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Gravity and Falling Objects · Acedra
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Gravity and Falling Objects
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0:00
Hey, Vsauce. Michael here.
0:03
Down here.
0:05
But which way is down? And how much does down weigh? Well, down weighs about a 100th of a gram per cubic centimeter. It is light and airy, which makes it a great source of insulation and buoyancy for water birds. But if you let go of down... It falls down. So that's which way down is. It's the direction gravity is pulling everything in. Now, for someone on the other side of the Earth, my down is their up. But where are falling things going? Why do things fall?
0:38
Are they being pushed, or pulled, or is it because of time travel? First things first: let's turn the Sun into a black hole. We can do that using Universe Sandbox 2, this simulator will blow your mind. I love it. In fact, I love it so much I put a code to get the game for free in the current Curiosity Box. If you're not subscribed to the box yet, you are missing out! Okay, look, for the purposes of this video, we want the Solar System.
1:06
And here it is. Notice that everything's moving pretty quickly around the Sun. That's because we currently have the game set so that every second that passes for us, is 14 days, almost, in the game. If I change this to one second, we're looking at the Solar System in real time. You'll notice that it almost looks like it's frozen. Even though the earth is traveling around the Sun at about 30 km/s, it barely appears to be moving. That is how vast space is. Anyway, let's go back to 14 days
1:35
I like that motion. Now look at the Sun It is not, currently, a black hole, but we can change that. What we need to do is compress the Sun. So let's lock its mass so that it doesn't change while we make its radius smaller. Let's make its radius as small as we can. And, oh, where'd it go? Well it's still there, it's just become a black hole. Pretty spooky, but now, let's look at the rest of the Solar System. Alright, zooming out and- huh. Nothing's... changed. I mean something's changed.
2:11
It's colder and darker, but nothing's flying off into space or getting sucked in. You see, by shrinking the Sun, we didn't change the direction of down for the planets. They're always being pulled by gravity towards its middle and making it smaller didn't move where the middle was. But also, the strength of that force pulling them to the middle of the sun stayed the same. That gives us a clue as to what down is. The clue is the other thing we didn't change: mass.
2:40
Mass is a measure of how hard it is to accelerate something; to change its motion. Now right now, these two balls have zero motion relative to me. Slapping around this hollow plastic ball
2:54
is pretty easy, but doing the same to this solid steel ball
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is a lot harder. Now gravity and weight have nothing to do with this. Gravity acts downward, not against my horizontal slapping. Of course, gravity does contribute to friction, but friction works against me when I start moving the ball, but works with me when I stop the ball. And the steel ball is harder to stop than the plastic ball. The difference is mass. The steel ball is more massive It's more resistant to having its motion changed.
3:30
Mass is an intrinsic property; it does not depend on what's around or change from place to place. It can sometimes be thought of as the amount of matter something has. Your mass is the same regardless of where you are. On the moon, on earth, in the middle of intergalactic space floating around. But all of this said, mass does seem to care about what's around. Mass loves company. Things with mass and/or energy are attracted together by a force that we call gravity.
4:03
The feeling of gravity is just you and the earth being attracted to one another. Now every portion of an object with mass attracts other portions towards it. The average of all this pulling is an attraction between centers of mass. Giant things like Earth exert an obvious pull, but everything does. Even a baseball. These two baseballs are attracted together by their own gravities.
4:36
Except their masses are so small, the force is minuscule, and it can't overcome friction or push air out of the way. They're never gonna come together But if you put two baseballs one meter apart in the middle of empty space where no other forces could act on them They would literally fall together and collide. It would take three days to happen, but it would.
5:01
Isaac Newton found that the strength of the force bringing two things together is equal to the product of their masses Divided by the distance between their centers of mass squared times big G, the gravitational constant. If you make one of two objects more massive, or move them closer together, the force will be stronger and this force of attraction is what we call weight So mass is intrinsic, whereas weight depends on what's around.
5:31
Now, a weird thing happens when you weigh yourself on most scales. Weight is a force, but scales display pounds or kilograms, which are units of mass. What's going on is that a scale is activated by a force. Any force. It doesn't have to be caused by gravity. The scale then displays what amount of mass near the surface of the earth would be attracted to the earth with the force it's detecting.
5:57
Now since scales tend to be used on the surface of the earth, by people, on which the only force acting is gravity, they tend to not be very far off. But they can be easily tricked, and they further lead to the confusion between mass and weight.
