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Main content
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Video transcript

everything in human experience and really human history or human civilizations experience is that everything seems to fall to the earth that if it's if they have water particles they don't just if they're large enough they don't just float up they don't if they're small enough they're being held up by the wind and all of that but if they're if they're large enough if they're large enough they will fall that you don't have people that are able to just float around they'll fall you don't have taxicabs that float around they'll fall and not only will the water fall it'll hit the ground it'll puddle up and if there's a gutter it'll fall into the into the into the gutter it's just trying to get lower and lower and lower or if I were to drop a bunch of needles they would just fall they don't if I have a needle at rest here doesn't automatically for no reason all of a sudden jump and and and or fly upwards or start to float and and so this is a thing that's just fundamental to everything that we've ever ever experienced and so for most of human history or human civilization we just accepted it as a given we thought well look that's just obvious everything would just everything should just fall down that's just the way the universe is to think otherwise would be crazy and that's why this guy right over here is one of the greatest geniuses of all time and he did many more things than just the things I'm going to describe in this video each and in any one of those things would have earned his place in history but this is you could have you might already know this is Isaac Newton Isaac Newton easily one of the top-five minds in all of human history so a pretty fascinating dude and one of his big insights about this whole thing's falling down problem is do they have to fall down is this just something that we should assume about the universe that if you know if your that things just need to fall down and he says it that and he or at least it were told that he did tell people that he was somewhat inspired to come upon this way of thinking by observing an apple falling from a tree it's probably not true that you'll see in some cartoons on TV that the Apple hit his head or or hit his head while he was sleeping and gave him the idea but if most people were to see let me draw a tree here if most so that's a twig right over there maybe I'll draw some leaves so if most people if most people so that is and let me draw the Apple over here so this is the Apple right over here so if most in for most people if I were to kind of snap this twig right over here it's completely common sense the Apple would fall and if most people were to observe that they would just think it's a normal happening in the universe but for Isaac Newton at least on that day when he observed that Apple he says well you know why did that why did that Apple fall and this to some degree is a great example of out of box thinking because something that for thousands of years or tens of thousands of years human beings had taken for granted just because that's the way it always was he actually asked the question why does it always have to be that way and that question took them down an entire line of reasoning that set up the basis for all of classical mechanics which for the most part we still use today they've been - it's been tweaked a good bit by this gentleman in the last hundred years but for most purposes when we're engineering things or dealing with things on the surface of the planet and we're not done and we're not going close to the speed of light we can still use the mathematics that Isaac Newton came up with from this simple question and not only was he able to kind of think that there's something there's something that might be pulling somehow acting on this Apple bringing it to the earth but he actually formulated an entire an entire I guess law around this thing so as you can imagine the thing that Isaac Newton believes brought the Apple to the earth is gravity is gravity and he formulated the universal law of gravitation or the law of universal gravitation either way and in it he he theorizes that the force between two objects and it's a vector quantity it's always going to attract the two objects to each other so the direction is towards each other the force of gravity between two objects is going to be equal to the big G which is really just a number it's a number and we'll see in a second and it's a very small number maybe I'll write it there this is a small number I'll cook I'll give you that number in a second it's equal to this constant this universal gravitational constant which is a super duper small number times the mass of the first object times the mass of the second object divided by divided by the distance between the two objects the distance squared so this is distance distance between between two between both of those two objects so if you're talking about the force of gravity on earth this right over here you'd pick one of the masses to be earth so this mass over here if you were talking about on earth you would pick one of them to be earth this is the object that you're that's on earth maybe it's me and then this is the distance from between the center of masses of both of those objects so between the center of me if you were to if you and I won't go into the detail that'll make a more detailed video on center of masses and the center of the earth so it's roughly the distance from the surface of the earth or if I'm about five foot nine about half of that distance of you know where I get the distance from my bellybutton about to the center of the earth is this number right over here so right when you see this before we even talk about you know me in and earth or needles and earth or or taxicabs and earth and that force of gravity you might something bizarre might be raising up in your brain you might say wait the way the way gravity is defined by Isaac Newton or this this this formula that we were given right here it's saying that we have gravity between any two objects and you're saying look I'm looking at I'm looking at a computer screen right now so you're looking at a computer screen right now and let me draw it take my best attempt at drawing a well this is an old school computer not a flat-panel but gets the job across so you're looking at a computer screen right now how come you aren't attracted to the computer screen how come it doesn't fly into your face the answer there is is that this number this number is really small and there actually is there actually is some force of attraction between you and the computer it's just that it's more than over over compensated for the friction between the computer and the desk the the friction between you and your seat and which is frankly being caused by the force between you and the earth the force of gravitation the force of gravitation between the computer and the earth that both of you and the computer such small masses that you you really can't notice it you really it's really negligible it's being overpowered by other forces that are keeping the