll talk about gravitational fields and you will see that universal law of gravitation will emerge naturally from the descriptions of gravitation as a field.