Guys, in this video, we're going to talk a little bit more closely about a force that we've seen before in our free body diagrams, the force of friction. And specifically, we're going to talk about kinetic friction. In a later video, we'll talk about the other kind of friction. So let's get started. Kinetic friction is written with the symbol \( f_k \), \( k \) for kinetic. And basically, what it is, it's a resisting force that happens whenever you have two rough surfaces that are rubbing or slipping or sliding past each other. So you'll see a few words for this: rub, slide, slip. The easiest example is if you take your hands and rub them against each other, and it gets warm, that's because of friction. So, up until now, we've been assuming that all of our surfaces have been frictionless. But we know that's not the case in everyday life. If you were to push a book across the table, eventually, it's going to come to a stop, and that's because of friction, this resisting force. So this kinetic friction tries to stop all motion that happens between the surfaces. For example, you have your book that's sliding to the right with some velocity, and so kinetic friction tries to stop it by acting to the left. If you were to put a book on an incline or a ramp, and it starts sliding down the ramp like that, then kinetic friction tries to stop that by going up the ramp like this. So, basically, we can see that the kinetic friction is always going to be opposite of the velocity. They're always going to be opposite of \( v \). So that's the direction. But what about this magnitude? The magnitude in the equation is very straightforward. It's just this letter \( \mu_k \) times the normal. Right? So the normal just means that we know that we have two surfaces in contact. Right? We have a normal force here and here. This friction force is actually proportional to this normal. And this other letter here, which is this Greek letter, what it is, it's called the coefficients; it's the coefficients of kinetic friction. Basically, it's just a measure of how rough these two surfaces are. It's just a property of the two surfaces that are in contact with each other, and it's basically just a unitless number between 0 and 1. So if we in our problems, what we've seen is when we have perfectly smooth surfaces, what that means is that the coefficient of kinetic friction is actually 0. There is no roughness. Right? These two things are actually perfectly smooth, and they just slide with no friction. But if you were to grab two, like, ice chunks or something like that and rub them against each other, there's not a whole lot of resistance. There's not a whole lot of friction. And this coefficient is actually pretty low. It's closer to 0 than it is to 1. And if you grab two cinder blocks or two bricks. Right? Just imagine grabbing two bricks and rubbing them against each other. There's going to be a lot of resistance, a lot of friction, and so that \( \mu_k \) is going to be somewhere high. It's going to be basically closer to 1 than it is to 0. But that's really all there is to it, guys. So let's go get to this problem here. Alright. So we've got this 10 kilogram box that moves on this flat surface at 2 meters per second. So I've got this box like this, and I've got it, the 10 kilograms. I know it's going to be moving to the right with \( v = 2 \). I'm told what the kinetic the so coefficient of friction is. It's 0.4 and I want to calculate the kinetic friction force and then the acceleration. Let's get started. So, in part a, what I want to do is I want to figure out the kinetic friction force, which is \( f_k \). The first thing I want to do is just draw a free body diagram for what's going on here. Right? I know this block is being drawn free body diagram for what's going on here. I know this block is being moved across this flat surface, but I want the free body diagram. So let's just draw it really quickly. Remember, we look for the weight force. This is going to be my \( mg \). Then we look for any applied forces or tensions. We don't have any applied forces. Now, if the box is moving to the right with some velocity, friction wants to stop that by acting to the left. So our friction force actually acts this way. This is our \( f_k \), and this is what we want to find here. So that's the free body diagram. So the next thing we want to do is we want to write \( f = ma \), but we actually don't have to do that in this case because we're not trying to find an acceleration. Remember, this \( f_k \) here has an equation that we just saw before, that we just saw. It's basically just \( \mu_k \) times the normal force. So we know this is \( \mu_k \) times the normal. So basically, if we want to figure out \( f_k \), we know this \(\mu_k \) is 0.4. Now we just have to figure out the normal force. So what happens is, what is this \( n \)? Well, if this box is only going to be sliding across the surface like this, and these
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7. Friction, Inclines, Systems
Kinetic Friction
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