 Let's say you need to push a heavy box across a horizontal surface, but you can't get it going. What do you mean you can't get it going? What's your problem? Well, maybe your problem is just friction. Friction is an interesting force. It's present whenever two surfaces are in contact with one another. Today, we're going to talk about dry friction, which is present whenever two solids move one against the other. There are two types of friction that we're going to study in Physics 20. Static friction, which is a friction present that holds an object in place when a force is applied to that object, and kinetic friction, which is a type of friction that acts in the opposite direction of the motion the object would have if there is no friction present. We have a formula to calculate the force of static or kinetic friction, but it's a weird one. The formula is the absolute value of the force of friction equals the coefficient due to friction multiplied by the absolute value of the normal force. Now, there's a lot going on here, so let's break it down. These two vertical lines are called the absolute value function. This is a cool little bit of math that basically takes any number inside of these lines, and if it's negative, makes the number positive. And if the number is positive, well, it keeps it positive. What this basically means for our purposes is that while a force can definitely be positive or negative, when we sub those numbers into this equation, we don't need to put in the negative signs, because the absolute value function will just make them positive anyways. In short, this formula is a scalar formula. It doesn't give you the directions of the forces in the formula. You've got to work those out on your own from your diagram. The direction of the force of friction is in the opposite direction of the motion the object would have if friction were not present. The next part of the formula is the weird looking u shape letter, which is the Greek symbol mu. That's right, mu, just like a cat says. Mu stands for the coefficient due to friction. This is a unitless scalar coefficient that exists between every two objects. And it's usually given on a table like this. There are coefficients for kinetic friction and static friction in your textbook and online. Lastly, we come to the absolute value of the normal force. In math and science, the word normal actually means right angle, or perpendicular. And if I had my way, we would always call it the right angle force. The normal force is always at a right angle to the surface the object is sitting on. If you're on a horizontal surface, your normal force is pointing straight up. If you're on an inclined plane, your normal force is still at a right angle to the surface, but now it isn't pointing straight up anymore. You'll notice on your formula sheet that there isn't a formula to calculate the normal force. That's because we work it out from a free body diagram. If you're on a horizontal surface, the normal force acts vertically upwards on the object, while the force of gravity acts vertically downwards. This idea comes out of Newton's third law. So on a horizontal surface, the normal force is equal to the force of gravity, but positive instead of negative. If you're on an inclined plane, the normal force will not quite be equal to the force of gravity, but we can put those two vectors together into a triangle and solve for the normal force by multiplying the cosine of the angle of incline by the force of gravity. If you'd like more details on how that works, check out this inclined plane free body diagram video. The last weird thing about this formula is that it actually gives the maximum value for the force of static friction. Here's an example. Let's say you push a 300 kilogram box across a horizontal surface with a coefficient due to static friction of 0.200. What is the force of friction acting on the box? Well, our formula can tell us the maximum value of the static force of friction acting on the box, which is 588.6 Newtons. But if I'm only pushing on the box with a force of, say, 200 Newtons, then the force of static friction is just negative 200 Newtons. It isn't the maximum because then friction would make the box move backwards towards me, which just doesn't happen. If I push harder at, say, 400 Newtons, then the force of friction pushes back harder too with a force of negative 400 Newtons. The force of friction will always match me until I finally push over the maximum, say at 589 Newtons. This is a little over the maximum static friction, so I can finally get the box moving. Friction hasn't disappeared, though. Now the resisting force is the force of kinetic friction. But luckily, the force of kinetic friction is pretty much always smaller than the force of static friction, so I can finally push this box wherever it's supposed to go.