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Static & Kinetic Friction

Patrick Ford
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Hey, guys. So let's check out this problem here. I have a 5.1 kg block, and what I want to do is I want to calculate the force that I need to get the block moving. And then I wanted to calculate the force. You need to keep it moving at constant speed. So there's really two different situations here that I'm gonna draw throughout the diagrams for you got 5.1 kg block on the ground. I'm going to be pushing it with some mysterious force here to get it moving. And then in the second case, I've got the block like this. Except now it's moving with some constant speed. So V equals constant here, and I want to figure out how far or how, how hard he to push it to keep it moving at constant speed. So there's two different forces here. All right, so we want to draw a free body diagrams. Let's just draw all the other forces that are acting on these blocks. I've got my weight forest, that's mg. And then I've got the normal force. All right, so in this particular case, the first one where you're trying to push it. You're trying to push it with enough force to get the block moving. So therefore, it's not actually moving just yet, Which means the kind of friction that you're going up against is going to be static friction. And the moment where you actually get the block moving, as we've seen in the previous videos, is that's equal to the F S. Max threshold. Then when you finally actually get it moving when it's moving with some constant speed now you're going up against kinetic friction because the velocity is not zero. So that's really the difference between these two diagrams here in one, you're going up against FS Max and then the other one, you're going up against kinetic friction. All right, so how do we then calculate these forces? Basically just use our F equals M A. So we have our f equals m a here. Now we just pick a direction of positive. It'll be to the rights for both of these diagrams here. So you've got f minus F s Max and then what's the acceleration? Well, the moment right, when I get the block to move, the acceleration is still equal to zero. So we're going to use a equals zero for this. Even though we're actually getting the block to move, we want to figure out the force that you need right before that happens when f is equal to F S, Max. So you have f is equal to F s. Max. Remember that has an equation that's mu static times the normal force. And so the normal force, if you're just looking at a block sliding horizontally, just going to be equal to mg, so basically F is equal to mu static times mg, and so this is going to be 0.7 times 5. times 98 and you're gonna plug this in, you're gonna get 35 Newtons. So basically, assuming that this is the coefficient of static friction, you have to push this block with at least 35 Newtons to get it moving. So then we can figure out the other force here by using basically the exact same method. So now we're gonna do the sum of all forces equals mass times acceleration. Here we know the acceleration has to be zero because the velocity is going to be constant. So your forces are F except now. It's not F s, Max, you're just using f k. So those have to cancel. So your f is equal to F k, which is mu k times normal. So your force is equal to mu k mg, right? Just like we had before. And so this is going to be 0.5 times 5. times 9.8. So now if you plug this in, you're going to get 25 Newtons. So let's talk about that. So we got these two different numbers here, which means that our answer is actually answer choice. See, it takes 35 Newtons to get this block to start moving. Once it actually is moving with some velocity. Then it only takes 25 Newtons. You don't have to push as hard to keep it moving at constant speed. So because the mu static is always greater than or equal to mu kinetic, what that means is that always is harder to get something moving than it is to keep it moving. This is something you've definitely experienced before in everyday life. You push something really, really heavy and you have to push really hard at first. But once you actually get it to move, basically the kinetic friction coefficient decreases. And so it's easier to keep it moving. You don't have to push as hard. All right, so that's it for this one. Guys, let me know if you have any questions.