Transcripts
1. Gravitational Fields - Introduction (Video 3.0): in this class, you will learn the concept at the heart of Newtonian gravity gravitational fields. When you hear the words gravitational field, do you know what is meant by the word field? This would be made very clear in the first video. You will see how this concept is really super simple. After you've understood what a field is, we will dive deeper into gravitational fields. First, we will describe the quantity associated with every point off a gravitational field, gravitational field strength. This would be followed by a series of exercises aimed at making you comfortable with this notion. In the following lesson, we will blend in some vector mathematics. Yes, the gravitational field strengths is a vector quantity. It also has a direction again. Many exercises would be proposed to train your new knowledge. When writing these exercises, I tried to make them as interesting as possible. For example, we will look at the effect on gravity of a star that explodes, losing some of its mass. We will also find out how strongly the black hole in the center of our galaxy attracts our own solar system. Cool stuff and what's even cooler is that after taking this class, you will know what to do when confronted questions like these. The presenting a gravitational field with an array of gravitational fear string vectors is no very practical to get a global view off the field. This is why I will introduce in the final video the concept off field lights. This glass on gravitational fields is the third part of a course named Gravity. The Basics If you're not family, always. Newton's universal law of gravitation have recommended Checked last number two first videos five and six. Off this class use vector mathematics. So if you need a refresher, I suggest you consult the glass called Vector for physics here on secure share. The level of this class is around end of high school or entry university, which makes it a great tool for high school students taking physics and preparing exams. This class is also suited for any person that wishes to revive the knowledge regarding Newtonian gravity. Now jump to the next video and let's get started
2. What is a Field? - Gravitational Fields - Video 3.1: electric fields, gravitational fields. Magnet feels either names. You probably heard many times, even for those of you that never studied physics. But you may say, What the heck is a field? Well, let's have a look at this together. Having a clear understanding off what is a field is essential in physics. So what is it? A field is a region of space for which each point is associated with a specific physical quantity. Let's look at this map. What you see here is a regional space. More specifically, a surface for which each point is associated with the number. That number is temperature in Celsius. What we're seeing here is a temperature field. Every time you are watching away the forecast, you actually consulting some data from a field? Of course, this is a two dimensional field for which the values correspond to the temperature at ground level. You can easily imagine the same thing in three dimensions where the higher you get, the colder it becomes. What would be the temperature where my finger is 20 degrees close to my face? 22. And what about just under my chin? 25. Yes, the heat of my body has a direct effect on the temperature field around me. In meteorology, one could think about a field where each point of the atmosphere is associated with the pressure expressed in Pascal's or Mileva. That would be a pressure field. One could imagine also a humidity field, where each point would be associated with the percentage of water vapour in the air. In oceanography, one could consider a volume of ocean and assigned to each point of this volume a value like acidity or salinity. Or what of a para meter? Scientists in this area deal with all these fields have in common to be, Skela feels that means that the specific physical quantity associated with each point can be represented by a number also known as a scallop. That's for scallop feels. Now let's look at this one that you can see in any weather forecast to every point of this region is associated the speed of the wind and also its direction, a quantity that groups a magnitude and the direction is a vector. Here in this field, each point is associated with the vector. Therefore, the wind field is a vector field in oceanography. You could easily imagine a vector associated with each point off a volume of ocean, which would quest form to the speed and direction off water currents. This water count field would be a vector field, another one electric fields in an electric field, each pointed associated with the magnitude and the direction of a force that would experience a charge of one cooling placed. At that point, the forces of Vector, therefore, an electric field is a vector field. Another vector field that we will look at in detail in the next videos is the gravitational field. A gravitational field is a regional space where each point disassociated with the magnitude and the direction of the gravitational force that is exerted on a massive one kilogram placed at that point.
