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Solving for Forces Using Newton's Second Law

Patrick Ford
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every once we've gotten some practice with using F equals Emma. And in this video we're gonna take a look at how we saw for forces using Newton's second law using the same list of steps and equations. Let's check it out. So we got this 10 kg box and it's accelerating to the rights. It's being pushed by two forces. So I've got this box like, Here's 10 here. I actually know what the acceleration is. A equals nine and I got to force is one of them pushes to the left with 30 Newton's. So this is 30 here, and so I want to do is I want to find the other force. So what does that mean? Well, I've got one force pushing it to the left, but it accelerates to the right, so I know I have to have another force that's pushing it to the right as well. So this is my mystery for us here. This is f A, and I'll call this FB just like we have before, and I'm trying to figure out what s f A is, so I know I would have to use F equals M A. But first what I want to do because I want to choose the direction of positive and just like we have before, we're gonna usually gonna choose the right direction. So direction of positive is going to be the right like this. And now we get into our f equals m a here. So we have f equals m A. And remember that when we are expanding the sum of all forces, we have two rules forces along our direction of positive, written with a plus sign and against our direction of positive or written with a minus sign. So, for example, here we've got our f a, which is positive, even though we don't know who it is. And then we got our negative FB here because it points to the left and the Sequels. M A. Now we just replace the values that we know, right, So we have f a plus and this is gonna be negative. 30. And this is gonna be, uh, 10 times nine. So when we move the 30 to the other side, where you saw for you're gonna get 90 plus 30 equals 120 so that's your answer. You've got 100 and 20 Newtons here. So now let's take a look at our answer choices. Well, because all of our answer choices are positive that we don't have to worry about any signs or anything like that. We could just go ahead and choose. Answer be. That's going to be our correct answer. Let's move on to the second one here. We have very similar scenario here. The 10 kg box accelerates to the left this time. So we got this 10 kg box. Now you know the acceleration is to the left. Even though it points to the left, We're still going to write it in our diagram as six. But we're going to indicate it with the correct direction. And we have two forces. We've got one That's to the left. Sorry, once to the right, this is ethical. 70. We want to calculate the other force. So we have another force just like we had before. That accelerates to the left. There has to be a force that's pushing it to the left. So this is our mystery force here, and I'm gonna call this F B, and this is f A. So now we want to figure out f B in this scenario. So we got to choose our direction of positive. We actually don't need to, because we're going to assume the direction of positive is to the right that's given to us in the problem here. So now we write our feet was m A. So now we just expand the forces that we know, Remember, uh, along the direction of positive is written with a plus sign. And then we've got our negative FB here, and this equals mass times acceleration. So now we just replace the values that we know. We know this is 70 plus negative f b and then this equals 10. And then do we write six or negative six? Well, remember, assuming the direction of positive is to the right, our acceleration actually points left. So this section brings us up brings up an important point here. Whenever we write f equals m A. We're always writing the letter A as positive meaning you would never write em times negative A. For example, if you knew that it pointed to the left. However, when you actually know the value of the acceleration and the direction you're going to plug in the correct sign. So you plug in the correct sign if you actually know it. So, for example, here we've got six, but it's actually gonna be negative six, because our acceleration points to the left. All right, so now we've got here is we're gonna We're gonna rearrange and solve for this force. So we've got we're gonna move this over to the other side, and this is gonna be 70 plus 60 equals f B, which is 130. So if you take a look here, we've got FB is 100 and 30 Newton. So let's take a look at our answer choices. We actually have to. We have 100 and 30 and negative 130. So which one is right? Well, one of things you might have noticed here is that in previous videos, whereas when we saw for a we get a positive or negative, which is basically just the direction our final answer gives us the direction when you're solving for forces. However, you actually always get a positive number. Notice here how in these examples, When I saw for a right pointing force, I got a positive and a left pointing force. I still got a positive number. Always get positives because basically, you're solving for the magnitude of these forces. So what you do here is there's actually a couple of ways to solve this. You could indicate the direction by actually writing it into your answers. So you Professor knows that you know the direction of the force. Another thing we can do here is look at the look at the look at the problem itself. We're going to assume the direction of positive is to the right, which means if we get a left pointing force between these two answer choices, it's actually going to be negative. 130 Newton's. That's it for this one. Guys, let me know if you have any questions.