Inclined planes and friction
Force of friction keeping velocity constant
I want to make a quick clarification to the last video, and then think about what's friction up to when the block is actually moving. So in the last video, we started off with the block being stationary. We knew that the parallel component of the force of gravity on that block was 49 newtons downwards, down the slope. And when the block was stationary, we said there must be an offsetting force. And we said that's the force of friction, and it must be 49 newtons upwards. And so they completely net out in that direction. Now, what we said is we're going to keep applying a little bit more force until we can budge this block to start accelerating downwards. And I said I kept applying a little bit more force, a little bit more force, until I get to 1 newton, and then the block started to budge. So at that point, when it started to budge, I'm applying this 1 newton over here, right over here. There was already 49 newtons of force, or the component of gravity, in this direction. So combined, we're providing 50 newtons to just start budging it, to just overcome the force of friction. The one thing I want to clarify here is this whole time the force of friction was not constant at 49 newtons. When I wasn't messing with this block, and the parallel component of the force was 49 newtons, then the force of friction was 49 newtons. When I started to press on it a little bit, apply a little bit of force, maybe I applied a tenth of a newton on top of that, then the force of friction was 49 and 1/10 newton, because it was still providing enough force so that this block was not moving. Then maybe I applied half a newton. And so the total force in the downward direction would have been 49 and 1/2 newtons. But if it still was not moving, then the force of friction was still completely overcoming it. So the force of friction, at that point, must have been 49 and 1/2 newtons, all the way up to the combined force in the downward direction being 49.999999 newtons. And then the force of friction was still 49.99999 newtons, all the way until I hit 50 newtons and then the block started to budge, which tells us that the force of friction now, all of a sudden, or at least the force of static friction all of a sudden now couldn't keep up and it started to accelerate downwards. So in that static scenario, the force of friction changed as I applied more or less force in this downward direction. Now with that out of the way, let's take a different scenario. Let me just redraw that same block, just since all of this is getting messy. So we have the same block, and as we said in the last video, we're now assuming that this is wood on wood. So this is the wedge. This is the block right over here. We know that the component of gravity that is parallel to the plane right there is 49 newtons. We know that this is 49 newtons. We know the component of gravity that is perpendicular to the plane-- we figured out this two videos ago-- is 49 square roots of 3 newtons. We know that this block is not accelerating in this normal direction, so there must be some force counteracting gravity in that direction. And that's the normal force of the wedge on the block. So that is going in that direction at 49 square roots of 3 newtons. And now instead of assuming that this block is stationary, let's assume that it's moving with a constant velocity. So now we're dealing with-- let me do that in a different color. So now we're dealing with a scenario where the block has a constant velocity. And for the sake of this video, we'll assume that that constant velocity is downward. And so the constant velocity, v, is equal to-- I don't know. Let's say it is 5 meters per second down the wedge, or down the ramp. Or I guess we could say in the direction that is parallel to the surface of the ramp. So it's in this direction right over here. So that's the constant velocity. So what are all the forces at play? And be very careful here. There might be a temptation that says, OK, there's a net force here. We're moving. So maybe that's the net force that's causing the move. But remember, this is super important. This is Newton's first law. If you have a net force, if you have an unbalanced force, it will cause it to accelerate. And we are not accelerating here. We have a constant velocity. We are not accelerating here. So if you're not accelerating in that direction, then that means that the force in that direction must be balanced. So there must be some force acting in the exactly opposite direction that keeps this thing from accelerating downwards. And so it must be exactly 49 newtons in the opposite direction. And as you can imagine, this is the force of friction. This right over here is the force of friction. And the difference between this video and the last video is last time friction was static. Even at 49 newtons, the box was stationary. You had to keep nudging until you get to 50 newtons, and then it started moving. Here we're just jumping into this picture where we just see a box that's moving down the slope at 5 meters per second. So we don't know how much force it took to overcome static friction. But we do know that there is some force of friction that is keeping this box from accelerating, that's keeping it at a constant velocity, that is completely negating the parallel component of the force of gravity, parallel to the surface of this plane. So given this, let's calculate another coefficient of friction. But this is going to be the coefficient of kinetic friction, because now we are moving down the block. And I'll do a video on why sometimes a coefficient of static friction can be different than the coefficient of kinetic friction. So the coefficient of kinetic friction-- we'll write it. So this is the Greek letter mu, and we put this k here for kinetic, or we can kind of say moving friction. It's going to be equal to the force of friction, or I should say the magnitude of the force of friction over the normal force. I should say the magnitude of the normal force. And you can derive this experimentally. One, if you just observe this whole thing going on and you knew the mass of the block, so you knew this component of gravity that's going in this direction. If you knew this angle was 30 degrees from the last situation, you could figure out this coefficient of kinetic friction. And what's cool about this is this is in general going to be true for any two materials that are like this. So maybe this is a certain type of wood on a certain type of wood, or a certain type of sandpaper on a certain type of sandpaper-- whatever you're talking about. And then you can use that to make predictions if the incline was different, or if the mass was different, or even if you were on a different planet, or if someone was pressing down on this block. That would change the normal force. So given this right here, let's figure out-- for the sake of doing it-- the coefficient of kinetic friction here. The force of friction here, completely offsetting the parallel force of gravity parallel to the surface, is 49 newtons. And the normal force here, the force of contact between these two things, this block and this wedge, is 49 square roots of 3 newtons. So we get 1 over the square root of 3. And let me get the calculator out to get an actual number here. So we have 1 divided by the square root of 3, which gives us 0.5-- I'll just round. 0.58. It is equal to 0.58. And there's no units here, because the units cancel out. It's a unit-less measurement. Now the interesting thing here is that the way I've set up this problem, the coefficient of kinetic friction is lower, if we assume the same materials, than the coefficient of static friction was. And for some materials, they might not be that different. But for other materials, the kinetic friction can be lower than static friction. You never see a situation where the coefficient of static friction-- at least that I know of-- is lower than kinetic friction. But you do see situations where the coefficient of kinetic friction is lower than the coefficient of static friction. Once something is moving, for some reason-- and we'll theorize why that might be-- friction is a little less potent than when something is stationary. So we can say this generally, that the coefficient of kinetic friction is less than or equal to the coefficient of static friction. It's a little bit easier, or friction provides a little less than or equal to the force when something's moving than when something is stationary. So I'll think about that a little bit deeper in the next video.