3. Gravitational Fields - Lesson Video - Video 3.2: a gravitational field is a region of space where body feels the force because of its mass. Let's consider the board like an empty space on in this empty space. A place a mass little. So what happens to little end? Well, nothing. It's hanging out there, relaxing at west, and suddenly I take my magic, warned and create a mass Begin what happens to my nicely toe end? Well, now it feels a force that they take too well to begin. So what happened in the perspective of massive toe? It was just relaxing. Then suddenly mass became appeared and something changed. Something fundamental changed to the space where little and was now the state's gain, the property and this property is that at each point of this space, if I place a point us and at this point than this mess will feel a force. So it seems that mass began has changed space around it. It has created a field, and for each point off this field, if I place a mass and there this last one, feel a force, suppose that a place a mass of 10 kilograms within this field say here this mass would feel a force because it is within the field. What were the magnitude of the force dependent? Well, if we depend on two things first, how much stuff are placed there? What will be the mass A place at this point. And second, it will also depend on how strongly to feel the faxes mass. At this point, it will depend on the strength off the field. At this point, if I want to characterize the strength of the field at this point, it is much better if I use a quantity, which is a force. Thank you. This quantity will not depend on the massive place. At the point, it will only depend on the strength of the field. Well, this is gold of gravitational field strength. This is expressed in new terms of the mass and pillows. The gravitational fields Shanks is expressed in new terms. Peculiar. So, for example, if I had 100 new tools there, that means the strength of the field at this point would be 100 delayed by 10 10 new times per kilogram. Each kilogram a place there would feel a force of 10. You talk. This idea defines the gravitational fields, drinks G equals f ever. Let's read this in English. The gravitational fear strength at a point in a gravitational field is equal to the force that would experience a point mass placed at that point. Pilyeon. In this, we'll put you so we see that this definition expresses a consequence off the field for the Mass M, which is based in the field. That's a consequence. But what causes it well, the mass biggane. So we can also they find the gravitational fear strength at the point days on its schools. When the mass end changes and gets, for example, bigger. What happens to the strains of the field at a given point? Why get stronger, right, so the gravitational fear strengths would be directly proportional to the mass that creates a field. Now, if I consider point, which is much further away, it is quite untreated to realize that well, further, the point weaker will be the effect off mass began. The math creates a field to weaker will be the few and yes, the gravitational fear strengths inversely proportional to the distance squid and finally, well, we have to cost a Doha proportionality constant. G G is a universal gravitation constant. It is a constant of our universe. So now we have two ways to describe the gravitational field strength for the consequence the effect of the fear. And from the course, what causes a field? I will teach you something which I really love to do is to read an equation in English. Do you remember, for example, when you were kids and you had the sentence like this? Say cat beats Patty so you would take your pen with different colors and say, Oh, this is a subject. Oh, this is vote. Oh, and this is a compliment. It's a drop. Well, we can do the same thing Enough. Yeah, use. I think this one g equals f of This is a subject. This is a verb on either compliments. And when you give a subject you save a cat, you don't take cat right? So you have to describe what she is. You can't say Jeez, effort. Boo him doesn't mean anything. What you see instead is the gravitational field strength at that point within a gravitational field is equal to the force experience by a point mass placed at that point per unit mass try It pulls a video, try to repeat what I just said just by reading. No, by memorizing. But by reading the equation, let's try with this one. G equals G m of a d squared. If I just say g equals game of it is quite that doesn't mean anything to you. What means something to me is to say the gravitational fear strength at that point within a gravitational field is proportional. This is my verb now is proportional to the mass that creates a field on the inversely proportional to the square of the distance between that mass. At that point, yeah, I mentioned the point before. I repeat, so gravitates to fear strengths at a point within a gravitational field is proportional to the mass. It creates a field and inversely proportional to the square of the distance between that mass and that point. Being able to read math and translate it into English allows two things first, to get a good market, your test. But second, to understand what you're doing when you have an exercise and you start getting lost sight . But with all these new notions, just recite for yourself a definition because you already understood it right and it will clarify everything. Really learn how to translate for math to English. It's a useful anyway, back to what we were talking about back to gravitational fields. Note that these two definitions can be put into Well, let's do something fun. I change color of the I feel em will be equal to GM of these. Quit how we arranged this by multiplying by them on both sides. I get f equals G and on over the squid. This is a universal law of gravitation with discussed earlier. It emerges from the description of gravity. Okay, let's do an exercise now to get used to these notions and also to the numbers which are associated with them in this exercise, were required to determine the gravity's for fear. Strengths on the surface of the earth. Well, we can just use the formula. The gravitational fear strikes is equal to G m. Of this squared. I'm like in the numbers. So 6.674 by 10 to the minus 11 were supplied by the massive creates a field. So here's your F 5.972 by 10 to 24 divided by the square of the distance between the point massive periods of field on the point where, considering for the gravitational field strengths. So here is the distance between the center of the earth. In surface I eat rages, so 6378 kilometers bike under the three because we want to be meters on square. The number I found it was 9.798 You till's killing. No doubt. In each case I've got four significant figures, so I don't exam. I will need to give my answer with four significant figures. He recognized this number, right? This is man's 18 It's a peculiar You've seen this in mechanics that when you want to find out the weight off a ball, say, which is a ball, which is 10 kilograms, you want to find its way to say its gravitational force. Just apply MGI. It's a 10 by nine. Today you hear 98 new talks have to wait off the ball. Well, there's gravitational fear. Strengths is this guy. Let's play a little bit with this notion of gravitational field. Click in my white board, which is my empty space. I include two masses and one and them too. Both masses will create a gravitational field around them that's focus on the gravitational field created by nurse and one at the point where enter is located. There'll be therefore gravitational fear strength. G one equals G M. One, the mass creating the field divided by the distance between the two centres of masses. It's quality. So I'm to is a mass located within a gravitational field. Therefore, it will feel a gravitational force if we be cool to and to a G. Well, I think plug ins You were here getting me m two g and one over these. Quit on. Just rearrange it. This would be the force due to mass one on into one master section. Why did Nighties? Now let's consider the field created by the Mass and to at the position where the Mass and one is located. There'll be a gravitational fear strength G two whose G and two over these quit therefore the math and one will be subjected to a force f equals N one G two on I can. But this down on rearrange that would be the force due to Mass to on one so to over one. Now notice this. These forces are off the same magnitude. So this goes straight into the definition off the universal law of gravitation that emerges from the description that we had off gravity using fields. I hope this video has helped you understand what the gravitational feelings as well as what is a gravitational field strength. Now it's time to train your new knowledge. Jump on the next video, we would go through various exercises that prepared.
