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Khan Academy Presents: Correction of definition of "normal force" and an introduction to the coefficient of friction.
Tags:Introduction to friction,coefficient,educational videos,force,friction,khan academy,khanacademy,math lessons,math tutorials,normal,physics,salman khan
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Introduction to friction
Welcome back. I actually want to make one—I guess technical correction to what I was teaching you in the last video. And then I’ll introduce you to friction. So this is where we left off from the last video. And I was calling this the normal force; this. And I really should have called it the component of the gravitational force that it is—I guess we could say perpendicular or I guess, we’d say normal to the surface that the mass is on.
Because—and the reason why I’m making this distinction is because this is the pull of gravity. And actually the normal force is the offsetting force; right. Newton’s third law every action, there’s an equal and opposite reaction.
The normal force is officially the force that this inclined plane is actually exerting on the mass and keeping the mass from falling into the inclined plane. So the normal force is actually by definition; this force.
That doesn’t change how we did that last problem but I just want to make sure that that we have our definitions correct and you don’t go and argue with your teacher. That no, this is a normal force― No, no. I am sorry. I was always bad with labels and this is another label but this shouldn’t be the normal force. This could be the—you know force of gravity that is perpendicular. You know force of GP or something.
So I just want to correct that and now with that out of the way, let’s learn a little bit about friction. And hopefully that made a little sense to you. In magnitude, the normal force is equivalent to this force. It just goes in the opposite direction, right? Because you have an equal and opposite force and that keeps the mass from falling into the inclined plane.
So let’s clear this and get rid of the inclined plane temporarily so that we can just simplify things and learn a little bit about friction. So everything we’ve been doing so far involved a mass on a sheet of ice so that we had no friction. But now, we’ll have a mass on a sheet of dirt. I thought I was using the line tool. Well, that’s good. This—my attempt to draw a line looks like a surface that has friction on it.
Let me put a mass on it now. So instead of ice on ice, we’ll have a dirt brick. There is my dirt brick sitting on the ground. And let’s say this dirt brick is 10 kg; so 10 kg dirt brick. And let’s say that I pull or I push—either way, it doesn’t matter. I push in that direction with a force of—I don’t know—1000 N.
So the force—so this force is—force is equal to 1000 N. If we had no friction—if this was ice on ice. This would be a really easy problem; you just say F equals MA. So the force is 1000 N in the right direction, divide that by the mass and you’d get a 100m per second square. So you’d get this really tremendous acceleration.
But now we have friction. We have the contact between the brick and the ground and it’s going to make a little bit harder; pushes you’ve experienced when you were pushing something on ice, it’s easy or especially on oil on ice or something like that when you push it on the ground or on your carpet, it’s much more difficult.
So how do we think about friction? So I will introduce you to a concept called the coefficient of friction and the letter that people normally use for it is this—I think it is called Mu. This is kind of like an M. And this is called the coefficient of friction. Coefficient—it has two Fs; I think it does. Coefficient; it’s a good thing I’m not teaching you spelling.
Coefficient of friction and every surface or especially when you’re kind of rating one surface touching another surface, it will have an associated coefficient of friction. And so, I saw an ice or I saw an oil or oil on ice might have a very, very low coefficient to friction and I'll show you how we use this. And if we have sand paper on sand paper, that will have a very, very high coefficient of friction.
So this is really just a constant term that tells you how much friction there is between a surface and the object. And this is how we use it. This term tells us that the level of friction is always going to be proportional to the normal force on this object and that’s why I wanted to make that little technical correction.
And what’s the normal force on this object? Well, we know that the force of gravity is pulling down on this object, right? The force of gravity is pulling down. And what’s it pulling down, it will—acceleration of gravity reset—you know for approximation purposes is 10meters per second squared.
So 10 meters per second squared times 10 kg ― let me show you 9.8 but 10x10, it’s a 100 N, right? So that’s the force of gravity. The force of gravity is equal to 100 N and the normal force is essentially the force that this ground exerts upward on the block that keeps the block from falling into the ground. So the normal force has to equal and opposite to the force of gravity so the normal force and—I’m almost getting a little bit messy—is the exact same magnitude but is going in the opposite direction. And it’s going to be a 100 N upward.
And the force of friction—and what is the force of friction? The force of friction is essentially always acting against whatever direction you’re pushing in or pulling in. So, if I am trying to pull the block in this direction, to the right, the force of friction is going to be going to the left. But if I was trying to pull the block to the left, the force of friction is going to the right and they also call this a shear force. And it’s always acting against you. And—you know—and wind does the same thing. Wind resistance is also a frictional force.
So, that’s why you should think it’s kind of interesting, you know. You would think that at some point it would work for you but no; no matter which direction you push in, it’s always working against you. And so how do we calculate it?
So let’s say that—you know, I was just told by the people who made this ground in this block that the coefficient of friction of these two materials when they rub against each other is .2. So then in this example, the coefficient of friction is equal to .2. And if you have it on the Physics exam, they’ll tell you that the coefficient of friction is point something, something.
So what do we do with that? This tells us that the frictional force. The frictional force; the force of friction or the shear force is going to be equal to .2 times the normal force or .2 times the force of gravity. You can do it both ways. I always think of it the force of gravity but you could use either one because they have the same magnitude.
So you can say that the force of friction; the force of friction or the shear force is always going to be equal to—you could say the force of gravity with the normal force—the normal force—the—times the coefficient of friction. And that makes sense because if I put a—if I had the same surface but I had a much heavier block? Then I’ll have lot more friction. That just makes intuitive sense to you― you can—you are able to push something that’s pretty light on your carpet. But like your—you know, a chest of drawers or your bed, it’s a lot harder to push in your carpet because that’s just—it’s a lot heavier.
And so that’s why the force of friction—and it’s—well, lucky for us that it’s proportionally. It could have been—you know quadratic or something. But it makes the math easier that the force of friction is actually proportional to the weight of the object or the—we could either say it’s proportion to the weight of the object or the force that the floor is exerting upward on the object to keep the object from falling in to the floor.
So either way, let’s just do this problem. So what’s the force of friction here? The force of friction in this problem is going to be equal to the normal force or the force of gravity. We could use either one. So that’s a 100 N times our coefficient to friction. They’ll always give you that. Sometimes you have to solve backwards for it but—then you get the points.
So the force of friction is going to be equal .2x100N, its force of friction is going to be =20N and forces is a vector. So, what direction is it going to be acting in? Well, it’s going to be acting in the opposite direction that I am trying to push the object. So it’s going to be going to the left.
So what is the net force on this object? I’m pushing to the right in a 1000 N and then friction is essentially kind of pulling back at 20 N. SO the net force; the net force in this direction—so we can call it the force subnet which equals what you can 1000 N—it’s going to be in this direction because a 1000 is much bigger than 20s, so it’s a 1000 - 20 = 980 N to the right.
And so, if I wanted to figure out how fast is it accelerating? Well, to the right, it’s accelerating at—well force equals MA so force net is equal to mass times acceleration. So 980 is equal to 10 kg times acceleration. So acceleration is equal to 98 meters per second squared in the right word direction.
And that makes sense because my force of friction is relatively small compared to how fast I am pulling the—or how hard I am pulling and maybe I should have done this with a 100 N. But I think you get the point. And if there is no friction, the acceleration would have been faster. It would have been slightly faster. It would have been a 100 meters per second squared.
So hopefully I’ve given you a little bit of an intuition on what friction is and I’ve corrected my labeling mistake on normal force. And I’ll see you in the next video where we’ll apply our friction skills to back to the inclined plane problem. I’ll see you soon.