(host) So, apparently, ice blocking is a thing. You put a towel on top of a block of ice and slide down that on a grassy hill. And it's so ridiculously fun. And as a 31-year-old child, I visited a park recently to try it out and ended up with grass in more places than I imagined. But it motivated today's lesson, because I tried the same scooting with just a towel and no ice. And no matter how hard I scooted, of course it didn't work. But why? Well, that's the whole point of today's lesson. Hello, and welcome to lesson 6 of Dianna's Intro Physics Class, also known as AP Physics 1 Review, also known as Physics by Dianna. Today's lesson is about friction.

(Describer) She rubs her table.

Part of the lesson, we'll be working with problems that involve slopes or inclined planes. Some people say these problems are the coolest we've done yet, and I'm "inclined" to agree with them. Today's theme is slipping and sliding.

(Describer) A banana peel flies past her head, repeatedly.

You can try to hit me in the face.

[laughter]

Today's theme is slipping and sliding.

(Describer) The banana peel hits her face, and she gives a thumbs-up.

[laughter]

Whether you're into water slides or snowboarding, friction and slopes are key to all sort of slippery shenanigans. Friction is super important. Without it, we would be slipping and sliding everywhere all the time. That might sound fun, but imagine trying to get anything done when you're constantly sliding off your chair or shooting down a slightly tilted sidewalk in directions that you don't want to go. By the end of today's video, we'll know what friction is, what causes it, and how to calculate how much friction there is in some certain scenarios. So what is friction really? You might have this general idea that friction is something that resists slipping or sliding, or something that comes from rubbing, like when you rub your hands together and they feel warm. Well, there's something happening there that's resisting the motion. That's what friction does. Friction exerts a force in the direction opposite of the motion. There's other kind of friction that happens when things aren't moving, and we'll get to that in a minute. But where does friction come from? Think about floating in space. Is there any friction to slow you down? No, there's effectively none. There's like 1 atom in every cubic meter. That's crazy. It's slightly more in the space around our solar system, and there's a lot less in the space between galaxies, but there's, like, no friction. So friction comes from something. It comes from the interaction between things, specifically between surfaces. So no friction in space. But if I'm sliding across the kitchen floor in my socks, well, it's slippery, but there's still friction, and I'm still slowing down. But why? No, really, why do two surfaces rubbing on each other have friction? Because the surfaces are rough-- blah, blah, blah. Yes, that's part of the answer. But even when something feels really smooth, like glass, or like a smooth tabletop, or like a waxed surface, or like a book, even those are bumpy when you get down to a small enough level. But why do these bumpy surfaces resist sliding? Well, Dianna, you say, because the bumps catch on each other. OK, but why? Why did they catch? Why do they stick? If the surfaces are rough, it means that they're only touching at certain points, and why would those contact points catch on each other? The answer is actually kind of from chemistry. Those tiny little bumps, those tiny points, are made up of molecules. And those molecules like to stick.

(Describer) She holds two magnets.

Maybe from chemistry class you remember learning about forces between molecules-- the intermolecular forces, the negatively-charged end of a water molecule attracts the positively-charged end of another water molecule, stuff like that. When you bring two molecules close to each other, sometimes the electrons in them will actually shuffle around a bit to make the molecules have negative and positive ends, if they didn't already, and that causes the molecules to stick. This molecular stickiness is actually what's happening to surfaces when they touch each other. It's forces between tons of tiny molecules that make friction happen. So saying that friction comes from rough surfaces isn't wrong, but it's not the whole story. Fun fact, scientists have actually measured the friction from a single molecule sliding across a surface, and you can't exactly call a single molecule a rough surface. So there will be friction when two surfaces touch each other. How much friction will there be?

(Describer) She moves a cover for a box, then the box itself.

That depends on two main factors. Can you figure out what they are? First, let's think about the surfaces. Have you were tried to go ballroom dancing in socks? It doesn't really work-- not a lot of friction there. But if I put on rubbery climbing shoes and hit the climbing gym wall, there's a lot more friction between my rubbery feet and the wall. No slipping and sliding there. So that's our first factor: the friction between the two surfaces is going to depend on what the surfaces are made of.

(Describer) She moves the cover and the box again.

This is like a lot smoother, and this is a lot more rough. OK, what else? Try this--rub your hands together.

(Describer) She does it.

Now, rather than harder. Now harder. You can feel it. The more force between your hands, the more friction. So that's factor number two: the size of the friction force between the two surfaces depends on the size of the force between the surfaces. Physicists call this force the normal force. Normal means perpendicular in physics speak, and that's the force that we want, the force perpendicular to the surface-- this way. When you push harder, the normal force gets bigger, and the friction force resisting your motion gets bigger as well. So we've got it. The amount of friction depends on these two factors-- what are the two services made of, and what is the normal force at the interface between the surfaces? We will represent this with a straightforward equation.

