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Stacked Block Tied to Wall

Patrick Ford
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Hey guys, how's it going? So we got this problem here, we've got these two blocks on top of each other, but there's a twist to this one, which is that the block is actually tied to the wall. The idea here is that we're gonna be pulling on this first block, the bottom block with a force of 45 newtons. And we want to figure out the tension that's acting on block A. What is the tension force that's basically keeping block A. To the wall. So let's go ahead and get started here. We know we're gonna have to draw our free body diagrams. So, let me do the first block A. So we've seen this kind of thing before, we have the mass times gravity, that's the weight force of A. Then we have basically attention force. This is basically what we're trying to find here. We have a normal force because these two services are in contact, that normal force is between the two blocks. I'll call it N. B. A. So if these were the only forces that are acting on the object, then obviously the block would have to accelerate to the right. But that doesn't make any sense. It's going to be tied to the wall. There has to be a force that acts to the right, and this is gonna be the force of friction. So, let's go ahead and talk about Block B. Now, Block B is gonna look like this, It has a weight force that acts down, this is MBG. Then we have the applied force. This f. We know that F is 45. And we also have the normal force is there's two of them. There's the normal force on block B from the ground and there's also the action reaction pairs. This is N A B. Right? So these two things are action reaction pairs. There is another action reaction pair. Because we know that if A has a friction force that acts to the right, then B has to have a friction force that acts to the left. So these two things are opposite of each other. So what I'm gonna do is I'm gonna call this F A. B. It's the friction between the two blocks and it has an action reaction pair as well. This is gonna be F A. B as well and these two things have to be equal to each other. However, there's also one more friction force that we have to consider Remember that the coefficients between the two blocks is going to be 0.2. But we're told that the coefficient between all surfaces is 0.2. So that means that there's also some friction because of the bottom surface. So, because this block is being pulled and moves to the rights with some velocity, that means that we also have another friction force that acts to the left. There's two friction forces that actually cause this thing or that actually act backwards. All right. Now we just move on to figuring out what type of friction we're dealing with. And there's two clues that help us out here, we know that we're only given the coefficient of kinetic friction in this problem and we're also told that the block B. Is gonna move to the right. So there's some velocity here, which means that all of these frictions are going to be kinetic friction. So these are these are all kinetic frictions. So I'm gonna call this F A B K. F A B K F B K basically just indicating that they're all kinetic frictions. So let's go ahead and start writing our F. Equals M. A. We would start with the simplest object here, but remember which is actually object A. And also remember that we're trying to figure out the tension force. So we're gonna start with object A. So the sum of all forces equals mass times acceleration. So we just pick a direction of positive. Let's go ahead and choose the rights. Which means that we have F A. B. K. The kinetic friction force between the two blocks is equal to minus the tension is equal to mass times acceleration. Now, what is the acceleration of block A. Well, here's the thing if block A. Has has this tension force that's tying it to the wall then that means that the acceleration of A. Is equal to zero. So there is no acceleration and this thing has to be equilibrium because it's tied to the wall. All the forces have to cancel. So we have our kinetic friction force is equal to the tension. Now this kinetic friction force is kind of weird because we usually have kinetic friction when something is moving. But it really what happens is that the surface, the relative velocity between these two surfaces is moving. That's why we have some kinetic friction even though Block A actually stay still. Okay, so we we expand this force. The friction between the two surfaces is gonna depend on the normal between the two surfaces. So we're gonna use N. B. A. And the Sequels of attention and remember we can solve this N. B. A. And this is really just equal to the weight force. These two forces have to cancel out because the block doesn't accelerate vertically, right? So we have everything, we need to figure this out. This is really just gonna be mass times gravity. This is gonna be the tension force. We don't even have to go into block B. We can just go ahead and sell for this. This is gonna be zero point to the massive A. Is five G. Is 9.8. If you go ahead and solve for this, you're gonna get 9.8 newtons. And that's the answer. That's the tension that's holding this block to the wall. So that's answer choice B. So that's it for this one. Guys. Hopefully that made sense