welcome to our third example. Video on freed up body diagrams in this video will consider what are the effects of acceleration and velocity on a free body diagram. The quick answer to this is absolutely nothing, but that's not always evident. For example, here is a problem that will be looking at closely in the next section, which is We're riding in an elevator and we're standing on a scale and we want to figure out what is the scale going to read. Based on the acceleration of the elevator, we may be accelerating up. We could be accelerating down, or we could be even traveling at a constant velocity. It all depends on how the problem reads now. The difficulty in this problem arises from this that we go to draw everybody diagram and we say, Okay, well, I have forced to to gravity pushing me down always. Then I have a force pushing me up. That's due to the scale, and when I combine these two, so these are my only forces that are acting on this person in the Y direction and there's zero forces in the extraction, so it's actually all the forces when we go to write. This is Newton's second law. We say Okay, well, I have the four scale up, and I'm gonna minus the force due to gravity down. That has to be time equal to mass times acceleration in the Y direction. So notice that I didn't say Oh, well, the elevators accelerating up. Which means I need a mass times acceleration up or something like that. That would have been a mistake, because then I would have ended up with a third term on the left hand side. Here, remember the some of the forces. The net force is equal to the mass of the object multiplied by its acceleration, whatever direction we're working on. So we have f scale minus four. Studio gravity is equal to mass times acceleration or, in other words, the force of the scale is going to be equal to F G plus mass times acceleration Now say, we had said that the acceleration was up, then this would work perfectly. We would add in F G plus mass times acceleration. If we had said the acceleration was down, then we have too often options. We can either define a Y a Z equal to negative 1 m per second squared, for example, and then just plugged it in at the end. Or we could have started out by writing an equation that looks like this F scale minus F G is equal to negative m times a wife because we know that the acceleration is down and we know that the force due to gravity is down. Therefore, they have the same sign. When we write out the equation, F net equals mass times acceleration. So either one of these ways we call this A and B method and method be both work a za long as you remember that up here, you have to define acceleration like this. Well, down here, you only have to remember the magnitude of the acceleration. So if you are going to put the direction into the equation by putting in negative science to say that this is opposite to that, then you must do it consistently. If you're going to see, for example, we could have just said eff scale plus F G and then to find that F scale is positive. So it's greater than zero and that F G is equal to negative 9.8 meters per second squared times mass. So negative. M times g. So if we have defined that negative in there and then plug it in, we'll turn out just fine. No issue here. Um, but it does become more complex if we're not plugging in things correctly here. Noticed that when I do this math, then I would end up with a negative scale equals negative f g. So when I put it in here and still get positive, which is the same rule I had result I had before. So it's really up to you how you want to run this, whether you want to put the negatives into your equation, to define direction or if you want to put it into your variable definitions and then just plug in to do the math afterwards. Generally speaking, I will do it in the technique of method, because I like to see which direction things air pointed from the very beginning. And then I just plug in the raw numbers, the absolute values of all my variables at the end of problem

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## Video Transcript

welcome to our third example. Video on freed up body diagrams in this video will consider what are the effects of acceleration and velocity on a free body diagram. The quick answer to this is absolutely nothing, but that's not always evident. For example, here is a problem that will be looking at closely in the next section, which is We're riding in an elevator and we're standing on a scale and we want to figure out what is the scale going to read. Based on the acceleration of the elevator, we may be accelerating up. We could be accelerating down, or we could be even traveling at a constant velocity. It all depends on how the problem reads now. The difficulty in this problem arises from this that we go to draw everybody diagram and we say, Okay, well, I have forced to to gravity pushing me down always. Then I have a force pushing me up. That's due to the scale, and when I combine these two, so these are my only forces that are acting on this person in the Y direction and there's zero forces in the extraction, so it's actually all the forces when we go to write. This is Newton's second law. We say Okay, well, I have the four scale up, and I'm gonna minus the force due to gravity down. That has to be time equal to mass times acceleration in the Y direction. So notice that I didn't say Oh, well, the elevators accelerating up. Which means I need a mass times acceleration up or something like that. That would have been a mistake, because then I would have ended up with a third term on the left hand side. Here, remember the some of the forces. The net force is equal to the mass of the object multiplied by its acceleration, whatever direction we're working on. So we have f scale minus four. Studio gravity is equal to mass times acceleration or, in other words, the force of the scale is going to be equal to F G plus mass times acceleration Now say, we had said that the acceleration was up, then this would work perfectly. We would add in F G plus mass times acceleration. If we had said the acceleration was down, then we have too often options. We can either define a Y a Z equal to negative 1 m per second squared, for example, and then just plugged it in at the end. Or we could have started out by writing an equation that looks like this F scale minus F G is equal to negative m times a wife because we know that the acceleration is down and we know that the force due to gravity is down. Therefore, they have the same sign. When we write out the equation, F net equals mass times acceleration. So either one of these ways we call this A and B method and method be both work a za long as you remember that up here, you have to define acceleration like this. Well, down here, you only have to remember the magnitude of the acceleration. So if you are going to put the direction into the equation by putting in negative science to say that this is opposite to that, then you must do it consistently. If you're going to see, for example, we could have just said eff scale plus F G and then to find that F scale is positive. So it's greater than zero and that F G is equal to negative 9.8 meters per second squared times mass. So negative. M times g. So if we have defined that negative in there and then plug it in, we'll turn out just fine. No issue here. Um, but it does become more complex if we're not plugging in things correctly here. Noticed that when I do this math, then I would end up with a negative scale equals negative f g. So when I put it in here and still get positive, which is the same rule I had result I had before. So it's really up to you how you want to run this, whether you want to put the negatives into your equation, to define direction or if you want to put it into your variable definitions and then just plug in to do the math afterwards. Generally speaking, I will do it in the technique of method, because I like to see which direction things air pointed from the very beginning. And then I just plug in the raw numbers, the absolute values of all my variables at the end of problem

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