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And we're going to assume that we have constant acceleration just so that we can simplify our derivation here. And then what's the distance we're going to travel? Well, the distance is going to be the average magnitude of the velocity, or we could say the average speed, so I'll write it like this, times the time that i... | Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3 |
Well, this is just going to be the velocity divided by the acceleration. Think about it. If you're going trying to get to a velocity of four meters per second, and you're accelerating at two meters per second per second, four divided by two is gonna leave you with two seconds. And if you're starting at a speed of zero,... | Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3 |
And if you're starting at a speed of zero, and you're going to a magnitude of a velocity or a speed of v, and you're assuming constant acceleration, your average velocity is just going to be v over two. So this is just v over two. And then we get a little bit of a drum roll right over here. We see that acceleration can... | Calculating kinetic energy Modeling energy High school physics Khan Academy.mp3 |
These are a great way to visualize conservation of energy, and even better, they force you to think about what's part of your energy system and what isn't part of your energy system. And if you don't know what an energy system is, maybe that's where we should start. An energy system is an object or a collection of obje... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
This isn't Laugh Out Loud, this is an energy chart. A circle, we're gonna define our system, and then another chart. So to understand what these Lull Diagrams mean, let's just look at an actual example. Let's say you took a mass, M, and you released it from rest from a height, H, and this mass falls down. The first thi... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Let's say you took a mass, M, and you released it from rest from a height, H, and this mass falls down. The first thing we should do is choose what is gonna be part of our energy system. Whose energies are we gonna keep track of and whose are we not gonna keep track of? The way people typically do this problem when the... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
The way people typically do this problem when they're doing conservation of energy, they would say it starts with potential energy, and then it turns into kinetic energy, and if you're doing that, what you're really doing is you're saying, I'm taking my mass, that's gonna be part of my system, so I'm gonna take this ma... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So this is the Earth right here, it's got continents, and it's got California, and Mexico, and South America, and there's Florida, and then there's all kinds of stuff here. So now that we've selected our system, we can go ahead and start charting what the energies look like. So what kind of energy was there initially i... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
There was gravitational potential energy, because this mass M started a height H above the Earth, so I'm gonna represent that with this bar. This is gonna be a bar chart. I'm gonna just go up four units. So I'm gonna say there were four units of gravitational potential energy. You might be like, how do you know there w... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So I'm gonna say there were four units of gravitational potential energy. You might be like, how do you know there were four? How do you know there weren't like three, or five, or 4.2? Well, it doesn't really matter too much. The real value in this Lull diagram is being able to conceptualize what's happening to the ene... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Well, it doesn't really matter too much. The real value in this Lull diagram is being able to conceptualize what's happening to the energies. No matter what you draw over here, you just wanna be consistent when you then draw this diagram over here, and I'll show you what that means in a minute. So for now, let's just s... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So for now, let's just say there were four units of gravitational potential energy to start with. Was there any kinetic energy? Nope, because it was released from rest. So if we drop this mass, it starts with no kinetic energy, and this U.S. here is gonna be any spring energy. We won't have that for this example becaus... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So if we drop this mass, it starts with no kinetic energy, and this U.S. here is gonna be any spring energy. We won't have that for this example because there aren't any springs, so there won't be any spring or elastic energy. So that's it. We just had gravitational potential energy to start, and then what did that ene... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
We just had gravitational potential energy to start, and then what did that energy turn into? If this was the initial position, what kind of energy do we have when the mass gets right above the surface of the Earth, right before it's gonna hit the Earth? What kind of energy is there? There's gonna be kinetic energy, so... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
There's gonna be kinetic energy, so this mass is gonna have kinetic energy, and we know it's gonna have kinetic energy because it's gonna be moving right before it hits the Earth, and kinetic energy is the energy an object has because of its motion. So it's gonna have kinetic energy. How much kinetic energy is it gonna... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Well, energy's gonna be conserved in our system, and since the energy's gonna be conserved, if I started with four units of gravitational potential energy, I should end with four units of kinetic energy. Now, you might be confused. You might wonder why wasn't there any gravitational potential energy. Well, I was assumi... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Well, I was assuming that this ground was the H equals zero line, and we know that the gravitational potential energy is MGH, and where H equals zero, the potential energy is zero. So when this mass gets down to the final point, which I'm representing in this diagram, it no longer has any potential energy since the H w... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So the Earth is exerting a gravitational force downward. The object's moving downward through some displacement. That means the Earth's doing some positive amount of work on this mass, giving it energy. Doesn't that mean the energy of the system's gonna change? And the answer is no, and the reason is this Earth is also... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Doesn't that mean the energy of the system's gonna change? And the answer is no, and the reason is this Earth is also part of our energy system. So the Earth did do work on the mass, and this mass gained kinetic energy, but since the Earth and the mass were both part of the system, this work was internal to the system,... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