4. Gravitational Fields - Exercises 1 & 2 - Video 3.3: and exercise appears on the screen. Also, video on work on the question When you're already resumes the video on view the collection . In this question, we have a star that explodes. By doing so, it uses 1/3 of its mass and its timing to his divided by two. We are requested to determine the new gravitational fear strings on the surface of the star compared to the one before the explosion. This looks very much like a case. One case to question you will see often these questions are growing in media choice exams. So let me show you how to handle these. Well, you have the star before the explosion. That's case one and the star after it exploded. Case, too. What is it? Para meter That they asking us to Valerie to change the gravitational fierce drinks. So you should put this pyramid to a subject of an equation. So here's keys. He's just going to be G equals G m over these quit. So let's apply it to the two cases. G one. It waas g m one over. The ones quit and then in the case to G to just waited here easier. G two equals G and two of details. Quit now right down the relationship between the perimeters that change and for which, you know the changes. You know that the math of the stall, it had to decrease by fed so and two equals 2/3 off them well, and you know that the damn it of the star decreases by half. So it's radios. We do so also. So you get two equals 1/2 off one. No blood this into their G two equals G, 2/3 off them, one divided by 1/2 off, one squared. Don't forget to put the coefficient inside the square. And now put the numbers underside. You separate numbers and letters. I feel what you're trying to do. You're trying to produce this formula, so you got 2/3 divide by 1/4 1/2 squared. What a plot by G m. One of our once quit. What is this? Well, this is G one. So 2/3 divided by 1/4. That's 2/3 by four G one. So 1/3 of g one, the gravitational fierce drinks has increased by a factor of 8 30 This is how you solve these case. One case to problems. Sometimes it's quite straightforward and you can go quite fast. Sometimes when you have mood people power meters which are changing, it's a good idea to go on the slow way. We want to find the gravitational fear strength at that point located 20,000 kilometers about the surface off Saturday. Well, we can just use the form gravitational field track that the point is proportional to the mass. It creates fear, divided by the square of the distance between that mass on that point. So I just plug in the numbers 6.67 intended demands 11 supplied by the Mass of Saturn, which is five from 68 by 10 to 26. If I did by the square of the distance between the center of Saturn on the point, of course, the great say it's a radius plus 20,000 kilometers, therefore, 78,232 by 10 to the three because I want to be meters squint that you have found G is 6.19 meters per second squared with three significant figures because I've got three significant figures. Fan
5. Gravitational Fields - Exercises 3, 4 & 5 - Video 3.3: and exercise appears on the screen. Also. Video on work on the question. When you're already resumes the video on View the collection Here we have a natural note flying about planet on. This astronaut is feeling a gravitational force off 800 new times. The mass of the afternoon is 82. So the first question is, What is the magnitude of the gravitational fear string at the location of the astronaut? We're looking for G. The data we have is a consequence of the field, right? It's a full felt by a mass in place in this field so we can use the consequence definition off the gravity of fear. Strength. The gravitational fear strengths at a point in the gravitational field is equal to the force experience by a point mass placed at that point, putting it mass. So here 800 Utah's divided by 80 kilograms, giving you had very little fear strengths off 10 year olds. Particular question. Be what is the mass of the planet if the astronaut is three million meters from its center , so here we have the mention off the distance between the point mass and place in the field on the mass big am creating the field. Therefore, we consider the definition of the gravitational fear strength related to the cause of the field. So the evidence for fear strength at that point is proportional to the massive creative field anniversary proportional to the square of the distance between that mass. At that point, what are we looking for? We're looking for the mass of the planet. That is the mass that is creating the field. So this therefore, we just need to rearrange this a little bit. Um equals G d squared over G plug in the numbers 10 supplied by three million meters squared. And if I did by the gravitation constant. So six points 57 by 10 to the minus 11. The mass of the planet that I found is 1.35 I 10 to 24 Cuba. This number seems reasonable for the mass of a planet. You can compare it with some planets in our solar system. For example, with the earth, it could be around six by 10 to 24 kilograms. Jupiter is in the 10 to 27 kilograms range. Saturn 10 to 26. The moon tempted to 22. These are the kind of values you could expect for the massive planets. Four stars expect more from 10 to 29 to 10 to the 33 34. The mass of the sun, for example, is to buy 10 to the 30. When we think about Norm