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Normal forces on Lubricon VI

Whether the normal force balances the force of gravity for a frozen sock or banana. Created by Sal Khan.

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  • leaf grey style avatar for user Aditya
    Isn't the force of gravity equal to the force normal in both cases?

    Let's say that the moving block did have the same magnitude for both forces in the y direction, if it's true that the block would just leave the surface, then the block would no longer have a normal force. So wouldn't the force of gravity pull it back down to the surface?

    I agree that the object does not have a net force of 0 because the initial force push (the one that set it into motion) is continuing to act on the object due to the frictionless nature of lubricon.

    But why does the force normal not equal the force of gravity?
    (51 votes)
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    • leaf green style avatar for user ChristopherTyndall
      You're correct in thinking the block would no longer have a normal force and gravity would pull it back down if it left the surface. But the block doesn't have to entirely leave the surface for the normal force to decrease. It can decrease at a very small scale since the surface is slightly curved and the block keeps wanting to continue in a straight path and leave the surface. It just isn't quite as dramatic as the block flying off the surface and being pulled back down, but more subtle like the feeling you get when driving a car over a rolling hill. In that case, the normal force on you decreases, and there is a net force pulling you down the hill and you can feel it in your stomach. The net force on the block is at a much smaller scale than this because the curvature is that of the entire planet (and not just a hill).

      As far as the initial force goes, after the force has been applied to get the object moving, it goes away. Afterwards, the only forces involved are from gravity and the normal force.
      (64 votes)
  • male robot hal style avatar for user Conor McKenzie
    At , he says that the banana has no tangential velocity, and that the sock will retain it's velocity (which, actually, should be speed, since its direction changes as it orbits). Would the banana and the sock not have a gravitational effect on each other, causing them both to accelerate towards each other?
    (68 votes)
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    • piceratops ultimate style avatar for user Jacob R
      They would have an acceleration of of G*m1*m2/d^2/m1 and G*m1*m2/d^2/m2 or a total speed towards each other of (G*m1*m2/d^2/m1 + G*m1*m2/d^2/m2) * t
      G = gravitational constant = 6.67*10^-11

      This means that if the distance between the two objects was 1 km (d = 1000), m1 = 1 kg and m2 = 2 kg, the speed after 10^8 years would be 0.421m/s

      I might be totally off though :)
      (13 votes)
  • leafers ultimate style avatar for user BorkusMalorkus5
    Why can't a non-rotating planet have an equator?
    (16 votes)
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  • leafers sapling style avatar for user Peter Collingridge
    If the planet were rotating, what effect would that have on either block? Would it make a difference if the sock were going around the equator or the poles?
    (18 votes)
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    • leafers ultimate style avatar for user Marco Merlini
      No effect, since there is no friction. However, there is the problem of the relative speed. When we say moving at one km per hour in the East, is that relative to the planet's surface or to an observer in space? If it were relative to the surface, and the planet was rotating at 2 km per hour to the East (measured at the surface), then the object would be moving 3 km per hour to the East.

      tldr:
      No effect
      (24 votes)
  • purple pi purple style avatar for user northernexposurelanai
    I"m completely confused. The sock is traveling at a constant velocity, not accelerating. Why is there any tangential force?
    (11 votes)
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    • blobby green style avatar for user fckutwtr
      The sock's speed is constant, but it's velocity isn't.
      Yes, it's moving at 1km/h, but it's direction is constantly changing. For the sock to circle around the planet (which, in this case, would be the same as orbit around it), it needs a centripetal acceleration curving it's movement inwards, keeping it from flying away.
      If it's velocity were constant, the sock would move tangentially away from Lubricon VI and into deep space.
      (30 votes)
  • starky sapling style avatar for user Sprintingwildebeast
    How is there gravity? Doesn't the planet need to be rotating inorder to be able to have a gravitaional force? Or is this just theoretical gravity?
    (14 votes)
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    • starky tree style avatar for user Moksha Prasunadh
      The planet doesn't have to be rotating to have gravitational force.Gravitational force is the force between any 2 objects in the universe.Anything in this universe that has mass, would bend space, which results in gravity.Gravity acts between any 2 bodies in the universe (including you and me, but its magnitude would be very very small).So, a planet doesn't have to be rotating to have gravity, as long as it has mass, it would have gravity
      (5 votes)
  • leafers ultimate style avatar for user Joseph Frimpong
    If the frozen sock block's movement comes Fg being greater than Fn, why does the sock block move around the planet instead of sinking into the center of the planet (the direction of the net force unbalance.
    (5 votes)
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    • blobby green style avatar for user Teacher Mackenzie (UK)
      The movement of the sock is not caused by the force Fg.
      That motion has been caused by some other means that we have not been told about. We do know that it was a force with a component TANGENTIAL to the surface of the planet.
      The sock is now travelling with constant speed around the friction-less planet

      He is saying that Fg must be greater than Fn because there is a centripetal acceleration (that the banana does NOT have) simply keeping the sock moving in a circular path and nothing else and that Fg is providing this centripetal force