And if that was confusing, think about it this way. Let's say you and your friend, instead of the Earth and the mass, there's you and your friend, and instead of energy, we'll talk about money. You, the Earth, give your friend, the mass, $10. Instead of 10 joules of energy, you give him $10. And I ask you, how much tot... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Instead of 10 joules of energy, you give him $10. And I ask you, how much total energy is there between you and your friend? Well, there's still the total amount. You lost $10, your friend gained $10, but between the two of you, you still have the total amount of money you had when you started. And the same is true wit... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
You lost $10, your friend gained $10, but between the two of you, you still have the total amount of money you had when you started. And the same is true with energy. Whenever work is done internally between objects in your system, there's no change in the total energy from one chart to another. That's why I had to dra... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
That's why I had to draw the kinetic energy as four units, because no energy entered or exited our system. And something that's really useful about these Lull diagrams is that you can translate them straight into a conservation of energy equation, because whatever initial energy that you start with, plus any external w... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So if you start with 10 joules of energy, and you transfer five joules of energy into the system, you've gotta end with 15 joules of energy. So we can just plug straight into this. What did we have for our particular scenario? We started with potential energy, so our initial energy was mgh, plus external work. There wa... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
We started with potential energy, so our initial energy was mgh, plus external work. There was no external work. There was only internal work, so this would be zero. And that's gotta equal the final energy. The only type of energy we had to end with was kinetic energy, 1 1 2 mv squared. And then if we had numbers, we c... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
And that's gotta equal the final energy. The only type of energy we had to end with was kinetic energy, 1 1 2 mv squared. And then if we had numbers, we can plug into this formula and just solve for the height or the speed or whatever we wanted to solve for. So what would an example look like where energy wasn't conser... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So what would an example look like where energy wasn't conserved? In other words, where there was external work done on the system? Well, we could use this same example. I just need to take the Earth. I'm gonna stick this Earth outside of our system. So now our system is just the mass m. What that means is that the wor... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
I just need to take the Earth. I'm gonna stick this Earth outside of our system. So now our system is just the mass m. What that means is that the work done by the Earth on the mass is now gonna be external work. And since there's external work done on this system, the system's energy has gotta change now. It's not gon... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
And since there's external work done on this system, the system's energy has gotta change now. It's not gonna stay the same. You're not gonna see the energy of this system remain conserved since something's giving it energy. The Earth is giving this mass energy this time because it's doing external work. So how would t... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
The Earth is giving this mass energy this time because it's doing external work. So how would that change our Lull diagram? This mass m still ends with kinetic energy. I mean, just by imagining the Earth as not part of the system, that doesn't change what actually happened. The mass still has to get down here with four... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
I mean, just by imagining the Earth as not part of the system, that doesn't change what actually happened. The mass still has to get down here with four units of kinetic energy. It's still moving just as fast as it did before. But our system, which is this mass, has to be gaining energy and the way that's possible is t... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
But our system, which is this mass, has to be gaining energy and the way that's possible is that the mass does not start with any gravitational potential energy. So people don't like this. People are like, wait, what? Of course this mass starts with gravitational potential energy. It started up here. But technically sp... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Of course this mass starts with gravitational potential energy. It started up here. But technically speaking, gravitational potential energy is an energy that exists between two masses. Takes two to tango and it takes two masses to have gravitational potential energy. If I stick one of these masses out here, it can do ... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Takes two to tango and it takes two masses to have gravitational potential energy. If I stick one of these masses out here, it can do work on the other mass. We wouldn't say that it started with any gravitational potential energy. So this would now be zero. But we would say that there was external work done. So that's ... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So this would now be zero. But we would say that there was external work done. So that's where this energy comes from. The Earth is now doing how much work? Well, if the mass gained four units of kinetic energy, then the work done had to be four units of work. So if you stick the Earth outside of the system, the system... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
The Earth is now doing how much work? Well, if the mass gained four units of kinetic energy, then the work done had to be four units of work. So if you stick the Earth outside of the system, the system no longer has gravitational potential energy. The Earth is doing external work on the mass and this might bother you. ... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