6:12
Notice that weight is mutual. You are pulled down by earth with the same force that you pull up on earth. According to a scale, I weigh 180 pounds on earth..
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And the earth weighs 180 pounds on me.
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But because the Earth's mass is so much greater than my own, and because the more massive something is, the more it resists being moved, our equal and opposite weight forces accelerate me a lot more than the earth. If you drop a pencil from a height of 6 feet, the pencil doesn't just fall to the earth. More precisely, they both come together. They're attracted to each other by equal forces but the same force moves the pencil a
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lot more than the earth. When you let go of the pencil, the earth is literally pulled up to the pencil by the pencil's own gravity, a distance equal to about 9 trillionths the width of a proton. That same force moves the pencil the remaining distance, which is still pretty much six feet.
7:26
At the height of the International Space Station's orbit, you and earth are attracted about 10% less than when you're on the surface; about eight point eight times your mass, but not zero. For this reason, weightless astronauts in zero gravity are neither weightless, nor in zero gravity. Their weight force fails to bring them and earth together, because they move horizontally so quickly that they fall just as fast as Earth's surface curves away from them.
7:58
And even though they're experiencing 90 percent of the gravity you and I are feeling right now, (That's why they don't just fly away) There are no forces, called g-forces, to resist their weight, since everything around them is falling too. It's resistance to your weight force, stress, deformation, that is needed for you to feel weight. What astronauts in orbit actually lack is apparent weight. Likewise, a helium balloon has weight.
8:29
I mean, it's made out of matter it clearly has mass, so it's attracted to the earth. Let's try to measure its weight force.
8:43
Okay, it has negative apparent weight. That's because its attraction to the earth is weaker than the buoyant forces from the air around it that push it up. Now, while it moves up, It pushes air molecules down, but they transfer that force widely. Not just directly down onto the scale. Buoyant forces are caused by the fact that whenever you are immersed in a fluid like water or air, molecules lower down are at greater pressure. They're being pressed by the weight of all the molecules
9:13
above them and are closer to earth, so they're pulled to it with a stronger force. Now having greater pressure means they pack a bigger punch when they collide with things. So, horizontally, those collisions cancel out, but vertically, the stronger collisions from below win out, providing lift, a buoyant force. This even happens on your own body. Across its surface area air lifts you with the force of about one
9:38
Newton, which is equal to the weight force of an apple. So if you weighed yourself in a vacuum you would weigh about this much more. But that's not all Earth's spin causes it to bulge at the equator so the closer you are to it The further you are from Earth's center of mass and the less your actual gravitational weight will be down is Always changing, I mean where is Earth's center of mass? It would always be the same as Earth's geometric middle if Earth's
10:11
composition was uniform, but earth contains pockets of massive rock at different depths water mountains It's got moving changing insides and air and seasonal ice and though they're far away Gravity extends forever from everything so the moon the Sun the planets all of them pull on you negligibly, But truly. You weigh about a millionth of your weight less when the moon is directly above you This chunky shifting balance of material on earth and ever where else in the universe means that down is
10:47
always changing on top of that Earth's spin Skews what you consider the direction of down away from its center of mass because the push you get from Earth's spin Seems to slightly lift you reducing your apparent weight and bending down towards the equator The net result is an apparent weight reduction at the equator of about half of a percent if a scale guesses your mass must be 200 pounds at the poles it'll guess that you're 199 at the equator. The 9.8
11:18
Multiplier used so often in physics is calculated based on how these factors affect someone at 45 degrees latitude all of these influences on the direction of down result in a total vertical deflection. That's only ever at most a few arc seconds anywhere on earth That's not enough to be felt, but changes in direction and strength can be used to study the shape of the seafloor Determine what's under you or even help you discover ancient buried rooms?
11:48
Point is all of our downs aren't a bunch of radially symmetric lines Down is an uncombed mess. Now since solids don't flow they can have shapes that don't pay much mind to this but water can Flow so ignoring influences like wind and tides the surface of oceans and lakes and puddles is always perpendicular To down if water could pass through land, or if earth were submerged in water Gravity would be the same everywhere along its bumpy surface
12:21
Such a surface is called a geoid and can be drawn at any altitude If you wanted to build a table that completely enclosed the earth it would have to have rolling undulation Z' nearly 100 meters at some points in order to be Level so that a ball placed anywhere on it wouldn't roll Here is Earth's G. I exaggerated a thousand times You'd weigh about a hundredth of a percent less a few grams here? Then you would say here where gravity is a bit stronger point is the strength and direction
12:54
Down is variable by location and changes over time So down is a fluctuating vector easy enough except? Why should matter attract matter in the first place?
