[Music] hi there we're taking a look at friction and newton's laws today specifically how friction affects the motion of an object the ways that we can find the force of friction and a little bit about what we call the coefficient of static and kinetic friction the first thing about friction is how it behaves it always opposes motion there are a lot of forces that do this kind of stuff but specifically when we're talking about friction right now we're talking about the motion of one object sliding relative to another um life would actually be really difficult without friction in spite of our attempt to always get rid of it in a lot of our physics experiments so it's good to ask yourself the question what would happen without friction um of course the idea of living in a world without friction is actually kind of disturbing because there's so many things you couldn't do specifically you couldn't walk or drive or ride a bike or stand or sit or hold a pencil or do much of anything because everything that you think of as slippery right now is nothing compared to a world where there is no friction at all so if we think a little bit about how friction behaves and we we can reveal a few things by if you imagine taking an object and pulling it across the table or at least trying to and if you pull on it a little bit or give it a little bit of a push but it doesn't start to move there's clearly a force opposing your push or your pull and that is static friction the friction that keeps things from sliding keeps them from moving and if we solve newton's uh you know second law or first law actually sorry in this case because it's at rest in the x direction we would find that there is you know a pulling force minus a static frictional force and that force means that the pulling force is equal to the static frictional force and you can pull with different amounts of force right you can pull with a very small amount of force or a pretty big force until it finally starts to move and then the friction changes you can also do this once it starts to move now in that case we no longer call it static friction but if you could pull something at a constant velocity you know the net force on it is zero and so in order for the net force to be zero the kinetic friction we call it in this case has to be equal to the pulling force and this is really nice because it's a way for us to quickly figure out what those frictional forces are in situations where we have access to something like a spring scale static friction there's a couple of important things about it because of the way it behaves we say it keeps objects at rest there's a little asterisk next to that because with relative velocity we really mean at rest relative to thing it could slide over and it keeps growing it goes from zero no value when you're not applying a force to a maximum value just before things start to slip what we have in this video and corresponding graph is the uh force readout from this little force probe in newtons over time as i drag the object across the table so if we watch the little video right i pull and then eventually it breaks free and i slide it across the table now we can go back to the beginning and we can actually watch the force read out as we go i pull it's not moving and then suddenly it breaks free and then it moves across the table right uh in that case there are really three zones to worry about there's the before it starts to move where it's a you know static frictional case there's this peak that happens when it breaks free that's our maximum friction and then we've got a area where it's relatively constant and that's our kinetic or moving friction so we can take a look at that video you know an example that i just did and kind of break it down into pieces the first little bit as the frictional force is building up and up and up it's at rest then it lets go right after you hit the peak that's where your fs max exists then there's this relatively constant mode here where it is moving um at you know we would think probably at constant velocity the fact that it's not perfectly flat leaves me to believe it's accelerating a little bit there um but that constant uh kinetic frictional force as it gets pulled along uh the surface now we can ask ourselves what does friction depend on it turns out it depends on the normal force and the materials but let's take a look at why that works and how that plays out we can also take a look at a few other things we can look at the difference between an object you know being pulled across a table or what happens if i pile more mass on top of it this is a block with two three one two three and four kilograms of mass placed on top and that becomes pretty dramatic that the more mass you pile on top the bigger the frictional force so it kind of makes you think oh is this just the mass changing well we can also add in one where it's the same amount of mass as the original as the purple one but in this blue one i'm actually uh or i'm sorry the pink one i'm actually pushing down on the block instead of adding more mass so it doesn't really matter whether we're adding mass so to speak because those masses don't change the mass of the block it just changes the amount that it's being pushed down and therefore the normal force between it so those various graphs that i just showed you right are all here together we build up from the least amount of force when we just have the block and then as we keep adding more mass sitting on top of it which serves not to really change the mass of the block because that can't happen but what it does is it pushes down on the block harder meaning the normal force increases we can do this without placing masses on the top these graphs came from me just pushing down with my hand while i slid it across and so again we can increase the normal force and therefore increase the frictional force involved we can also take a look at what happens if instead of just being pulled across a piece of paper we pull it across the board right block on paper block on board different materials in contact or maybe drag it across the table we see that all three of these have slightly different amounts of maximum static friction force and then kinetic friction force while it's moving um it also depends on the materials right here are three different poles there's the starting one that we've done a bunch of times just the block on a piece of paper then there's the block on just the board no paper and then there's the block on the table and each of these have a slightly different you know fs max and then sort of relatively constant or constant region kinetic frictional force so the materials involved also affect the force of friction so the things we want to know about friction there's kind of these four things on the list the first three are really important the fourth is helpful to remember friction always acts in the opposite direction of the motion this is where that question what would occur without friction really helps right if something would just keep sliding forever say to the right or to the left then you know the opposite direction is the direction that friction is acting friction is proportional to normal force so the bigger the normal force the bigger the force between those surfaces and this could be accomplished by applying a force squeezing them together this is how brakes on a car your bike work between two surfaces that affects it or the materials themselves this is why you know different shoes are better for gripping the ground as you're running and moving around and why you know snow tires and studded tires exist for snowy icy conditions for vehicles the last thing is that for solid objects and this is why it's the last one and there's no highlights friction doesn't depend on area of a contact of contact so it doesn't matter if you've got a big block of wood or a tiny block of wood if it's the same normal force and the same material you should get the same amount of static and kinetic friction for things like fluid like once you add something like water to the picture that's a completely different thing and gets more complicated and area does matter so how do we figure out values for this certainly we can drag things across with a force gauge and it turns out that's really what we have to do we can't just come up with some theory that tells us how big this frictional force will be we have to test it we have come up with a way of describing this we call the coefficient of friction it gets the greek symbol mu lowercase one and that is also the symbol that is used for the metric prefix micro mu is sometimes how you see it written in english it sounds like the sound a cat makes mu but we generally drag objects at a constant speed and we measure that force and figure out the coefficient and it is defined as the amount of frictional force divided by the normal force so it's basically telling you how much of the normal force gets translated into frictional force if you look at a bunch of different materials this column with mu s the static friction you notice those are always bigger than the kinetic frictional force something useful and something we saw from that peak if we were to do an example we might say let's drag an object across a rough and rough is physics word problem code for there is friction smooth is code for no friction it's pulled by a 75 newton force as shown we're given two coefficients of friction which means we could calculate the maximum static frictional force and the kinetic frictional force that could be on this object as soon as we find the normal because there's nothing pushing down on it or lifting up the normal force and the force of gravity are going to be equal in magnitude about 150 newtons and if it's being pulled with 75 newtons to the right we calculate the fsmax which ends up being 74 newtons um you know it's important to remember here that the static friction could be less but we need to know what the maximum is if it doesn't end up moving then whatever the pulling force is less than static friction max is the static friction but since the static friction max is 74 newtons and we're pulling with 75 we can say oh we're going to overcome that we're going to break it away and once that happens it starts to slide and we're not worried about static friction we're worried about kinetic friction which in this case is 44 newtons and once we know that we have all four of the forces that are acting on this object and we can find our net force pulling force minus kinetic friction divide that by the mass to get the acceleration and then we can solve a bunch of kinematics problems so what are the big takeaways from friction well friction resists motion and that's relative motion or motion relative to the ground or the you know reference frame it doesn't matter but it keeps things from sliding or resists sliding static friction is generally speaking greater than kinetic friction for a given pair of objects and friction depends on two things the materials that are touching each other and the normal force between those surfaces