The Earth is doing external work on the mass and this might bother you. You might be like, wait, but it's the same situation that's happening. All we did was change whether we considered the Earth part of our system. So how can that change the math? It didn't really. I mean, if you think about it, instead of the four u... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So how can that change the math? It didn't really. I mean, if you think about it, instead of the four units of energy existing initially as this potential energy and having no work, we're just saying that there was no potential energy to start and there were four units of external work done. It's just a different story... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
It's just a different story. The numbers will come out the same and it's all gonna be consistent. But depending on whether you stick that Earth outside of your system or inside of your system will determine whether you say that there was initially gravitational potential energy or whether you say there was external wor... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So let's look at another example. Let me get rid of this. Let's instead consider this example where a mass starts compressed against a spring from rest. That'll be our initial point. And it fires the mass and the mass goes up this incline and comes over to here and then it's moving with some velocity over here. We'll m... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
That'll be our initial point. And it fires the mass and the mass goes up this incline and comes over to here and then it's moving with some velocity over here. We'll make this our final point. So if we wanna make a Lull diagram, we first have to pick what's part of our energy system because if we don't know what's part... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So if we wanna make a Lull diagram, we first have to pick what's part of our energy system because if we don't know what's part of our system, we don't even know what's gonna be eligible to have an energy in here. So again, let's make the mass part of our system. So the mass will be part of our system. Let's make the s... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Let's make the spring part of our system. So we'll put the spring in here. And let's again put the Earth into our system. So what would this Lull diagram look like for this scenario? Well, since we start from rest, we don't start with any kinetic energy. And even though the Earth is part of our system, which means our ... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So what would this Lull diagram look like for this scenario? Well, since we start from rest, we don't start with any kinetic energy. And even though the Earth is part of our system, which means our system could have gravitational potential energy, I'm just gonna assume that the mass starts at H equals zero. So let's ma... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So let's make the ground H equals zero. That way, this potential energy term, MGH, starts as zero. So there'd be no gravitational potential energy to start with. And the only energy we would start with is the fact that this spring is coiled up, ready to explode and fire this mass forward. All this energy is stored up a... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
And the only energy we would start with is the fact that this spring is coiled up, ready to explode and fire this mass forward. All this energy is stored up as spring or elastic energy. So we will have elastic or spring energy to start with. Let's just say we started with five units of spring energy. Again, this is som... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Let's just say we started with five units of spring energy. Again, this is somewhat random. For a particular problem with numbers, you could solve for exactly how much spring energy you started with. Because remember, spring energy can be found using the formula 1 1 2 KX squared, where X is the compression of the sprin... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Because remember, spring energy can be found using the formula 1 1 2 KX squared, where X is the compression of the spring and K is the spring constant. But to keep things simple, let's just say we start with five units of spring energy. So what would our final energies look like? If this mass is up here moving, if it's... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
If this mass is up here moving, if it's moving, we know it's got kinetic energy. So I can say there's kinetic energy. How much? Again, to figure out exactly how much, you'd have to solve for your particular problem and know this height. But to give you an idea of what conservation of energy says, let's just say there w... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Again, to figure out exactly how much, you'd have to solve for your particular problem and know this height. But to give you an idea of what conservation of energy says, let's just say there were three units of kinetic energy that you ended with up there. What other kinds of energy do you have up here? We're gonna have... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
We're gonna have gravitational potential energy because this mass starts above the H equals zero line. So since the mass is higher up in the air, it's got gravitational potential energy. So now if I say there's three units of kinetic energy and I started with five units of spring energy, if energy is conserved, I bette... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So I could draw two units and now I'd make sure that if I started with five units of energy, I've ended with a total amount of five units. That would say energy is conserved. Let's check. Is energy of our system gonna be conserved? We can determine that by just figuring out whether there were any external sources of wo... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Is energy of our system gonna be conserved? We can determine that by just figuring out whether there were any external sources of work. Did anything external to our system do any work? If not, the total energy's gotta stay the same. This five units has gotta turn into five units over here. And if we assume that these s... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
If not, the total energy's gotta stay the same. This five units has gotta turn into five units over here. And if we assume that these surfaces here are frictionless and that there was no air resistance or no loss in energy due to dissipative forces, there will be no external work done because everything's part of our s... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