13:09
Isaac Newton was able to describe attraction, but not explain it humanity got closer however when Albert Einstein introduced his general theory of relativity
13:20
Einstein thought a lot about the fact that everything falls to the ground At the same rate no matter How massive something is when dropped it will accelerate towards the earth down gaining about 9.8 Meters per second for every second that it falls. That means that a hammer That's quite massive, and a not so massive feather when dropped from the same height will hit the ground at the same time
13:47
Okay, what just happened... was an "air"ror. awkward laugh In order to fall through air a thing has to push air out of the way But if it has a large surface area and a low weight force it will have a lot of air to move But won't be able to move that air very quickly. In a vacuum, things do fall at the same rate regardless Of mass. This was famously demonstrated by Apollo 15 commander David Scott on the moon
14:14
And I'll, uh, drop the two of them here and hopefully, they'll hit the ground at the same time.
14:20
How 'bout that? That's weird right? I mean if a more massive object is pulled with a greater force Shouldn't it fall faster? Well Newton's explanation was simple: Larger masses are attracted with greater forces But will also require more force to be accelerated the same as a less massive thing Something a hundred times more massive might require a hundred times the force, but it will be pulled by gravity 100 times more so everything falls to earth at the same rate What a fun coincidence right?
14:56
Maybe not Einstein realized that there's another way for things to appear to fall together
15:03
of their masses Imagine a feather and a hammer floating in space in a room if the room is suddenly accelerated up at 9.8 M/s^2 the feather and the hammer will hit the floor at the same time furthermore whether it's the room coming up to meet them or gravity being suddenly switched on Neither object will feel any force pushing them There's no way to tell which of these happen. This is Einstein's famous equivalence principle He once admitted that his greatest thought ever was that of a man
15:40
falling off of a roof While falling the man would not feel any forces on him even though. He's speeding up freefall is Indistinguishable from floating alone in space from having no forces on you from not being moved What if gravity isn't a force at all what if things fall not because they're being pushed or pulled But because they're not being pushed or pull To see how this could be we need to talk about straight lines
16:13
What I have here is a retractable ID badge holder This is a great way to test for straight paths Because the string is always kept taut the card I have behind has two lines drawn on it And if while I pull the string out it always stays between those two lines I will know that I never turned While I pulled it because any turn will translate into a different angle between the lines on the card and the string
16:40
Now if I put two of these on a flat table and pull them out, always ensuring that they go straight ahead They will never meet. They will be forever parallel, but now let's put them on a sphere a curved surface Again, I pull both strings forward making sure that they always are pulled out straight. No turning Wait they came together
17:06
Well, they didn't turn look Maybe there's some kind of weird force that pulled my hands together and just like gravity. I didn't feel it, but it happened No What happened was not the result of a force it was just a natural result of? Curvature you might be thinking wait a second are those really straight lines. I mean they don't look that straight to me Also, what if they've just moved along latitude lines then they've never come together and those look pretty darn straight
17:38
But they're not a straight line never turns and although latitude lines look straight at first glance following one requires Turning to find straight line paths on surfaces whether they're flat like this or curved I love the ribbon test. Now you can use an actual ribbon But I have found that a strip of paper works. Even better. Let's take a look at this path right here It's straight at first, but then it curves now if two people are traveling along this curve
18:10
And they want to stay together the person on the inside will have to cover a shorter distance than the person on the outside Since both sides of this strip of paper cannot change their lengths They'll help us find a straight path if the strip of paper can lay flat We'll know that we have found a straight line and as you can see The strip can lay flat and follow the straight part of this path But when it comes to the curve in order to follow the path now
18:36
The strip well it has too much material on the inside and that material Bunches up and leaves the plane therefore we know that this part of the path is not straight
18:47
Let's use the ribbon test to find straight lines on the surface of a cone Well from the looks of it aligned directly from the base to the tip seems like it would be straight and sure enough Yeah, the ribbon lays flat on that path, but what about a ring around the cone? Nope doesn't work shorter distances around nearer the tip of the cone mean that there's too much ribbon up at the top So doesn't lay flat
19:13
Let's see what else is there though besides this well if I start here and just allow the ribbon
19:20
to lay flat Huh I get a little curvy looking shape like this I say curvy looking because while to someone say at the base this path might seem to go up Slow down change direction and then fall down faster and faster since a ribbon on such a path is flat It's actually for inhabitants on the cones surface Perfectly straight if we trace the ribbons path on to the cone We can see this clearly because a cone can be flattened a straight line on a curved surface is called a geodesic
19:56
Here is a geodesic on a sphere the Equator is one Here's another a line of latitude is not a geodesic It's not a straight line to see why let's try to follow it with the ribbon you Know what I have to keep kind of lifting it Yeah, see distances around the sphere becomes shorter as we go up So there's too much material on the ribbon up here and it leaves the surface this path contains turns and in order to turn a Force has to act on you if no forces
20:27
Did this is the path you would take notice that the ribbon begins moving due east, but then falls south Falls Einstein realized that curvature could cause things to be seemingly attracted to one another Without needing to invent the existence of forces like gravity but attraction only happens if things move along the surface if they stay still they Well, they don't come together so for something at rest. How does falling begin?