it, we have immediately in our head maybe something like the moon. While the what satellite worthy of all the earth around the sun that the sun also is in orbit. It's actually in orbit around a massive black hole in the center of our galaxy, all stars in our galaxy actually orbiting the black hole. It's massive. Four million times the mass of the sun. We are given in the exercise of distance from the stand to the black hole, 28,090 years and also the math of the sun. Calculate the gravitational fear, strengths, experience by our solar system. Due to the black hole. Well, I just use a formula G equals g. M of these quit So the mass will be the mass of the object creating the field. So here the black hole. So this is equal, full 1,000,000 solar masses. So that's full back into the six multiplied by 1.99 10 to the 30 kilograms. What about the distance? Whether unit used here is light years 20,000, 90 years, So a night here is the distance covered by light in a year. So to find out this value in meters because we need to protect meters, we can write the equal the Uberti so D equals Bt. That would be the distance, the velocity of light and t the time because from two year in seconds. So that's 365 days, 24 hours and a few 1006 100 seconds in. And now this is actually equal to 9.46 by 10 to 15 meters. So here the would be 20,000 with a glide. By this distance, I'm on 46 by 10 to 15. It is so let's plug in the numbers G equals 6.67. I tend to the minus 11 multiplied by full bite into the 61.99 30 divided by 20,000 well supplied by 9.46 10 to 15 that I square the value have found was G equals 7.62 by 10 to the minus 15 meters per second squared. So you see it's a pretty small value, but it is a value nonetheless, and the sun is subjected to this force. If you wanted to find the force, you multiply it by 10 to the 30. I get something like 10 to 50 Newtons that so it's not negligible on for the little story. It takes about 200 million years for the sun to make a full orbit around the black hole. The requested in this exercise to prove that the gravitational field strength can be expressed in meters per second spread. The gravitational field strengths is a force experience by a point mass and placed in a field of seven point per unit mass killer. So the our new terms kilograms, so the gravitational field strengths expressed in new terms killer back. But you know that you can white ethical that may therefore, new terms is equivalent to lighting kilograms five meters per second squared, so new terms peculiar them is equivalent to kilogram by meters per second squared, divided by kill over the kilograms. Cancel on the end up with meters per second squared, so the gravitational fear strings can be expressed in meters per second squared
6. Gravitational Fields are Vector Fields - Lesson Video - Video 3.2: way have seen that the gravitational fusions is a force experience by a point mass placed in the gravitational field playing mass killer. So here in the white space, I will create a mass begin on this mass began will create its own gravitational field around it. Now, in the gravitational feared are placed a mass little this massive toe Emery feel a force that elected tools begin. It's fools would be cool to the mass little emplaced at that point with the blind by the gravitational field strings. At that point, this force has a direction on the magnitude. It's a vector, sir. Quantity with magnitude and marry shipped off the force Is Victor the mass being just number? The gravitational fear strings is therefore also a vector. Yes, the gravitational field strength as a magnitude and direction. It's a vector. So a gravitational field is actually a vector. Your field to each point off this field is associate ID a vector, the gravitational field strength. At this point, for example, you have a victim like this, this one like this. You see that the direction of the gravitational field strength is two worlds mass, creating the field and we could calculate its magnitude like we've seen last time. G iss, the gravitational constant. Glad by the mass, creating the field. Reply by the distance from that mass to the point because it drink squared. I raised the masses for my way boat. Yes, I'm like God, that's my space. My universe and I can put masses and raise them for a cool. So I decided to raise it because I want to put in to masses which each would create the gravitational field. So I've got everyone here and let's change color for him, too. And to him, what would be the gravitational field strengths at that point? Well, im one is creating. You spend gravitational field and tools, so that would be to gravity for fear strength. At that point, they'll be G one under B G two directed tools into. So if I place a little mass, I'm here. Where would it go with four g one g two. I cannot take two parties at the same time. What it would do it would follow the result gravitational field strings. To find the result of gravitational field tricks, you need to add to two vectors G at that point would be cool to G one class G two. Do you remember how to add vectors? Graphically, you take the 1st 1 and then you slide. The 2nd 1 says that the terror of the 2nd 1 reaches to tick off the 1st 1 There's something like this. And now there's no way nice with something like this. And now you go