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Static Friction & Equilibrium

Patrick Ford
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Hey, guys. In the last couple videos, we talked about kinetic friction and this video. We're going to talk about the other type of friction, which is called static. They have some similarities, but static friction is a little bit more complicated, so let's check it out. So remember what we talked about kinetic friction. We said that this happens when the velocity is not equal to zero. You push a book, and it's moving and status are kinetic. Friction tries to stop that object and bring it to a stop right. Static friction happens when the velocity is equal to zero. Imagine this book is like, really, really heavy, and it's at rest on the table. What static friction tries to do is it tries to prevent an object from starting to move. So imagine this book is really, really, really heavy. You try to push it, and no matter how much you push, the book doesn't move. That's because of static friction. So the direction of kinetic friction right was always opposite to the direction of motion. Right? So you push this book across the table, it's going to the right kinetic friction opposes with to the left static friction is kind of similar, except the direction is going to be opposite to where the object wants to move or would move without friction. So this heavy book, right? You're pushing it without friction. It would move to the right, so static friction is going to pose you by going to the left. So this is FS. Lastly, let's just talk about the formulas. So the equation for F. K. The kinetic friction is the coefficient of kinetic friction times the normal for static friction. It's very similar, So we're just going to use the coefficient of static friction times the normal. We'll go back to this in just a second here. This coefficient of static friction is really just another number just between zero and one just like him, UK is. One thing you should know about this coefficient, though, is that it's always going to be greater than UK. Normally they're going to be given to you. Uh, you know, an example of this is that we have 0.6 and 0.3, So, actually, let's just get to the example right now. We're gonna go ahead and come back to this in just a second. So we've got this 55.1 kg block that's at rest on the floor like this. Now we're giving the coefficient of static and kinetic friction. Like we just said, This is my us, and we'll see that it's actually greater than UK. And so what we're trying to do in this problem is we're trying to figure out the magnitude of the friction force on the block when we push it with these forces. So this F is 20 and this f is 40. So let's go ahead and get started. I'm just gonna draw really quick sketch of the free body diagram. So we have our MG that's downwards. We've already got our apply force, and then here's our normal. And then whether this object is moving or trying to move, we know that friction is going to oppose that by going to the left. We just don't know what this kind of friction is. So which equation we're gonna use our We're going to use Mu uh f k. Or we're going to use F s. Well, if you think about this, this block is at rest on the floor, which means that the velocity is equal to zero. So we said that the velocity is equal to zero. We're going to use the static friction, um, formula here. So our f s is equal to use static times the normal. So that means our friction force here is going to be 0.6. Remember, that was our arm us times the normal force. Well, if this block is only sliding horizontally and we have two forces in the vertical, that means that they have to cancel. So that means that our and is equal to mg. So that just means that we're gonna use 5.1 times 9.8 and you'll get a friction force that's equal to 30 Newton's. So let's talk about this. You're pushing with 22 the rights. But the friction force that we calculated was 30. So even though you're pushing to the rights, friction force would win and the book would actually start accelerating to the left in the direction of friction. That's crazy. Doesn't make any sense. So what's happening here? What happens is that when we use this formula, this mu s times the normal, this is actually called a threshold this is basically this is basically just the amount of force that you have to overcome to get an object to start moving This mu s times normal is the maximum value of static friction. So we do is we actually call this F. S Max, and this is equal to mu s times the normal. So when we go back here, we have to do Is this static friction formula we use is actually the maximum static friction. This is basically just the threshold that we have to overcome in order to get an object to start moving. So what happens is this threshold is not always the actual friction that's acting on an object to determine whether we're dealing with static friction versus kinetic friction. What we always have to do in problems is we have to compare the forces to that static, that static friction threshold. Basically, we have to figure out whether our force F is strong enough to get an object moving. There's really just two options. You either don't or you do So let's talk about those. If you're f is not strong enough to get an object moving right, that means your force is less than or equal to that static, that maximum static friction. At that point, the object just stays at rest, right? It's not enough to get it moving. And if the object stays at rest and the friction is just gonna be static friction. So basically, what happens is if you haven't yet crossed this threshold, this is kind of just like a number line here where you know you have increasing force, then your static friction basically always has to balance out your force. What I mean by this is that you're if you're pushing with 10, your friction can't oppose you is stronger than your pulling. So that means that the static friction in this case is just 10. If you're pulling harder with 20 static friction opposes your poll with 20. And if you're pulling with 30 static friction just opposes your poll with 30. It always knows how much you're pushing, and it always basically balances out your force so that the object stays at rest in the acceleration zero. Now, what happens if you actually do overcome that threshold? Basically, if you have strong enough force to get the object moving in your force is greater than Fs Max. And what happens here is that the object starts moving and if it starts moving, then your friction switches from kinetic and actually sorry from static, and it becomes kinetic friction. So what happens here is that this kinetic friction we already know is just equal to U K times the normal. So let's go back to our problems here and figure out what's going on. So what we're doing here is we're basically comparing our F two r f s Max. That's how we figure out which kind of friction we're dealing with. So our f is 20 and this is actually less than F. S max, which is equal to 30. So what that means is that our friction force actually is going to be static friction. And it's just basically going to balance out our poll. So are static. Friction is going to be 20. So this static friction here is going to be 20 Newtons. Even though your maximum is 30 now in part B, we don't need to recalculate the maximum. We are. You know that Fs Max is 30 but now we're actually pulling with 40. So basically what happens here is that our f is equal to 40. It's greater than your f s Max, which is equal to 30 which means that the friction becomes kinetic friction. And so we can calculate this by using U K times the normal. So basically, our kinetic friction force is going to be 0.3. That's the coefficient that we were given times 5.1 times 9.8. And if you work this out, you're going to get 15 Newtons. So what happens is here we've actually crossed that maximum static friction threshold. And so therefore, the friction that's opposing this book is actually gonna be kinetic, and it's going to be 15 Newtons. So those are the answers, right? We have 20 Newtons when you're not pulling hard enough and then 15 once you've actually overcome. So basically, what this means is that once you pass this threshold, it actually doesn't matter how hard you pull, because the friction force that supposing you is just gonna be f K. And so this is just gonna be 15. If you if you were to pull a little bit harder with 50 Newtons, it doesn't matter because this mu k times. The normal is it's just a fixed value. So even though you're pulling with 50 kinetic friction would still oppose you with 15. All right, so that's it for this one, Guys, hopefully I made sense. Let me know if you have any question.