So like work was done in here. The spring did work on the mass, giving it energy. There was internal work done, but since there was no external work, the energy had to be conserved. We can write this in an equation again by saying that the total energy we start with, the spring energy, which would be 1 1 2 kx squared, ... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
We can write this in an equation again by saying that the total energy we start with, the spring energy, which would be 1 1 2 kx squared, plus any external work done, but the external work done was zero since everything is internal, has to equal the final energy. And the final energy here is the kinetic energy, which i... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
But you might be wondering, what if there is friction between the mass and the ramp? What if there is friction over here? What would that do? Well, there's two ways we can handle it now. You know there's two ways. We can include these surfaces as part of our system, or we could say that those surfaces are outside of ou... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Well, there's two ways we can handle it now. You know there's two ways. We can include these surfaces as part of our system, or we could say that those surfaces are outside of our system. If the surfaces are outside of our system, we would represent that as them taking energy away. Now there's external work done, but i... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
If the surfaces are outside of our system, we would represent that as them taking energy away. Now there's external work done, but instead of the external work giving our system energy, the external work is taking energy away. This friction is taking energy and turning it into thermal energy. That's what this extra spo... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
That's what this extra spot is here for thermal energy. But since the surfaces are now not part of our system, we wouldn't show that over here. We would just include that as part of the external work done so there would be some negative amount of work done. Maybe the surfaces did negative one unit of external work. Wha... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Maybe the surfaces did negative one unit of external work. What that would mean is that if we started with five units of energy and there was negative one unit of external work done, we've got to only end up with four units of energy. But my potential energy's got to be the same. I mean, I ended up this high, so that c... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
I mean, I ended up this high, so that can't really change. So that means my kinetic energy's now gonna be smaller, and that makes sense. The friction slowed this mass down. I end with four units of energy, even though I started with five because there was negative one unit of external work done by the friction on these... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
I end with four units of energy, even though I started with five because there was negative one unit of external work done by the friction on these surfaces. That's one way to handle this problem, and that's all consistent. The other way to do it, we could just say that our surfaces, which we said were external, are no... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
That way, this external work done is no longer external. This work done is now gonna be internal. The surface took the energy. It still did negative work, but since it's inside of our system, that's now gonna be part of our energy system. So how would we represent that? It'd no longer be a negative one here. We wouldn'... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
It still did negative work, but since it's inside of our system, that's now gonna be part of our energy system. So how would we represent that? It'd no longer be a negative one here. We wouldn't say that this is done. We'd essentially, conceptually, move that negative one over by adding one to both sides, and that mean... | LOL diagrams Work and energy Physics Khan Academy.mp3 |
Everything in human experience, and really human history, or human civilization's experience, is that everything seems to fall to the earth. That if you have water particles, they don't just, if they're large enough, they don't just float up. If they're small enough, they're being held up by the wind and all of that. B... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
But 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 taxi cabs 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 gutter. It's just tryi... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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 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. If I have a needle at rest here, it doesn't automatically, for no reason, all of... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
If I have a needle at rest here, it doesn't automatically, for no reason, all of a sudden jump or fly upwards or start to float. 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 thou... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
We thought, well look, that's just obvious. 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.... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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 any one of those things would have earned his place in history. But this, as you might already know, this... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
Each and any one of those things would have earned his place in history. But this, as you might already know, this is 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 things falling down problem is, do they have to fall do... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
So a pretty fascinating dude. And one of his big insights about this whole things falling down problem is, do they have to fall down? Is this just something that we should assume about the universe? That things just need to fall down? And he says that, or at least we're told that he did tell people that he was somewhat... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
That things just need to fall down? And he says that, or at least we're 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 hit his head while ... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
But if most people were to see, let me draw a tree here. If most of that's a twig right over there. Maybe I'll draw some leaves. So if most people, so that is, let me draw the apple over here, so this is the apple right over here. So for most people, if I were to kind of snap this twig right over here, it's completely ... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
