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Shmoop! Calculating the force, of friction. The force. The reason for that burning

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sensation. Yeah, just moving right on from that, catching up on friction.

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[mumbling]

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[mumbling]

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All right,

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here we go. Well you know sliding isn't as easy as

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it seems. Sure it might look like a fun time,

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kicking up dirt, as you slide into second base. But you have to make sure you know

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when to start your slide, which means you have to think about how much friction

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you're going to encounter, otherwise you know, things could go badly. [man on baseball field]

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Well friction is one of those things we just know. We don't really think about it,

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but it's such a part of our everyday life, that we have an intuitive

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understanding of it, at least on some level. But as we've seen before, our

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intuitive understanding doesn't necessarily match up with what's

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happening, in terms of physics. So while you intuitively know how far you can

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slide across the floor in your socks, without crashing into a wall like Tom

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Cruise. Well you probably aren't thinking about the coefficient of friction, as you

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glide along there. Well the physics definition of friction, is the force

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that's exerted by two objects as they rub, or slide across each other.

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Alright well friction occurs, because there's no such thing as a perfectly [man in glass store]

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smooth surface. A piece of glass might look and feel perfectly smooth to us. But

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if you look close enough, under a microscope, you'll see all kinds of nooks

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and crannies on the surface. Rub your finger across a piece of sandpaper and

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you'll feel the rough surface slowing your finger down. There's no material

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that's perfectly smooth, at least not that we've discovered yet. But hey, if you

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can invent a frictionless material, you'll probably become a gazillionaire [man sitting in private library with bags of money]

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and be able to buy your own baseball team. So you know, go for it. Alright,

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well the second factor, that determines the strength of friction, is how much

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force is pressing the two objects together. Rub your finger down the

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surface of your table, or you know baseball bat, if you have one lying

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around. Just barely graze your finger across, pretty easy right? Now really mash

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your finger down on to the table and drag it across. Well it takes a lot more [man with baseball bat]

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effort to move your finger, when it's pressed hard against the table. Well

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here's the mathematical formula to figure out friction. This equation says

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that the force of friction, that F there, equals the coefficient of friction, which

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is that mue symbol there, times the normal force, which is what the big n thingy

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there, stands for. Well the normal force, is the force that's pressing the two

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objects together. That's normal. The coefficient of friction is, kind of

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like a measurement of how smooth the two object surfaces are. If the objects move

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across each other smoothly, like two pieces of telescope reflector mirror. [man in workshop]

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Well the coefficient will be low. If they really dig into each other, like two

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pieces of sandpaper, or you know something rubbing the barnacles on the

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bottom of a boat. Well the number will be really high. The coefficient of friction

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is a value, that can only be determined experimentally. We can't just look at two

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materials and put a number on there coefficient of friction. We have to

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actually rub two materials across each other, to see how much friction they [scientist preforming an experiment]

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generate. We'll get deeper into that coefficient thing in a minute. Well there

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are two kinds of friction, static and kinetic. Static friction, is the force

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between two objects, when they're in contact. But not moving. When they're

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touching, you know just sitting there. Kind of like a congressman. Kinetic

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friction, is the force of friction, between two objects that are sliding

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across each other. Kinetic friction is almost always weaker

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than static friction and you've probably had experience with that, if you've ever

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pushed a car, you know it takes more effort to get it moving, than it does to [two men pushing car]

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keep it moving. Of course it takes even less effort to remember to fill up the

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gas tank in the first place, but that's topic for neurology, not physics and good

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luck with that. Why is static friction stronger than

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kinetic friction? Well when two objects are stationary, those nooks and cranny's

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we talked about earlier, have a chance to really get in close with each other.

