https://youtu.be/kekePB2_BSQ
PHYS 1101: Lecture Eleven, Part Seven
The next force that a surface can supply is a frictional force. You’re only going to have this when a surface is rough and there is either direct motion, real sliding against the surface, or there is a tendency that the object would like to slide, or would slide, if the surface were ice.
For example, if my surface is sloped, your intuition tells you, if the surface were a sheet of ice, the object would slide down the slope.
So, once you, you go around your object, you hit a surface, after you identify and draw in your normal force, then ask yourself, “Do you need to include a frictional force at that surface?”
Do I have real sliding from the part of this object that’s touching the surface, right at that interface, sliding, between the surface it’s touching and the object? Or would it slide if the surface turned to ice?
In both cases, I’m going to have a frictional force I need to include, and the nature of them is slightly different. And that’s what I want to describe for you.
First case is kinetic friction. The word “kinetic” means “motion”. This kinetic adjective, in front of friction, is telling you you have real sliding of the object surface against the surface’s surface.
How big is our friction force? Friction, when you have sliding, we’re going to use f-sub-k to denote that, and the magnitude of the kinetic friction force is the product of what’s called “the coefficient of kinetic friction”.
This is just a number. There is no units associated with it. It’s between 0 and 1. It’s purely a result of the nature of the surfaces, how rough these two surfaces are.
To this coefficient, you then have to multiply the magnitude of the normal force. You’d have to go back to what I wrote about the normal force, and you’d have to look at the problem and figure out how big the normal force is, the magnitude of it. The product of these two sets the magnitude of the frictional force.
Okay. How about in terms of direction? A friction force always opposes the motion. So you’re going to draw this blue arrow to represent this frictional force, opposite to the motion.
If the thing is moving to the right, and I have it sliding against a surface, I right away know I have to have a frictional kinetic force that’s to the left.
Okay, static friction. This is a frictional force you have to include if the object, I have here in quotes, “wants to slide”. If the surface were to turn to ice, would it slide?
The value, the magnitude of the frictional force falls under two regimes, or two possibilities. So let me write, the magnitude of this force, f-sub-static, “static” meaning that there is not any sliding between the surface. That the two, well, there isn’t any sliding.
The value of the static frictional force can be one of two things. Either it’s whatever it takes to solve F equals MA, meaning it’s determined in the same way that the normal force is. So let me copy that and paste it.
So value based on A equals FM, F divided by M prediction. Or the static friction value could be the max value that it’s possible for it to be. I’ll explain that in a minute. Let me write, max value possible.
If you have a scenario where the static friction is opposing the motion, and it’s as large as the nature of the roughness allows it to be, then the size, the magnitude of the static friction force is given by a coefficient of static friction times the normal force.
The static friction force also always opposes the motion, but you don’t have motion yet. So the best way to indicate that is that it opposes the motion, I’ll put it here in quotes, “tendency”.
Again, say to yourself, “If all of a sudden the surface turned to a sheet of ice, what direction would the object slide?” And then, make your static friction force opposite to that direction.
Okay let’s go through this in more detail, this description that I gave about static friction. First of all, all sources of friction, kinetic or static, the nature of it comes from the roughness between the object you’re focused on and the surface.
If you were to zoom in at an interface, with very high magnification between these two surfaces, you would see that the surfaces are never very smooth, that they’re jagged.
And at the location where these jags, these parts of the surface are actually touching, you have real forces there, a whole collection, many, many small forces that all add up to this effect of forces, right-left, that impact the motion, or the tendency of motion of one surface over the other.
If you look at a real atomic scale, at a molecular scale, it translates to real chemical bonds that are having to be broken, and then they reform, as a book, say, slides along the surface.
So with this in mind, let’s think about the static friction and the idea of the static friction.
Let’s start with pushing a book along, at a steady pace. So I know then, my motion diagram looks like this. Acceleration is 0. Without thinking about the forces in detail yet, at all, I know that whatever forces I draw, they have to balance out to 0.
What forces do I have? Here’s my object. Snapshot, one instant of this motion diagram, if you will. I know I’ve got gravity, the weight. This object, as I go around it, the only thing I’m in contact with, on the bottom, is a surface. For sure, I have to have a push, upward from that surface, my normal force.
That’s the only vertical forces I have, so this vertical force has to balance with the force due to gravity, to give me the vertical acceleration, to give me Ay is 0.
Next, let’s think right-left. The object’s moving along at a constant speed. So I know Ax is 0, just as Ay is. Well, going around this, I know I have contact here. This person is pushing straight horizontal, so that’s a force I have to include.
Now, if I’m pushing along at a steady pace, and I know I have to have right-left forces balancing, then I know, if I have a force to the right, there has to be a force opposing that. How big is it? It has to exactly balance the forward push.
This force has to be the frictional force. And that frictional force comes from the real microscopic contact and the real forces that are exerted between these two surfaces as this book slides along.
Okay. Here’s the picture for kinetic friction, and how the sizes of these forces have to balance to be consistent with Newton’s Second Law. Let me point out a counter-intuitive component to this.
Let’s imagine the surface was a sheet of ice and I didn’t have any friction. So, notice I’ve erased this frictional force; there is no interaction between any jags on these surfaces causing small little forces, and so some net effect.
