載入中...

相關課程

登入觀看

⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.

相關課程

0 / 750

- Everything in human experience, and really human history or human civilizations experience, is that everything
- seems to fall to the earth, that if you have water particles, they don't just float up.
- If they are small enough they are being held up by the wind and all that, but if they are large enough, they will fall.
- That you don't have people that are able to just float around, they will fall.
- You don't have taxi cabs that float around, they'll fall.
- Not only will the water fall, it will hit the ground, it will puddle up, and if there is a gutter it
- will fall into the gutter. It is just trying to get lower and lower and lower.
- If i were to drop a bunch of needles they would just fall. They don't... If i had a needle at rest here
- it doesn't just automatically for no reason jump and fly upwards and start to float.
- And so it is just a thing that is fundamental to everything that we have ever
- ever experienced.
- And so, for most of human history or human civilization, we just accepted it as a given.
- We thought, "well look it's just obvious, everything should just fall down, that's just the way the universe is.
- To think otherwise would just be crazy." And that's why this guy, this guy right over here, is one of the greatest geniuses
- of all time. He did many more things than just the things I am going to describe in this video,
- and any one of those things would have earned him his place in history.
- And this, as you may already know, 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 'things falling down' problem is:
- Do they have to fall down?
- Is this just something we should assume about the universe?
- Things just need to fall down, he said, or we were told he said that he was somewhat inspired by
- observing an apple falling from a tree. It's probably not true that you'll see in some cartoons
- on television that the apple hit his head or hit his head while he was sleeping and gave him the idea.
- Most people were to see... Let me draw a tree here.
- That's a twig right there, some leaves. So if most people... So that is an apple over here.
- So if most people... If i were to snap this twig over here, the apple would fall. Pretty much common sense. The apple would fall.
- And if most people were to see that, they would just think it's a normal happening in the universe. But for Isaac Newton, at least on that day,
- he asked himself, "Why? Why did that apple fall?"
- And this, to some degree, is a great example of "out of the box" thinking, because something
- 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 him down a entire line of reasoning that set up the basis for all of
- classical mechanics for the most part we still use today.
- It has been tweaked a good bit by this gentleman in the last hundred years. [Albert Einstein]
- But for most purposes, when we're engineering things on the surface of the planet,
- and we are 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 theorizes that the forces between objects
- now 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 this big G, which is really just a number, its a very small number.
- I'll give you that number in a second. It's equal to this constant, this gravitation 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. Distance squared.
- So this is distance between two objects.
- So if you're talking about the force of gravity on Earth, this right over here...
- You pick one of the masses to be Earth, so this mass over here. You pick one to be Earth.
- This is the object on Earth. Maybe it's me. Then this is the distance between the center
- of masses between those two objects. The center of me and center of the Earth.
- So really it's from roughly the distance from the surface of the Earth or if I'm roughly
- five foot-nine [inches tall] then about half of that distance 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, you might have something
- bizarre raising up in your brain. You might be saying, "the way gravity is defined
- by Isaac Newton, this formula we're given right here, it's saying we have gravity between
- any two objects" 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 draw an old school computer,
- not a flat panel. How come your not attracted to the computer screen?
- How come it doesn't fly into your face? And the answer there is, this number, 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
- between you and the Earth, the force of gravitation between the computer and the Earth.
- That you and the computer have such small masses that you really can't notice it. 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 round
- it here, it's approximately 6.67 times 10 to the negative 11th Newtons.
- And we'll talk about Newtons, it is the metric unit of force.
- Let me actually make sure I say this correctly. Newton meters per kilogram squared. Newton times meter per kilogram, squared.
- It's this strange set of units here, but the units are really there. So when you multiply by two masses,
- which are in kilograms, and divide by a distance, which is in meters, you'll end up with Newtons.
- But I want to make it clear that this is a super small number.
- Ten to the negative 11th. If I were to just write 10 to the negative 11th, it would be 0.0 and
- then we would have eleven 0's. So this number right here is the same as 6.67 times
- this thing over here. So this is a super small number. And that is why if you multipy it by not so
- large numbers, if you don't use Earth, if you use yourself and a computer,
- you're going to end up still with a super duper small force. Something so small that you won't
- notice it. It is 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, 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 roughly the distance from the surface
- of the Earth to the center of the Earth for R, and you multiply that by G. All of these terms over here...
- So this term, if you multiply that times that term and multiply by this term squared,
- they simplify to what is sometimes called little g. Little g. So this right here, we can view that
- as the gravitational field at the surface of Earth. It's also the same thing as the acceleration
- of gravity at the surface of the Earth, and this, and once again I'm just going to round it
- for the sake... This is... This comes out to be, units wise, 9.8 meters per second squared.
- 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. We can say that the force of
- gravity can be this "little g" times whatever the mass is close to Earth. For example,
- if you were to take me, and I weighed 70 kilograms... So, in the case of Sal, Sal has a...Actually I
- shouldn't say weight, I have a mass of 70 kilograms. I have a mass of 70 kilograms.
- Weight is actually a force, but we'll talk about that, 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, times my mass, which is 70 kilograms. And let me get my handy T85 calculator
- out to figure this out. So I get 9.8 times 70. That gives me...686. So this is equal to 686
- kilogram meters per second squared. OR this is the exact same thing as this thing right over here.
- This IS the definition of a Newton. So this is a newton, which is appropriately named for
- the guy that is the Father of All Classical Physics.
- So my weight on Earth, which is the same thing as the force that Earth is pulling down on me,
- or that the gravitational attraction between the Earth and me is 686 newtons. Now I will ask you
- an interesting question.
- So here is Earth,
- and I am not even a speck of a speck on Earth, but say for simplicity let's say
- this is me, I'm hanging out in the Indian Ocean some place. So that is me.
- And we already know that Earth is pulling down on me with a force of 686 newtons.
- Now my question to you is, "Am I pulling on the Earth with any force? And am I pulling on the Earth with
- a larger or small force that is pulling on me?"
- And your gut or your knee-jerk reaction might be: Earth is so huge, Sal is so tiny.
- Clearly the Earth must be pulling with a greater force than Sal is pulling on the Earth.
- Unfortunately that is NOT the case.
- That I am. So the Earth is pulling on Sal with the force of 686 Newtons and Sal is also pulling on the
- Earth with a 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 I have a building over here, and 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 that the Earth is accelerating up to you. Wouldn't we notice that, every time someone
- were to jump off a building, that the Earth starting accelerating in a major way. And the way to think
- about that is that the force is the SAME. And we'll talk about that in other videos.
- Force is equal to mass times acceleration. So when we are talking about 686 Newtons, in terms of
- the force of Earth, the gravitational attraction between myself and Earth. And this is going to be
- 68 kilograms, then this provides a pretty good acceleration on me. So in this case, if you
- solve for A... Solve for A over here. You're going to get 9.8 meters per second squared. Now, if you
- do the same thing for Earth... I already told you that we are pulling on each other with the same
- force, 686 Newtons. Now if you want to find out how much is the Earth accelerating... That force
- you're going to get a... I'm not even going to put it here. You're going to put a huge number
- in here. Huge number times the acceleration of Earth towards me. And since this is such a huge number,
- very very very large number, this is going to be an immeasurably small number, super small number.
- And frankly it's probably averaged out by the acceleration of Earth, or the force of gravity
- 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, it would be negligible, you wouldn't even notice the acceleration of Earth
- towards me. But you would notice the acceleration of me towards Earth because of our vastly
- different masses. Even though we have the same force of attraction.