from the tail of the 1st 1 to the tip of the 2nd 1 to finally result in Victor's being read. And that will be gene. If I place a point mass and here it would follow this direction on the strength of the force would be the mass here, multiplied by the magnitude off the result gravitational field strength. So to get used to this left in exercise together. In this example of exercise, we have two stars both of the same mass given 10 to 30 kilograms, Trust separated by this to 50. We also consider point A that falls with the two stars on equilateral triangle. Maybe they're all sides are the same. So citizens between a and the first or is equivalent to the distance between a and the second the question is what is the gravitational field strengths at a magnitude and direction. Okay, so the first start is creating his gravitational field and therefore there with a gravitational field strength at a like this, that's quick g Well, on the second Star is also creating its gravitational field. On that A. There'll be a gravitational field strength to the result of gravitational Fierce things will be the sum of the two. So we would add a sum of two. Now you notice that I made it straight upwards. Well, I know because I had to say mass on the same distance from the point A that my gravitational field strengths D one and D two will have a say 92 therefore, and may sense to draws a vato. However, how do we prove that? And how do we find this? My needed where we need to add two vectors. Gravitational field strength is G one plus two. So we can easily do this graphically. How do we do this analogy? To find the resulting vector G, we need to find the components off this result in Victor. So we're looking for the g X and you. Why? How do you find these components where each component will be the some of the components off the individual vectors, so G X would be G one X class G. Today's, for example. But here what we realize is that we have to define some access and reconsider components that because the magnitude of the same on the angle here will be the same because we're equilateral triangle. The magnitude would have the same value on because their vectors one is this way. One with the other way they compensate each other on the some would be zero. To be more precise, GX is actually affected. It has a direction. A sequel to G one X glass, G two X. Now if I want to look at the magnitudes I need to call to do their damage now g x She wanted on the negative direction so minus few one Thanks. And he, too, will be in the positive dynamics G two weeks now, because I have to say magnitude and same angle. We know that G one X and V two X will have the same magnitude. Therefore they cancel the show so we know that the X component is zero entreaty, Lee. We could have guessed it. That's what got you. Why here? It will not be the case. Two vectors are both elected to all the positive direction of the Y axis. So we find the component off G one on the why access We have any well here, which is 30 degrees. Yes, it's an equilateral triangle. So 60 degrees, which corner and 30 degrees with its heart. So this is going to be G one course of 30. I'm the same for G two. That's G to costs off 30. Now we know that G one is equal to G train magnitude because M and D are the same values. Therefore, we could write down two times g m over the squared multiplied. I cost 30 and cost 30 is square root of 3/2, killing the two there. Now let's plug in the numbers 6.67 my 10 to the minus 11 by 10 to the 30 divided by two by 10 to 10 squared. I want to try by square to three and I found so your 0.29 new tones per kilogram. So this is a magnitude of the y component. I want a magnitude off the results of gravitational field. I haven't two components. They should be easy. I just need to apply the standard formulas that the magnitude of the gravitational fierce trains will be equal to the square off with some of the sum of the square of its components with it. Jack zero. Therefore, that's going to G Y 0.29 new times particular. What about the island? Well, the any who is given by 100 minus one off the Y component on the X component. And that would be the angle compared to the X axis because of putting the X component on the denominator that this is you have 29 this is zero. So this is infinity. What gives me a constant equal to infinity 90 degrees or pi over two. All right, let's close to 90 degrees the museum. The angle off the results of gravitational field strings is 90 degrees versus the X axis. So straight upwards power to the Y axis. So your conclusion should be at the resultant gravitational fierce trance. You have a point. A has a magnitude of 0.0.29 newtons per kilogram has directed upwards along the Y axis. In this exercise, we have to deal with vector addition. Yeah, finally, the magnitude and the direction on the result of vector sum of two other victors. If you're experiencing trouble with this, I recommend that you check my course Mathematics for high school physics. Vector addition is dealt with in the second section with a bunch of videos that give you techniques on also exercises so that you can handle this quite easily. In the meantime, I recommend that to jump to the next video. In the next video, we would go through many exercises with you Is gravitational field strength from his victims?