computer from even drifting into your face or your face drifting into the computer so just to get a sense of that this G this this this you know this big G this constant of proportionality just to get a sense of how small it is this is and I'm going to round it here six point I'll write approximately six point six seven times times 10 to the negative 11th Newtons and we'll talk about Newton's Newton's is the metric unit of force Newton meters per kilogram squared or it's actually let me write it this way Newton Newton times now I want to say this correctly Newton times meter per kilogram meter per kilogram squared so it's this way it's the strange set of units here but the units are really there so that when you multiply it by two masses which are in kilograms and divide it by a distance which is in meters you will end up with Newtons but I want to make it clear that this is a super small number 10 to the negative 11th if I were to just write 10 to the negative 11th it would be zero point zero and then we would have one two three four five six seven eight nine ten 11 this is some see one two three four five six seven eight nine 10 11 so this number right here is the same thing as six point six seven times this thing over here so this is a super small number and that's why when you were multi apply it by not so large numbers if you don't use earth if you use you and a computer you're going to end up with a still a super duper duper duper small for something that's so small you won't notice it it's going to be overpowered by other forces so these things don't fly into each other but when you think about really massive bodies like the earth the force of gravity starts to become noticeable very noticeable and I'm not going to give you the mass of Earth in this video although that's interesting and you can look it up yourself but if you put in the mass of Earth right over here if you put it in right over there and if you put in the roughly the distance from the surface of the earth to the center of the earth therefore R and you multiply that times G all of these terms right over here so this term if you multiply that term times that term and divided by this term squared they simplify too they simplify to what's sometimes called little G little G so this right here you could view that as the gravitational field at the surface of Earth it's also the same thing as the acceleration of gravity near the surface of the earth and this is and once again I'm just going to round it for the sake this is the this is this comes out to be units wise 9.8 meters per second squared and then you're left with just the other mass so x times m1 so for simplicity if something is close to the surface of the earth the distance does matter but if we're if we're simplicity if we're close to the surface of the earth we can say that the that the the force of gravity is going to be this little G thing times whatever the mass is that is close to earth so if you take if for example you were to take me and I weigh let's say I weigh 70 kilograms so in the case of Sal Sal has a actually I shouldn't say way I have a mass of 70 kilograms I have a mass of 70 kilograms weight is actually a force but we'll talk will clarify that more later my mass is 70 kilograms then we can figure out the force that the earth is is pulling down on me which is actually my weight so this situation the force is going to be G which is 9.8 meters per second squared so it's 9.8 meters per second squared times my mass which is 70 kilograms times 70 times 70 kilograms and let's get my handy ti-85 out to figure this out let's so I get 9.8 9.8 x times 70 and that gives me 686 so this is equal to 686 kilogram meters per second squared kilogram meters per second squared or this is the exact same thing as this the same right over here this is the definition of a Newton so this is this is a Newton which is appropriately named for the guy that that's the father of all of classical physics so my weight on earth which is the same thing as the force that Earth is pulling down on me or that or that the gravitational attraction between me and earth I should say is 686 686 Newtons now I will ask you an interesting question now I will ask you an interesting question so here is Earth here is earth and I am not even a speck of a speck of a speck on earth but for the sake of simplicity let's say that this is me I'm hanging out in the Indian Ocean someplace so that that is me and we already know that Earth is pulling down on me is pulling down on me with a force of 686 Newtons now my question to you is am I is am i pulling on the earth with any force and am i pulling on the earth with a larger or a smaller force than it is pulling on me and your gut or just you know your knee-jerk reaction might be well look Earth is so huge Sal is so tiny clearly the earth must be pulling with a greater force on Sal than Sal is pulling on the earth unfortunately the that's not the case that I am so the earth is pulling on Sal at 680 with the force of 686 Newtons and Sal is also pulling on the earth with the force of 686 Newtons so Sal is also pulling on the earth it makes me feel very powerful with the force of 686 Newtons but you might say wait that doesn't make sense Sal if if I have a building over here and if you were to if you were to let's say jump from the building you're going to start the force of gravity is going to be acting on you and you're going to start accelerating downwards it doesn't seem like the earth is accelerating up to you wouldn't we all notice that every time someone were to jump off a building if the earth started accelerating in a major way and the way to think about that is the force is the same and we'll touch on this in more detail in other videos but force is equal to mass times acceleration so when we're talking about 686 Newtons 686 Newtons in terms of the force that earth the gravitational attraction between myself and earth and this is going to be equal to 68 68 kilograms then it provides a pretty good acceleration on me so in this case if you solve for a if you solve for a over here you're going to get the 9.8 meters per second squared now if you do the same thing for Earth I already told you that we're pulling on each other with the same force 686 Newtons but now the if you want to figure out how much is the earth accelerating from that force you're going to get a I won't even put it here you're going to put a huge number in here huge number times the acceleration of Earth towards me and says this is such a huge number very very very large number this is going to be an immeasurably small number super super small number and frankly it's probably averaged out by the acceleration of Earth - or the force of gravity between Earth and all the other people and things on the surface of the planet so it all averages out in the end but even if it didn't even if I was the only thing that the earth was interacting with it would be negligible you wouldn't even notice the acceleration of Earth towards me but you wouldn't notice the acceleration of meat or earth because because of because of our vastly different masses even though we have the same even though the force of attraction is the same