(Describer) She lays out a sheet of paper and catches a thrown marker.

All right, friction.

(Describer) She writes.

Friction force equals normal force times mu.

(describer) Written as capital F sub f

(Describer) (no standard option) Written as capital F sub-f equals Greek symbol Mu (mew) capital F sub-n.

equals Greek symbol mu, capital F sub N.

(Dianna) The mu is the coefficient of friction. It represents factor 1-- what your surfaces are made of. So the coefficient for ice skates on ice will be a lot smaller than the coefficient for rubbing your combat boots off on a mat. And yeah, check it out, there's no units, because we've got a force on the left and a force on the right, so mu cannot have units. It's just a number. You can actually look up mu for a lot of combinations of surfaces, like steel on ice or rubber on concrete, and these coefficients can also depend on things like temperature and whether the materials are wet or dry, so it can be pretty messy. So usually you just have to measure it. OK, let's jump into an example. Think about a car using its brakes. You slam on the brakes so the tires lock, and you screech across the concrete road. We're going to find friction. We'll use our tool, the free body diagram. So here's our car.

(Describer) She draws a square.

It's a beetle. It's moving in this direction, so there's a velocity vector this way.

(Describer) An arrow forward.

And when you hit the brakes, the friction force is going to be the opposite direction of the motion in this direction. We don't know the size of the friction force yet,

(Describer) Opposite.

but we're going to figure it out. What do we know? We know that there is a force of gravity pulling down on the car.

(Describer) Arrow down.

That's going to be the mass of the car times g. The mass of our car is, we'll say it's about 1,000 kilograms. And then g is minus, because we're going to say down is negative. Minus 10 meters per second squared. And that means that our downward force is about minus 10,000 newtons. Or another way of putting that is minus 10 to the fourth newtons-- scientific notation. Or you could also write it as negative 10 kilonewtons. So that's my force downward. But the car is sitting on a surface on a road. So Newton's third law tells us that there's a normal force pointing upward that's exactly opposite of the gravitational force.

(Describer) Arrow up.

So then our normal force is exactly opposite this. So it's also 10 kilonewtons. Or I'm going to write 10 to the fourth. So we just found the normal force. That's one part of finding our friction force. Now, we have to find mu, so we just look up the coefficient of friction for rubber on concrete. And it turns out that it's about 0.7. So the force of friction here as our car screeches to a stop-- F equals the force of friction equals mu times the normal force. My mu is 0.7. My normal force is 10 to the fourth newtons. So I get 7 times 10 to the third newtons. That's the force of friction, or that's also 7,000 newtons or 7 kilonewtons. Ta-da! That's a big force. But cars are pretty massive, so it takes a lot of force to stop them. Let's use F equals m a right now to find the acceleration real quick. So I've got my net force, F equals mass times acceleration. I know my mass was 10 to the third kilograms times a. That equals my net force, which is-- In this direction, My force is 7 kilonewtons. So that's 7 times 10 to the 3 newtons. Bring this down, 10 to the 3. And I get--kilograms-- my acceleration is 7 meters per second squared. That seems pretty reasonable. That's a decent amount of acceleration, but it's not going to knock you out. If this was all happening on a rainy day, so the road was wet, we would need to use the coefficient of friction for rubber on wet concrete, which is smaller. It's a smaller mu. So that gives us a smaller friction force. And that's why cars slide more and take longer to stop on wet roads. So here's a quick and easy example of friction. Take a book. Hold a book up against the wall. And if you push up on it, it makes total sense

(Describer) She does.

that you can hold it up against gravity and keep it from falling, right? But then you can also push straight into the book. I don't know if you can tell, but I'm pushing a little sideways now, but basically straight on into the book-- no up or downwards force. And I can keep the book from falling. I can even push down and into the wall, and the book won't slide. What is going on? It is friction providing the force that's

(Describer) She sits.

necessary to resist gravity. But wait, there's no sliding here, no motion. So how can we talk about friction? There are actually two kinds of friction. The first kind of the friction of things sliding against each other, like the locked car tires skidding across concrete when you brake. That's kinetic friction. And the other kind of friction is called static friction. This is the friction of objects that aren't moving, like the book that isn't sliding on the wall. Static friction resists starting your motion. Static friction has the same basic physics as kinetic friction. The force of static friction is still a coefficient of friction. So we've got a coefficient of friction times normal force.