7. G. Fields as Vector Fields - Exercises 1 & 2 - Video 3.6: you have learned about gravitational fields, you have learned also about the concept of gravitational field strength. On that, the gravitational field strength is a vector. This video is a training video. We will train your new knowledge through a set off three exercises. Now we have a piece of paper and a pen. Grab a calculator. Eventually prepare yourself a drink or a snack on Let's stop and exercise appears on the screen. Also, video on work on the question when you already issues a video on view the collection. In this exercise, they are two spheres. Sphere one is 500 kilograms of mass and sphere to 2000 kilograms of mass, so two spheres are separated by a distance of five meters. Go along the access that joins the center. Of the two spheres. There are two points. M and N Point M is located one meter to the left of the first fear and point, and is between the two spheres. Located three meters to the light off the first sphere, we're required to find the gravitational fierce franks at point n and point. Now there are two spheres, so two sources of gravity. Therefore, there to gravitational fields. So each point of space random there'll be too gravitational, fierce drinks to find a result of the one, you would have to add them together as victors. So let's do point, my point em that the gravitational fierce frank's due to the first fear. That's quite G one at point and there's also another gravitational field strength due to the second sphere as quick G two, the result of gravitational fear. Thanks g will be cool to G one plus g two. We are adding vectors. So we need to define a direction. I would choose a positive direction towards the light. Therefore now when I want to find the magnitude, I can add the individual magnitudes Danity because both are in the same direction. And now I just plug in the formula and now I can't like in the numbers I would fact allies JIA dissing so nice of the fierce fears 500 The distance is one meter so one meter square is one I am from the second mass is 2000 kilograms on the distance between end and the second sphere is six. So six squared is 36. If I plug this In my calculator, I find New Tone's killer, meaning that every kilogram are placed on point and we'll feel a force off people seven by tens of minus eight. Newtown. Too old to like. Let's deal now with point, and we'll also be subjected to to gravitational fields this time and is between the two spheres. So let's write down the individual gravitational field strings for each gravitational field , so grab a little Fear shrinks due to the first fear. G one will be in this direction. Tools. A sphere on G two will be to wards of seconds. Fear. Do you see that? No. In the same direction when I arrived, the result of gravitational fear strength is just a sum of the two vectors, but they're not in the same direction. So when I switched to magnitudes, I G equals minus t one plus three two. Giving me a formula G factor off empty of a detail squared minus M one over. The ones quit and I can just plug in the numbers G. He was 6.67 by 10 to the minus 11. The second masses 2000 kilograms the distance between end on the second masses to two squared is four. First mass is 500 kilograms. The distance between N and the first mass is free, so I get nine here and when applied the numbers in I get frequent zero by 10,000 minus eight new tunes per kilogram, meaning that if I placed one kilogram at point n, this kilogram would feel a force of three by 10 to the minus eight Newtons here way have two spheres. Fear number one is 10,000 kilograms in mass Fear number two is 5000 kuna. Granting that's the two spheres our distance from each other by 100 meters on the line that links to centers of mass a point P, a test mass placed at 20 p wouldn't feel any force. It would stay as it is. The question is, find the position of point P related leaders feel number one point p is located within the gravitational fears off those fears. So in point, P acts with reputational fear, strength for those additional fields and the result of gravitational field P, as we have seen before, will be the vector sum of the two. So the gravity for field strength due to fear number one would be dying tools feel number one on the one due to fear number two that I did tools feel Number two. We are dealing with vectors, so let's define a positive direction that's consider positive towards the left. That means that when I want to calculate the magnitude of my gravity for fear shrinks p it will be. Plus, you want minus t two. Now we know that if I place a mass would be, there's no force on this mass. Therefore, the gravitational field strings has to be zero. At this point, anything to G one equals G two. Plug in the form, and as I get this, I can kill the G's. The masses are 10,000 and 5000 the distance Well, actually, that's what we're looking for. We are looking for this distance Squid X. So this would be X squared on. The two would be this distance their 400 under sex. Let's call it 100 money sex and one is 10,000 and two is 5000. Well, why not divide everything by 5000 to simplify the calculations and we end up with something like this two X squared equals one of 100. My mistakes squared. Just rearranges to put it on the new For now your thought would be OK. I'm going to develop this. I get a quote allergic and I saw the quantity to find X. Yeah, but here I've got two squares equals to each other that can translate into scope of to 100 minus x equals X. I did not this in order to isolate X, giving me 100 square to minus X script of two equals X, which is 100 scripture to equals. X fact of one class quiver to to and I end up with valuable X X equals square root of two of one descriptive too by 100. And now you just plug in this in your calculator and you find X equals 58 meters
8. G. Fields as Vector Fields - Exercise 3 - Video 3.7: and exercise appears on the screen. Bolsa video on work on the question When you are ready to resume the video on view the collection. This exercise presents a system of three stars. Star one, which is 1.5 by 10 to 30 kilograms, start to slightly bigger, 1.8 by 10 to 30 kilograms and stuffy, which is the source styles. You 300.4 back into 30. The distance between style oneness style too, is 200 million kilometers. The distance between star Wonder staff is 500 million kilometers, and the access of process through the center of Stalin and tells fee is perpendicular to the axis. Passing food star one star too. The question is to find the gravity's for fear. Strength at the position of staff. Be in order later to calculate the gravitational force on it. So this position is projected to have additional fields that off star one and that will start to Therefore there will be two diabetes for fear strengths she wants and g two. The results of gravitational field strengths will be one thirsty too. We are adding vectors by here We are in three dimensions. We can't just I've magnitudes we have first to define to access. Find the components off, each credited for fear, strength at the X component together, the Y components together, and that would give us a components as a result of gravitational field strength. But to do that first we need to find the magnitudes off the gravitational field strength one and two as well as the angle between them. So let's get started. G one is proportional to the mass off the star that's proportional to the square of the distance. Between that point and that point say, if we plug in