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They're kind of hooked together, but when they're sliding, they don't

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have the chance to cozy up so much, or so deeply. So it's easier to keep things [car rolling on pavement]

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just kind of bump and moving along there. Let's get back that coefficient of

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friction thing. Well like we said before, the only way to find the coefficient is

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to actually rub the two things together. Luckily for us, some smart scientists

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have been rubbing stuff together for a long time. Which might sound

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inappropriate, but it's not. This is a g-rated video people. They've already

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discovered the coefficients of friction for a bunch of materials and you can

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find some of them right here. Alright well the coefficient of friction, is a [list of coefficients]

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ratio of the force of friction, between two objects and the normal force pushing

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them together. In most cases it's a number, between 1 and 0, because in most

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cases, the force of friction is less than the normal force.

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Now think about when you pressed your finger hard against the table and then

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slid your finger across it. The force you used to slide your finger, was less than [man rubbing his finger on bat]

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the force you were using to press down. Well there are some materials that have

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a coefficient that's higher than one. Like certain kinds of rubber, for example.

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Like the rubber hooks on to the other piece of rubber and the hooking this

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creates incredible friction and it's like very hard to slide it, got it?

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The coefficient can depend on a lot of factors though. The coefficient of

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static friction, is almost always higher than the coefficient of kinetic friction.

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Is the surface wet, or dry. Well ice is slippery enough, when it's below freezing

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outside. But what happens when that ice starts to melt? Well that's a recipe for [woman slipped on icey sidewalk]

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a broken tailbone. And when you're trying to stretch that single, into a double, it

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can seem like the coefficient of friction between you and the infield

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dirt is like somewhere around 60. So let's have some fun with friction.

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Let's say I struck out, just pretending here and I'm dragging my bat onlong the

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ground, as I head to the dugout. Hanging my head in shame. The bat has a

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mass of, 0.88 kilograms and takes 6.7 Newton's of force, to get it

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moving along the grass and 4.2 Newtons to keep it in motion at a constant [man dragging bat]

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velocity. Well, what are the two coefficients of friction, between the bat

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and the baseball field? Well, okay the force needed to get that bat moving is

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going to relate to static friction. After what was happening to the bat before we

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started dragging it. Well nothing, nothing at all. Nothing was moving it and anytime

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we have an object at rest, we know we have a first law situation. Where the [baseball player talking]

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forces are balanced. Newton's first law states that, objects at rest, tend to stay

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at rest, objects in motion, tend to stay at motion. Well the only way motion

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changes, is if a force is applied to it that is out of balance with any other

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forces affecting it. Something that's just resting on the grass isn't

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experiencing any imbalance of force. And the force to keep it moving is going to

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relate to kinetic friction. Since we have constant velocity when the bat is moving,

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we know we have balanced forces, here to. Remember when there's no acceleration,

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either positive, or negative. Then we have another case of balanced forces. So let's [equations on chalkboard]

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figure out the kinetic coefficient first. Alright, our formula tells us that

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friction equals the coefficient, times the normal force. We're trying to find

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that, mue thingy, right there. We'll go ahead and make a Freebody diagram for

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this. There we go and the square here is our bat and we've got our forces all

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lined up. Alright, we know our applied force and we know how to find the

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gravitational force. We don't know the force of friction, F sub F and we don't [diagram and equations]

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know the normal force, F sub n. So let's rewrite our friction formula, in terms of

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our FB D, so we don't get confused. Well F sub F, equals the coefficient, times F sub

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n. We know our applied force is 4.2 Newton's. Well since our forces are all

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nice and balanced. The force of friction has the same magnitude. Well how about

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the normal force? Well it's gonna match the force of gravity and we know how to

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find that out. The force of gravity equals, mass times the acceleration of [formulas on chalkboard]

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gravity. Well the mass is 0.88 kilograms and gravity is as reliable as it gets

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with an acceleration of 9.8 meters per second squared. So the bad has a weight

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of 8.6 Newtons and the magnitude of the normal force is exactly the same. Now

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that we have the numbers, we can find the coefficient. Well 4.2 Newton's equals, the

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coefficient of friction, times 8.6 Newtons.