(Describer) She writes the first formula again.

Static friction. Let's try it out. Get out a massive physics textbook and push on it gently.

(Describer) She does.

You can feel resistance even if the book doesn't budge. But if you push hard enough, the book will start moving with a bit of a jerk. That jerk happens because the situation is switching from static to kinetic friction. And for any given combination of surfaces, the coefficient for static friction is bigger than the coefficient for kinetic friction. So when the force resisting the book's motion changes from the bigger static force to the smaller kinetic force, the book accelerates a bit, giving you that jerk. Remember how we talked about friction coming from the intermolecular forces between surfaces? Well, the book goes from feeling static to kinetic friction, and all those intermolecular bonds are breaking, and the book can now slide across the surface. The molecules in the book still form little bonds with the table as the book moves, but not as many of them, because there's other physics going on. Isn't that wild? I just learned that about the bonds breaking from static to kinetic friction myself while working on this lesson. OK, so there's our introduction to friction. Now, we can solve some problems. Have you ever slid down a small hill on a piece of cardboard or something like that, or maybe a sled if you fancy? If so, probably noticed that the steepness of the slope affects how well you can slide down it. Let's look at--I've got my cow sliding down the slope.

(Describer) She tilts the textbook.

Not going anywhere until it gets steep enough, and then boom.

(Describer) The square cow slides off.

Also, here's an interesting place to look at materials. The force of friction is different for different materials. So here's my pen, and it already starts to slide at this angle,

(Describer) She tilts the textbook again.

whereas the cow got up to that angle. And then my phone case could get up to here. What else have we got? This is going to go flying.

(Describer) She sets a prism on it.

Oh, this is dangerous. OK.

(Describer) Again she slowly tilts the book.

Oh, actually, no. Yeah, that didn't make it very far.

(Describer) It slides and she catches it.

But also, this is heavy-- big normal force. So the steepness of the slope affects how well you can slide down it. If the hill, or the slope, or the ramp, or whatever is not steep enough, then it actually could be kind of hard to start sliding, which is what we saw. We're going to answer why steeper means easier. So here we are trying to slide.

(Describer) She draws an angle.

Let's think about the forces involved here.

(describer) She draws a square on the slope.

(Describer) (no standard option) She draws a square on the slope.

(Dianna) We have a downward gravitational force, m g. And to think about the friction forces, we need to figure out what the normal force is. We're looking for the force perpendicular to the surface. In the car example before, the surface was flat. So the normal force was just straight up and down, opposite gravity, pointing upward. But now gravity is pulling at an angle relative to our surface. And it's not a 90-degree angle. So now the gravitational force is doing two things. So let's break it up into its two components.

(Describer) She draws a full body diagram of a square on the slope. It has three arrows, Fg going straight down between them.

So I've got my F g. So gravity is pulling the cow into the surface of the ramp, and it's pulling on the cow along the slope of the ramp, trying to get it to slide down. So now we'll use our usual SOH CAH TOA tool to find the components of gravity. One component will be F g times the sine of theta, and the other is going to be F g times the cosine of theta. Now, which is which? One easy way to figure this out is to think about an extreme case. So if the ramp were totally flat, then the angle theta would be 0. And so there would be no sideways component of the gravitational force. It would just be up and down. So sine of 0 is 0. So the sideways component is going to be F times sine of theta, which makes the other F cosine theta. This is going to be negative m g sine theta, and this is going to be minus m g cosine of theta.

(Describer) ...down the slope. The force into the ramp surface is minus mg cosine of theta.