So if most people, so that is, let me draw the apple over here, so this is the apple right over here. So 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 it, they would just think it's a normal happening in the u... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And if most people were to observe it, 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, 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 ... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And that question took him 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. It's been tweaked a good bit by this gentleman in the last 100 years. But for most purposes, when we're engineering things or dealing with things on the surface ... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And not only was he able to kind of think that there's something that might be pulling, somehow acting on this apple, bringing it to the Earth, but he actually formulated 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. And... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And in it, 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 this big G, which is really just a number. It's a number, and we'll... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
It's a number, and we'll see in a second that it's a very small number. Maybe I'll write it there. This is a small number. 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... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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 the distance between the two objects, the distance squared. So this is distance between both... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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're talking about on Earth, you'd pick one of them to be Earth. This is the object that's on Earth. Maybe it's me. And then this is the distance between the center of m... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
Maybe it's me. And then this is the distance between the center of masses of both of those objects. So between the center of me, and I won't go into the detail of that. I'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. If I'm ab... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
I'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. If I'm about 5 foot 9, about half of that distance. I guess the distance from my belly button about to the center of the Earth is this number right over here. So right when you s... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
I guess the distance from my belly button about to the center of the Earth is this number right over here. So right when you see this, before we even talk about me and Earth, or needles and Earth, or taxi cabs and Earth, and that force of gravity, something bizarre might be raising up in your brain. You might say, wait... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And you're saying, look, I'm looking at a computer screen right now. So you're looking at a computer screen right now. And let me 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 attr... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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? And the answer there is that this number is really small. And there actually is some force of attraction between you and the computer. It's just that it's more than overcompens... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And the answer there is that this number is really small. And there actually is some force of attraction between you and the computer. It's just that it's more than overcompensated for the friction between the computer and the desk, the friction between you and your seat, which is, frankly, being caused by the force be... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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 big G, this constant of proportionality, just to get a sense of how small it is, this is, and I'm going to ... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
Newtons is the metric unit of force. Newton meters per kilogram squared, or actually let me write it this way. Newton times, I want to say this correctly, Newton times meter per kilogram squared. So it's a strange set of units here, but the units are really there so that when you multiply it by two masses, which are in... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
So it's a 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 11. If I were to just w... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
This is, let me see, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. So this number right here is the same thing as 6.67 times this thing over here. So this is a super small number. And that's why when you multiply 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 still a... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And that's why when you multiply 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 still a super, duper, duper, duper small force, something that's so small you won't notice, and it's going to be overpowered by other forces, so these things don't fly into eac... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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 roughly the distance from the surface of the Earth to the center of the Earth there for 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 ... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
And this is, and once again I'm just going to round it for the sake, this comes out to be units wise 9.8 meters per second squared. And then you're left with just the other mass. So times m1. So for simplicity, if something is close to the surface of the Earth, the distance does matter, but for simplicity, if we're clo... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
So for simplicity, if something is close to the surface of the Earth, the distance does matter, but for simplicity, if we're close to the surface of the Earth, we can say that 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, for example, you were... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
I have a mass of 70 kilograms. Weight is actually a force, but we'll clarify that more later. My mass is 70 kilograms. Then we can figure out the force that the Earth is pulling down on me, which is actually my weight. So in this situation, the force is going to be g, which is 9.8 meters per second squared. So it's 9.8... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
Then we can figure out the force that the Earth is pulling down on me, which is actually my weight. So in 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 kilograms. Let's get my handy TI-85 out to fi... | Introduction to gravity Centripetal force and gravitation Physics Khan Academy.mp3 |
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