      Hope that helps

      IM
      (4 votes)
  • leaf green style avatar for user Coco
    Is the force of gravity 'round'? That is, would an object with mass, hence gravity, get formed into a sphere? Why not a square planet? I assume the roundness is due to rotation, and a non rotating planet might lose its roundness....
    (3 votes)
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    • leafers ultimate style avatar for user Massimo Boscherini
      Gravity tends to shape large objects into a spherical shape because it is a central force. A point mass produces a gravitational field that extends radially from the point, and this type of field will try to redistribute all mass into a spherical shape. Keep in mind, though, that this is true if the object has enough mass. Many asteroids and some moons are not massive enough to have a spherical shape, and they are just lumps of rock. For instance, think about Phobos and Deimos, the moons of Mars.
      (7 votes)
  • spunky sam blue style avatar for user Nemath Ahmed
    Is gravitational force not equal to normal force even on earth?And why do they dont cancel each other in case of sock?
    (1 vote)
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  • marcimus pink style avatar for user shravaniongole
    1)How |Fg|>|Fn| if it so the frozen sock should accelerate downwards but it's not happening? But, there is an horizontal acceleration of the frozen sock so it moves horizontally right then how |Fg|>|Fn|(these are vertical forces right)
    (1 vote)
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Video transcript

Let's continue with our study of the planet Lubricon VI. Now the one thing I did not tell you in the last video is that Lubricon VI is not rotating at all. And because it's not rotating, it can really not have an equator. So when we talked about in the path of this frozen sock, instead of saying it's traveling across an equator, I should say it's traveling along a great circle. If you assume that earth is a sphere-- and it's not a perfect sphere-- but if you assume it's a sphere, our equator would be a perfect sphere. But in order to have an equator, you need to have some rotation. This right over here, we'll just say it's traveling along the largest possible circle that it can travel along. It's traveling along one of the great circles of this sphere, this block of sock right over there. And now that we know it's not rotating, I want to enter another thought experiment. Because this little frozen block of sock is not the only thing that's on the surface of Lubricon VI. Over here-- we were viewing it at a distance-- but right over there, if we were to zoom in, you would see sitting on the surface of Lubricon VI-- so once again, that's the surface-- is a frozen banana. So this right over here is a block of ice. And in that block of ice we have a banana. It's a frozen banana. So that's my best attempt at drawing our banana. And this relative to the surface of Lubricon VI is absolutely stationary. It has absolutely no tangential velocity like this block had and will continue to have for all eternity. This has absolutely no tangential velocity. And so my question for you, if we think about what are the forces acting on this? Well, we have the force of gravity towards the center of Lubricon VI. So we have the force of gravity. And I'm drawing all the forces from the center of mass of this block of banana. So once again, let me draw that same color. We have the force of gravity acting radially inward. And then we know that this banana is not plummeting straight into the center of the Earth. There must be some other force that is keeping it stationary. And that force is the force of the surface of Lubricon VI on the banana or on this block that's keeping it from plunging towards the center of the planet. So that, in this case, is the normal force. And my question to you is, are these two things equal in the case of the banana? Well, as far as we can tell, this banana is completely at rest. This planet right over here, at least relative to the planet, this planet right here has absolutely no rotation. And this banana has no relative motion towards the planet. It is not accelerating in absolutely any direction. And if it's not accelerating in any direction, the net forces on it in any dimension must all or must be 0, or all of the forces must cancel out with each other. So in the case of this banana, the normal force exactly cancels out the force of gravity. These two things, the normal force is exactly equal to the inward force of gravity. Or I guess we should say that they add to 0. They're going in opposite directions. So I should say the normal force plus the force of gravity are going to be equal 0. They have the same exact magnitude. They're going in opposite directions. So when you add them together, they are going to cancel out. Now, with that little thought experiment out of the way, let's return to the frozen sock. The frozen sock, as we already learned, is orbiting around this planet at a altitude of 0 for all eternity at 1 kilometer per hour. And we know that the force of gravity is acting on it towards the center of the planet and there is a normal force that's keeping it from plummeting, from spiraling towards the center of the planet. But my question to you is, in the case of the frozen sock right over here, are these two forces equal like they are for the banana? So in the case of the frozen sock, the traveling, orbiting sock, if these two forces had the same magnitude, but just going in opposite directions the way we've drawn it right over here, it would completely cancel out. And then we would have no net force. So let me make it clear. If the normal force plus the force of gravity canceled out with each other, if this equalled 0, then we would have absolutely no net force and the object would not accelerate in any direction. An object in motion will stay in motion. So this one right over here, if it had no net force acting on it, it would not stay on the surface of the planet. It would just travel in a straight line, in a tangential line from where it happens to be at this moment forever. So if it was right over here-- I know this isn't the path, it would just keep traveling forever off the surface of the planet. We know that clearly is not what's happening. It is orbiting around the planet. It has a circular path. And since it has a circular path-- so if I were to draw a cross-section of its-- if I were to look at its path from the side, it has a circular path like that. It is going like that. It is constantly being accelerated inward. There is some centripetal acceleration going on, inward acceleration. So in order for that inward acceleration to be going on, there must be some net inward force. So in this situation, in the situation for the stationary banana, these two guys cancelled each other out. But for the case of the moving frozen sock, the sock that is orbiting for all of eternity, it is in orbit. It has a circular path. So there are centripetal motion. There is some net inward force going on here. So In this situation, the magnitude of the force of gravity is going to be greater than the magnitude of the normal force. So we don't have this situation. In that situation, you wouldn't orbit. We have the situation where you do have some net centripetal force. The force of gravity, the magnitude of it, is slightly larger than the magnitude of the normal force. And an interesting thing to think about, and we might address it in a future tutorial, is what would happen if this started going faster and faster and faster, if the frozen sock were to accelerate. What then? How would the relationship between these two things potentially change, if they change at all?