There virtually is no chemical bonding that happens between this surface and that surface. It’s perfectly slick. Without this force, I then only have the force of the push, somebody pushing the book forward.
Newton’s laws would tell you, then, that the book would accelerate. It would have to start going faster and faster, every second.
The sensation to the person pushing the book then, would be to genuinely keep the size of this push the same, to feel the same pressure on the end of this person’s fingertips, you would have to move your hand forward, further and further every second, to maintain that same pressure on your fingers.
It’s kind of counter-intuitive. It really is true. A constant force alone causes something to speed up, not to move along at a constant velocity. If it’s moving at a constant velocity, because of my push, constant velocity means it’s not just my force of my push, but I’m pushing just enough to counter a frictional force. And it’s this combination that gives me the constant velocity.
Now let’s investigate static friction and think it through more carefully. Now my box is just sitting there. Case one, we have nobody touching it. Here’s my free body diagram. Acceleration is 0; velocity is 0; force is balanced.
Now, in comes the hand, and let’s say Angela gently touches the edge of this book. Velocity is still 0, so my acceleration is still 0. What does my free body diagram have to look like now?
Well, I walked through it above If there is any contact here, whatsoever, I have to have a force to the right. Call it “F-sub-A”. Maybe it’s small, but on this book, I know I have to have a force. Let’s call it “A” for “Angela”.
When you go through your identifying forces criteria, and you get them all, what’s the right free body diagram picture for this book? Remember, you have to have acceleration of 0; it’s not moving. As an aside, this is often something you have to reconcile in order for this.
Okay, now I want you to consider the scenario where I push a little harder. I’m going to draw this force a little bigger. That’s what my sensation would be on my hand; I would feel a little bit more pressure on the ends of my fingertips.
So force due to Angela just got a little bit larger. But it’s a heavy book; it’s still not budging. The surface is rough. I still have 0 velocity and 0 acceleration.
Now, what’s the right free body diagram? Be sure and compare the size of this force to the one previously. It does have to be bigger, when you answer this question.
Okay, let me walk you through this sequence. So this is what happens in real life, as you try to push on that. This is the picture of how Newton’s law is really working, and explains what you observe, your sensation when you try to push something and get it going.
You start out with the tiny push and the object still doesn’t budge. Your normal force and your weight balance, your push is balanced by real chemical bonds, and real forces at the surface that are opposing this push of yours. They are opposing the motion.
How big is the net effect of all that? Well is has to be the same size, because A is 0; it’s not accelerating.
You push a little more and the force you’re causing on the book gets larger. The net effect of all of this bonding and this interaction at this roughness, this interface, is still fighting, it’s opposing that.
How large? It has to be the same magnitude, because, again, it’s still not accelerating.
But eventually, you push hard enough and you’re able to push at a level which captures the largest possible resistance that the chemical bonds, the roughness between these two surfaces, is able to provide to oppose the motion.
These little strings that are shown above – let me show you here – they can only stretch so far. They can only pull so much before they break and give way. What’s that threshold? When will it break? What’s the maximum static frictional force you can have?
That’s determined by the nature of these two materials, the roughness of these two surfaces. And it’s also determined by the size of the normal force.
We’ll do examples where we will see this, but the size of the normal force is important in determining how much friction you have. Because the normal force, it sets, remember it’s the force of the surface that’s supporting the load.
The bigger the normal force, the more of the load there is on the surface, because they have to balance each other. Whatever the net load down is, from gravity, somebody pushing, net load down is supported by the normal force up.
So the normal force is a measure of how squished together, if you will, these two surfaces are. If there’s more of a load, if it’s a heavier book, you can picture that I’m going to have more contact between these two surfaces. I’m going to force these two surfaces, on a real chemical, atom level, molecule level, to be closer together. I’m going to form more of these chemical bonds.
So the size of the friction force depends on the size of the normal force. It depends on the load that that surface is supporting; it depends on how squished together these two surfaces are.
That’s why you see this, FN dependence for both the maximum static friction, and for the kinetic friction. Let me add to this picture here, our cartoon. Here was our tiny push, and then our push got larger.
Eventually, we push at a level which has the little molecular springs between these two surfaces at their threshold. They can’t fight it any more. This is the largest force they can supply.
So I’ve pushed now at the threshold. If I push just a little more, the book will break free and will start sliding on the surface. So the size of this should match these forces that I’ve drawn. My small push, larger, until eventually it breaks free.
So here I’ve added some text for you, maybe to help remind you that connection between the normal force and the critical role it plays and how big these frictional forces are.
The normal forces represents the size of the load that that surface is supporting. The bigger the load, the more chemical bonds you have, between the book and the table for example, between these two surfaces, the more contact you have between the two surfaces. And so the bigger frictional force you’ll have.
Okay, those are the main forces, and I have a page here, in your notes, which just on one sheet summarizes all of them. Let me change the magnification here, so you see on one page, I’ve written, again, what we’ve just been through.
It’s a summary of them, a comment about each. Each fundamental force that direction about that force, or the direction considerations, and the magnitude considerations. We have ropes, wires, bundles of hair; rope-like things provide tension forces. We have weight, normal force; this reflects the load. And then two kinds of friction force.
So these last three are forces that any surface can provide, or will impart on an object. You always have a normal force that’s always perpendicular to the surface. But if there is motion, or a tendency for there to be motion, you’ll have frictional forces you have to consider.