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Slow sock on Lubricon VI

What would happen to a slowly moving frozen sock on a frictionless planet? Explore the intriguing world of Lubricon-VI, a fictional planet with zero friction and no atmosphere. This video delves into the forces acting on a frozen sock sliding on its surface. It highlights the absence of tangential forces, ensuring the sock's eternal journey at a constant speed. Created by Sal Khan.

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Video transcript

This is a picture of the planet Lubricon-VI. And Lubricon-VI is a very special planet because it's made up of a yet to be discovered element called Lubrica. And Lubrica is special because if anything glides across the surface of Lubrica, it will experience absolutely no friction. So if this right over here is a sheet of Lubrica-- we're looking at it from the side. And if we have a brick on top of it, maybe gliding on top of it like that, it experiences absolutely no friction. Now, the other things we know about Lubricon-VI is it's drifting in deep space and it does not have an atmosphere. In fact, it is a complete vacuum outside of it. It's in such deep space, such a remote part of space, that there aren't even a few hydrogen atoms right over here. It is a complete, absolute vacuum. And it's also an ancient planet. The star that it used to orbit around has long since died away. So it's just this lonely planet drifting in deep space without an atmosphere. The other thing we know about Lubricon-VI is that it is a perfect sphere. It is a perfect, perfect sphere. Now, my question to you. For some bizarre reason there happens to be, on the surface of Lubricon-VI-- so this right over here is the surface of Lubricon-VI. There happens to be a sock that is frozen in a block of ice. So this is my sock and its frozen in this block of ice. And it happens to be traveling at 1 kilometer per hour in that direction. If we were to look at it from this kind of macro scale when we're looking at the planet, let's say then that is the frozen sock, and it is traveling along the equator. It is traveling along the equator of Lubricon-VI. So my question to you, given all of the assumptions we made that it has absolutely no atmosphere, it's a perfect sphere, and Lubrica has absolutely no friction regardless of what's traveling on top of it-- what will happen to this frozen sock over time? To answer that question, we need to think about all of the forces that are acting on this, I guess, frozen block of ice and sock. And first of all, let's think about these forces that are acting in the radial direction, inward or outward, of the center of the planet. Well, this planet has a mass. And so you have an inward force towards the planet's center of mass. And so you have the force of gravity acting on this block going radially inward to the center of the planet. So I'll draw it like this. So we have our force of gravity. We have our force of gravity going radially inward, just like that. But then we know that the block is not just spiraling towards the center of the earth. We have the surface here. It's not going to go through the surface of Lubrica. We can also assume that Lubrica is a very, very, very strong material. And so you also have a normal force. You also have a normal force that is keeping the block from spiraling towards the center of the earth. So this is a normal force. And one thing we'll think about now, and we'll address it directly in another tutorial, is whether this normal force is equal to the force of gravity. We'll think about that in a future video. But these are all the forces that are acting in the radial direction, either inward towards the center of the planet or outward. But if we think about in the tangential direction, along the surface of the planet, there are no net forces. And because there are no net forces in this tangential direction right over here, this block will not either accelerate nor decelerate. There is no air friction. Or I should say air resistance, which is really just friction with the particles if you had an atmosphere. It's a complete vacuum, so there's nothing there. There is no friction with the surface of the planet. So there's no friction there, which could have been a force in the tangential direction. So there's absolutely no forces in the tangential direction. So this block of ice will actually continue to travel at one kilometer per hour for all of eternity. So it'll just continue to do it given the assumptions that we've just made.