the numbers, we get 6.67 by 10 to 11. But by the mass of the star, creating the field to do 30 divided by this, this was quite careful. We have to stay in meters, so it's five by 10 to 11. It's quit. Let's do the same for the second star. She trickles G m two of the square, so if I play the numbers 1.8 10 to 30 because this is a stark reading the second field and divided by the distance, we need to find the distance. So to find a distant we can use speed ago. So hey, are the distance here would be screwed off? 500 square Class 200 squared if you calculate this 538.5 million kilometers. So I take it here so they get 5.39 by 10 C 11 squid. Now plug this in my calculator and I found this Juwan equals 4.0 zio by 10 to the minus four Newtown per kilogram and G two is 4.14 by 10 to the minus four u turns. Kill them. I have the magnitudes off the individual gravitational field thinks G one and G two in order to find components off the result of gravitational field strength. I still in the angle between geology to well, it's pretty easy because I have here 200 million kilometers, 500 million kilometres. Both our sides event tangled triangle. So when youse pension tangent off, this angle is 200 million divided by 500 million. And that's just in a show. I can just here you go, giving me an angle theta equal to 12.7 degrees. Is it Okay? So now I have the magnitude and the angle. I'm going to need some space. We have calculated the magnitude off the individual gravitational field strings as well as the angle between them. Now, from this data, we can quite easily find out the components off the result of gravitational fierce tricks. But first of all, we need to define some access. So I like to choose access, which are quite convenient so that the components will be positive. So say, for example, the X axis could be to write positive on the Y axis would be positive downwards. Okay, It's not G as to come. Bones on the X axis and the Y axis on the X axis. You have a contribution from G one? No, because it's perpendicular. What about G two? Yep. I have a contribution of G two on the X axis is going to be G two here. The angle is not between the access, and Victor is the other side. So it's fine. Sandaled. How about you? Why, where g one contribution? Yeah, fully. It's parallel to the y. So it's going to be for the G one on Fergie to where the angle to ties between the doctor and the access that is consigned GT I can just plug in the numbers now. GX will be G two was 4.14 by 10 to demands for Mitt applied by the sign off 12.7 and 40. Why is going to be so 4.0 by 10 to the minus four plus 4.14 by tense moments for that story too, but applied by co sign off 12.7. Be glad my calculator I found Jeanne GX is 9.10 by tens months five And you Why is 8.4 by 10 to the minors for on both and new to Cuba? Now that we have to components, we can easily find the magnitude and the direction off the result of gravitational field. I need a little space, something to erase regulations. So this is a position on how star three. And here our Access X and why G x is this amount. I'm 0.1 by 10 to the minus five. Do you? Why is this about so here? 8.4 by 10 to the minus four. I want to find a resultant I will need to have them that way. That's G. It's simple. Peter. Go now to find a magnitude. It's going to be this queried over the sum of the squares. So here, 9.10 by 10 to the miners five squared plus 8.4 by 10 to the minus four squid G equals. Let me grab again. My calculator. I found 8.9 by 10 to the minus four u turns per kilogram. What about the direction where the damage would be defined by the ankle to toe? Here? We can find this angle by writing down times in Quetta equals this over that. So that's actually the X component on the Y component. So 9.1 by tenders of my was five of 81 full by 10 to minus foot easily returned open 91 divided by 8.4. So deter would be found as tangent minus one off open 91 of four. Which gives me let me find my calculator again. 6.46 degrees. So this is 6.46 to be, So I would say that the result of gravitational fear strings at the position off Star three has a magnitude off 8.1 10 to minus four Newtons per kilogram on this direction is defined by a tangle of 6.5 degrees to the light of the Y axis downwards. Why did we calculate the gravitational fear strings at the location of stuff? Well, to find the force that is exerted on stuff, flee the gravitational force. That's question be f equals entry. The force on Star three with its mass with supplied by the gravitational field strength at its location. So here the mass was point full by 10 to 30 kilograms multiplied by 8.9 by 10 to minus for giving me 3.24 tenders of 26 yes, by 10 to 26 new towns that we only have to seeing if he configures here something to put 3.2. I hope this set of exercises has helped you realize how you can use the gravitational fear strength as effective. The gravitational field strength is a really good tool to describe gravity field at every point within the field, but it's not the only one. There's another one called Fear lights, so the next video will be about fear
9. Fields Lines - Radial Fields - Video 3.8 - Part 1: we have learned in people's videos that at every point off a gravitational field, his associative quantity, gravitational field, gravity, fear, strength at the point in a gravitational field, it's the force experience by one kilogram of mass placed at that point. So if I had a nice end here and I consider any point, say this one, they will be associated with this point. I gravitated. No fear, strength directed tools, the mass creating the field. If I wish to have a global view of the field, I could consider other points to draw a gravitational fear strings for each of them, as you can see if I do this for every point, is going to become quite messy. So this is not a convenient and not they readable to draw all gravitational field strength everywhere on the field to make it more readable. There was another tool we can use. Fear lines. A field line is an imaginary line represents the path that would take a mass place in the field. So let's remove all these Ivy Victor's except one. Give this one. If I place a mass here, I see that it will follow the direction of the gravitational fear strength. Actually, it would follow this fear life, You know, I could do another one for place of mass, and somewhere here it will follow this field. And I can do this for other points. Other regions off the field, a pattern emerges. I read your pattern. So this is quite a good view of the gravitational field created by the mass M. It gives me the path that would take a mask placed anywhere in the field. But actually, field lines can even give me more information. Information about the strength of the field. Yeah, look at that. When you come closer to the mass creating the fear, what happens to the density of the lines where they get more packed? And we also know that the gravitational field strength is inversely proportional to the square of the distance between the point consider on the mass, creating the field. So when you come closer to the mass and gravitational field, strength increases Therefore there, with a direct correlation between the density of the lines on the gravitational field strength. Now, here on my board, I'm talking to damage. But you can easily imagine the same thing in three dimensions with the lines going like this. And when you come closer to the Mass, you can also imagine easily that the density of the lions would follow an inverse square law.