So if there was no friction, the force of gravity along the slope, this m g sine theta part, would just make the cow slide down the ramp. But let's say there's just enough friction opposing this component of the gravitational force to keep the cow from sliding down the slope. So we've got now a friction force. So that's my F f, my force of friction. We know what that friction force is. It's the normal force times the coefficient of friction mu. And we know the normal force, because we know that it's equal and opposite to the component of gravity pulling the cow into the ramp surface. That's m g cosine theta. So this is going to be equal and opposite this direction. And we know that it has to be equal and opposite, because it's not accelerating this way. It's not going through the ramp. So that's my normal force, F n, equals m g cos theta. So the friction force that keeps the cow from sliding down the ramp here is mu times m g cosine of theta. So the net force that the cow feels along this slope is the sum of the gravitational force that wants to pull it down the slope and the friction force that opposes it. We said down was negative. And we specified before that the cow is not moving, because we said the friction force is just enough to keep it from sliding down the slope. So the acceleration is 0. This is useful. If acceleration is 0, then the net force is 0. And I can rewrite my equation to say that mu m g cosine theta equals m g sine theta. By the way, the negative went away, because if I say my net force is 0, then I say this plus this equals 0. So then I can just move this over to the other side. Check it out, the m g's cancel. Which means the mass does not matter here. That is something interesting to think about. Here, we're left with mu cosine theta equals sine theta. I can rearrange a bit and get that mu equals sine theta over cosine theta, which equals, if you remember your trigonometry, the tangent of theta. So, yo, I got something really interesting. Tangent of theta equals my coefficient of friction. So my coefficient of friction is just the tangent of theta. That's a simple expression for the coefficient of static friction between two surfaces. And we just came up with a super quick easy way to find it by using the two things we said were true. We said that there's just enough friction force on the cow to keep it from sliding down a slope. In other words, the magnitude of the gravitational force that wants to pull the cow down the slope and the friction force that's resisting that motion are equal and opposite. And if this slope with steeper, gravity would win, and the cow would slide down. And if the slope was shallower, then there's actually more friction force available than we need to keep the cow from sliding. So the angle of the slope we've picked is just the right steepness where the competing gravity and friction forces are equal. So if you want to measure the coefficient of friction between two surfaces, you can slowly lift your ramp to a steeper and steeper angle and stop it at just the moment that the object starts sliding down the ramp. That'll be pretty close to your just right, Goldilocks angle where gravity has just barely enough strength to overcome friction. Then, take the tangent of that angle, and, bam, you've measured the coefficient of friction. You can do this at home. You just need a protractor for measuring angles, something to use as a ramp, like a wooden block, a book, a piece of cardboard, anything, and a smaller object to put on your ramp, like a square cow. Everyone has those lying around. So that is Lesson 6, Friction and Inclined Planes.

(Describer) She pulls away the paper.

When they ask what you learned on YouTube today, here are your two key takeaways-- there are two kinds of friction, static and kinetic. Static is bigger. And F f equals mu F n, the force of friction is the coefficient of friction times the normal force. And because you can only really learn physics by doing the problems, here, again, are all the problems we did in the lesson. And you should definitely go work them again at home.

(describer) Problem one: The coefficient of friction between

(Describer) Problem 1: The coefficient of friction between your car's tires and concrete is zero point 7. Your car's mass is 1000 kilograms. If you slam on the brakes and the tires lock, what is the magnitude of the sliding friction force acting while you slide? What is your acceleration? Problem 2: You put your cow on a ramp. Moo. Then you tilt the ramp up, slowly. Just when your cow starts to slide, you measure the ramp angle as 34 degrees. What is the coefficient of static friction between the cow and the ramp?

you car's tires and concrete is 0.7. Your car's mass is 1,000 kilograms. If you slam on your brakes and the tires lock, what is the magnitude of the sliding friction force acting while you slide? What is your acceleration? Problem two: You put your cow on a ramp. "Moo." Then you tilt the ramp up, slowly. Just when your cow starts to slide, you measure the ramp angle as 34 degrees. What is the coefficient of static friction between the cow and the ramp? I want to tell you something interesting and weird about materials real quick. In some labs, physicists use lasers to cool down atoms to super close to absolute 0. Do you know what absolute 0 is? It's like the hypothetical coldest the universe could ever get. Like, you can't get colder than that. So only millions or billions of a degree above absolute 0, and that's how cold physicists get matter when they use lasers to cool them down. And this creates a weird new state of matter called a Bose-Einstein condensate, where all of the atoms clump together and they behave in the same way, almost as if they're all one giant atom. And you might learn more about this if you continue on and you take a physics class in quantum mechanics, or atomic physics, or something like that. I hope you do continue on physics. And now, a message for you from a special guest. Hi, everyone. My name is Naomi Rowe-Gurney, and I am a PhD student at the University of Leicester. I study the ice giants-- Uranus and Neptune. I look at their atmospheres using the Spitzer Space Telescope, and that's all in preparation for a brand-new space telescope called the James Webb Space Telescope that's being launched next year. So keep an eye out for that. I was never very good at maths in school, but now I'm a planetary scientist. So always persevere, and I'm really excited that you've decided to learn physics. Keep going, and good luck with your studies. Accessibility provided by the U.S. Department of Education.

(Describer) Titles: Executive Producer/Host/Writer: Dianna Cowern Lead Writer/Course Designer: Jeff Brock Producer: Laura Chernikoff Video Editor: Victoria C. Page Videographer: Levi Butner Curriculum Consultants: Lucy Brock and Samantha Ward Curriculum Consultant: Andy Brown Physics Girl Accessibility provided by the US Department of Education.