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To isolate coefficient, we divide each side by 8.6 newtons and that tells us

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that the coefficient of kinetic friction equals 0.49. [equations on chalkboard]

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That'll be mue sub K, so we don't get it all mixed up with static friction. Well

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to solve for that static coefficient, we just have to swap in the right force. Our

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equations already set up for us, it took 6.7 newtons to get the bat moving. We

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divide both sides of the equation by 8.6 Newton's. Giving us a static coefficient

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of 0.7 8 and that looks about right. The static coefficient should be higher, than

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the kinetic coefficient, in most cases. Right? But I'm mad about striking out. I

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want to get a hit and I'm so mad, I'll hit pretty much anything. Like say the[baseball player in locker room]

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shelf that the watercooler is sitting on. Great so now I've done it, I've broke

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the shelf on one side, creating an incline. The watercooler has a mass of

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6.6 kilograms and the incline has an angle of 38 degrees. Well if the water

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cooler and the shelf have a coefficient of friction of 0.48. How fast will the[watercooler on its side with equations]

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water cooler accelerate? Okay, let's figure this thing out, before the manager

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comes here to yell at me. Here's a force diagram of this mess. Which looks pretty

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familiar, to what stuff we've worked on in previous lessons, right? To make things

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easier on ourselves, let's tilt the diagram, so the incline is on the x-axis.

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There that's better. Only one diagonal line to deal with. We'll go ahead and add

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in the component vectors for gravity in the X and y directions. Before we go

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too far, let's set up our second law equations. Well Newton's second law tells

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us, that the sum of all forces along one plane, equals the sum of forces in the [formulas on chalkboard]

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positive direction, minus the sum of forces in the negative direction. The sum

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of forces on the y axis, equals F sub n, minus F sub G Y and the sum of forces

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along the x axis, equals F sub G X, minus F sub F. So let's tackle the Y forces

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first. Step one is to put F sub y in terms of F sub G and F sub G, equals mass

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times the acceleration of gravity. Well we'll do the math on that one real quick.[equations on chalkboard]

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6.6 kilograms, times 9.8 meters per sec

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second square, gives us a force of 65 Newtons. Our angle here, at the top of our

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component triangle, will match the theta angle, of our incline and we'll need that

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to figure out F sub G y. Trigonometry is gonna be our weapon of choice here.

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Cosign theta, equals f sub G y, over f sub G. Pop in the numbers and multiply both

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sides by F sub G, to solve for F sub G Y. Well F sub G y, equals 51 Newtons. Which [formulas on chalkboard]

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means the normal force F sub n, has the same magnitude. Alright, now for

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friction. What's our friction formula? Well friction equals the coefficient,

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times the normal force. Our coefficient is 0.48 and our normal force is 50 1.2

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Newton's. Meaning friction has a force of 25 Newtons, in this case anyway. Write

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that down somewhere, we'll need it soon. But first we need to figure out the X [person writing on paper]

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component of gravity. We'll use the sign function for that one.

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Well sign theta equals, F sub G x, over F sub G. The solving for F sub G X, gives us

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a force of 40 Newtons. Yeah, see what we did there. Now we can find the sum of forces,

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on the X plane. Well the sum of forces in the X Direction, equals F sub G X, minus F

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sub F. Well F sub G X, is 40 Newtons and F sub F is 25 Newtons, giving us a net

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force of 15 Newton's. Fantastic, now we have what we need to find the [man in locker room with broken water cooler]

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acceleration of this water cooler. Then we can see how fast I'm accelerated back

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down to the minors. Well force equals mass, times acceleration. Our force is 15

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Newtons and our mass is 6.6 kilograms, we divide each side by the mass to solve

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for acceleration. Meaning that cooler is accelerating at 2.3 meters per second

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squared. No friction is one of those things that seems simple, until we really [baseball game]

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start thinking about it. We've been running into a lot of these things in

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physics, but it's always good to get a deeper understanding of how stuff

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actually works. Well for one thing, now we know that there are ways to reduce

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friction. Like motor oil, which reduces friction in a car's engine. Yeah, if

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I want to steal second base, I can just pour motor oil all over myself and [baseball player running]

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reduce that coefficient of friction. What could go wrong? Is that legal?

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