10. Fields Lines - G. Fields with 2 masses - Video 3.8 - Part 2: Let's go sit there now to masses. Two identical masses. The gravitational field resulting from these two masses will be the combination off the two nd video gravitational fields. I would also drool here a sheer line separating the two in the middle. Let's place a test mast here at this point, what direction would it take? Well, it would take the direction off the result of gravitational field strength. We've learned in the previous video how to find it. We take the individual gravitational fear strength on we add them as vectors. So here I'll get something. Maybe I this Let's consider now another point closer to this one. Say here, Same thing. I draw the gravitational field strength for the first mass and also for the 2nd 1 And I add the two vectors together. I would get something, maybe like this, unless we take a point very close to this mass. Well, we got the gravitational field trips, which is pretty large on a much smaller one for this one. And if I added too well, actually the result of gravitational fear strength would look very similar to the one created by the first Masters. Maybe something like this so that each point the mass would take the Dacian off these black victors, meaning that the deck victors are the tangents to the feel like now I could draw the field line by making sure that Victor's attention to it. Here we go. And I could repeat this for all the points in the field. Let's do them roughly. And I could do it also for this one. You see, the lines are really straight when it's the other side, because the influence of the other half is baseball. Now we have a global view off the gravitational field created by these two masses. Yes, we take any point here somewhere here we put a mass there, and we know it will follow this path. You might wonder what? What about this region? Well, if I continue, I could I would get something maybe like this and say me. Okay, there's a point here. We're actually if I place master. Remember in the previous video, we went on an exercise looking at the point located between two masses and at this point of gravitational fear, strength was zero. Meaning that the gravitational fear strength off the first mass compensated exactly. The gravitational field strength you to the second Mass. So a test mass place there wouldn't feel any force. Well, this point is this one.
11. Fields Lines - Uniform Fields - Video 3.8 - Part 3: - let's consider all panicked the earth. The earth is a sphere, therefore its center is also its center of mass. The gravitational feel it creates because it's just a point will be radio feel, all of fear lines. Ah, for me a radio pattern and add elated towards the center of the earth and also because it's a sphere. All the fear lines are perpendicular to the surface of the earth. So let's take a part of this surface and zoo and zoom again. Here. The few nights are still perpendicular to the surface, but now the surface can because they don't like flat meaning that all the felines apart on over equidistant that we just seem that the gravitational field strengths vector is tangent to the fuming. Therefore, all gravitational fear, strengths, sectors, a poet. The force experience by a mass place in that field would follow the same direction, whatever the point in the future. In addition, we also saw that the density of the feline represent the strength of the field, so the magnitude of the gravitational field strength factor will be the same at any point in the field. So the force experience by one kilo any point in the field would be exactly the same. Same direction of state magnitude. Such a field is called a uniformed field in the uniformed field vector representing the property of the field. There's the same magnitude and same day I shall at any point in the field and the fear lines are all parallel or on have the same density there will equidistant from each other. This is a beautiful gravitational field. And this is why when we deal with mechanics problem on the surface of the earth, we can just use the same value in the same direction for the weight, the force due to gravity, Remember, weight is energy. Think about it when you're solving something in mechanics and you're considering the weight you just write down. Wait equals N G. And you use 1981 40. But what you actually doing? You actually calculating the gravitational force between whatever master, considering the mass of the earth and the square of the distance between the master con surgery and the sense of the But you know that this is the same value wherever you are on the Earth. Nine. Donate SG This video about felines closes this introduction to gravitational fields. In the next class, we will study circular motion. Why? Circular motion? Because by combining the knowledge gained by following the class and gravitational fields, where is the one you will get by following the class circular motion, we will be able to dive deep into all jumped is an X class. I see you there and discuss