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