21:02
I mean the thing has to move in this direction, but it's at rest right well Yes But it's only at rest in space and that's not the whole story up down Forward backward and left-right are all you need to describe where an event occur but a complete description will also need to describe When together these four dimensions form the setting in which everything in our universe happens
21:30
Space-time Since we can talk about a falling pencil using just one spatial dimension up and down we can use a piece of paper to model Space-time for it. Okay, so we've got up and down, but we have to add another direction the pencil moves in time Now if no forces act on the pencil it won't move through space It will only get older and as you can see if all it does is get older It won't fall if space-time was flat when I let go of the pencil
22:00
it wouldn't go anywhere, but now let's allow the earth which is massive to manipulate space-time into say a cone Now with no forces acting on it every part of the pencil follows a straight line But on a cone as we saw earlier such a path will look like this it will fall This is because distances around the cone are shorter higher up Time runs faster further from a massive object, but to go straight Not turn every part of the pencil must cover an equal distance in space-time like this
22:36
Only when the pencil hits the earth does the repulsion of their mutual electrons provide a force pushing the pencil off a geodesic For the earth time is a series of slices from this evolution the pencils force-free Geodesic is why it falls not a push or pull just the pencils natural tendency to follow a straight line Until something acts on it now. We only used one dimension of space and one of time because
23:04
Visualizing our universes three of space and one of time would take us beyond the limits of what could be shown on paper or screens but math Can take us there General relativity allows us to calculate how much mass and energy Curved space-time and has been used to explain things that Newton's older theory of falling as the result of Forces couldn't like anomalies in the orbit of mercury which orbits nearest the Sun and is therefore most affected by the sun's grip on
23:34
space-time many other experiments have confirmed general relativity's picture of the universe fitting the conclusion that There is no Gravity there's just Space-time its curvature and a us in it. As John Wheeler famously put it Space-time grips mass telling it how to move mass grips space-time telling it how to curve? Relative to the earth we don't move very fast even jet airplanes move negligibly close to the speed of light So relative to earth we move almost
24:10
Exclusively through time as such we are more affected by the way time is curved by mass Than how space is curved? This has led many to claim that for the most part you feel as though you're being pushed into the ground Not because of a force called gravity But because time is moving faster for your head than for your feet down is Relative and always changing, but it exists because of and is always in the direction of slower time Bertrand Russell called this the law of cosmic laziness
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Everything is naturally steered towards where time is slowest we call this falling going down So you don't have to keep anything on the down-low time will take care of that for you and
25:04
and as always Thanks for watching
25:19
Remember that you can support Vsauce and Alzheimer's research by subscribing to the Vsauce curiosity box the current one comes with a code to get a free copy of universe sandbox 2 Which is amazing and a whole host of other science toys and tools picked by myself Jake and Kevin I love it all so I hope to see you at brain candy live. We are coming to many many cities very soon Hopefully one near you by going to the show you can see Adam
25:45
And I doing things that will you may not have seen us do before we also explore the science and common misconceptions behind all things
25:55
Err. Maybe have said too much. Maybe not I hope to see you there and as always thanks for watching
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