6. Intro to Forces (Dynamics)
Types Of Forces & Free Body Diagrams
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Hey, everyone. So now that we've covered Newton's laws and the main types of forces that we'll see in this chapter, in this video, I wanna cover how to draw what's called a free body diagram. Free body diagrams are really important because they're simple diagrams that help you organize all the forces that are acting on objects in a problem. And more importantly, some problems will ask you explicitly to draw one of these diagrams as a first step. So even if your problem doesn't ask you to do it, you should do it anyways because it will always help you solve the rest of the problem. So let's go ahead and check it out here. So a free bond diagram which is sometimes written as FVD shows only the forces that are acting on a single object, and that single object is usually drawn as a dot or a box. Right? So some professors will just do dots. Some of them will do boxes. If they have a preference, you should stick to it. If not, you should just pick 1 and choose. I'm just gonna go ahead and draw mine as a dot here. Alright? So we're gonna draw basically this diagram of, you know, a hand with a rope pulling the box. We're gonna turn that into a very clean diagram showing only the forces acting on an object. And we're gonna do it by drawing all of the forces as arrows from the object's center, which we always do, but what I've done here is I've given you a particular order in which you consider all of the forces here. You won't see this in your textbook, but this is just an order that I think is the easiest so you don't lose track or forget any. Alright? So let's just go ahead and get started here with this example. I've got a rope that's sort of pulling this box across a rough surface like this. So the first force we're gonna consider is the weight force. And remember the weight force is always acting on any object whether it's resting or in the air unless otherwise stated. Right? So we're gonna draw this arrow here and we're gonna draw it basically straight down. Right? Presumably that's towards the Earth's center. So that's my weight force. Alright? So let's weight. So the next pair we're gonna consider are applied forces and tensions. Remember applied forces happen anytime you have something that's directly pushing or pulling the object. Do we have that? Well, you might think that this hand here means that there is an applied force, but actually there isn't because, remember, this hand here isn't applying a force on the rope. But remember that this applied force sort of gets transferred through the rope, and really what happens is that there is a tension that caused the that's caused on the box. So really there is a tension force, but there is not an applied force here. Be very careful when you consider these kinds of forces because you don't wanna double count them. Alright? There is an applied force, but that's sort of getting transferred through the rope and it's appearing as a tension. That's what's directly pulling on the box. Okay? So no applied force, but there is a tension. And so the next we're gonna consider is a normal force. This happens anytime you have 2 surfaces in contact. Do we have that? Well, yes, we do because the box is sort of resting on the ground like this, so there is a normal force and it's gonna be perpendicular to that surface. So in this case, it's gonna point straight up because we have sort of a 90 degree angle like this between the surface. The last thing we're gonna do is consider any friction, right? We have normal force. So when this happens, when you have the 2 surfaces that are in contact that are rough. So for the sake of argument here, we're just gonna assume that this this surface here is rough. So you're trying to pull this box over here, but there's gonna be some friction. Now what happens is the box wants to slide over here in this direction. It's not gonna go up like that in that angle here. So what happens here is that the friction force is usually gonna oppose that direction of motion here. So in this case, what happens is you do have a friction force, except it's gonna point to the left and try to slow the box down. Alright? So notice how this diagram gets really messy. And what happens is in more complicated problems, if you have lots of errors, you could lose track of them. And that's the whole point of a free body diagram. We're gonna take this and we're gonna turn it into a very clean diagram showing only the forces. So we have the dot, we've got the weight force, we've got our tension like this, we've got our normal force that points up, and then we've got our friction force that points off to the left. This is the free body diagram here. Alright? So, again, really important because it shows only the forces, but that's always how we're gonna draw this. Alright? That's all there is to it. So now what we're gonna do is we're gonna take our free body diagrams and what we know about forces. And for these example problems, we're gonna calculate the acceleration of these following situations. But what we're gonna do first is we're gonna draw the free body diagram. Alright? So let's get to it. So in this first example, we're gonna push a physics textbook to the right with some force. You're gonna know this with also gonna be some kinetic friction. Alright? So again, let's just stick to the order of the, forces. So what I'm gonna do first is I'm gonna draw a free body diagram. So again, I'm just gonna stick to a dot like this. First one is weight. So there's gonna be weight force and it's gonna act straight down presumably towards the Earth's center. We don't know. We can just always assume that it's down. Okay? And, let's see. So we've got a weight force. Is there any applied force or tension? Is there anything directly pushing or pulling my object? Well, yes, there is because you're pushing your hand, right? You're putting your hand in a box and pushing to the right. So there's gonna be an applied force that acts over here to the right. We actually know what that applied force is. It's 20. Okay? Now is there a normal force? We have 2 surfaces in contact. Well, yes, we do because the box is resting along the table. So therefore the normal force just like it did up in the previous diagram is gonna point up. That's gonna be my normal force. And last but not least is there friction? Again, there's gonna be friction because we have explicitly that's told to us that there's a force of kinetic friction. Now what happens here is that the box wants to go this way because I'm pushing it to the right. The friction force wants to oppose that motion, so just like it did above the friction force is gonna point to the left. Alright? Now that's gonna be my friction. What's really important here is that because we know the magnitudes of the forces, we draw the arrows sort of correctly. The applied force is 20 and the friction force is 8, so this arrow should be longer. Alright? That's the only thing to know about, free body diagrams. Alright. So that's your free body diagram right here. That's just that's all there is to it. In fact, that's what you're gonna do a lot of times for the first steps in problems. So we wanna do is calculate now the acceleration. How do we do that? We just do stick with f equals m a Newton's laws. So we've got f equals m a. We're looking for the acceleration here. We're just gonna expand all the forces. Now what happens is the the forces in the y axis like the weight and the normal force aren't gonna cause it to accelerate left or right. So we only really have to look at the forces in the x axis here. So I'm just gonna pick a direction of positive, you know, usually to the right is gonna be positive for me. So that means that my my 20, to the rights plus the eights to the left, which picks up a negative sign here, is gonna equal mass times acceleration. So in other words, 2 a. Alright. So you just go ahead and, work this out. It's gonna be 12 equals 2 a, and the acceleration will be 6 meters per second squared and that's gonna be to the right because because we got a positive number. Okay? That's how we do it. Just go ahead and pause the video and see if you can try this next one on your own. Alright? Okay. So for this next one, we're here we're gonna use a rope and we're gonna pull a box upwards. Alright? So we're gonna pull this box upwards and again what I'm gonna do is I'm gonna write I'm gonna draw a free body diagram. So get my dot right here. First force, is there a weight force? Yes. Even if there's nothing even there's just nothing underneath the box, even if it's floating in air, it always gets a weight force. So that's gonna act straight down. So that's my weight force. We actually know what that weight force is. It's 50. What about any applied forces or tensions? There's no applied force here because the hand is on the rope, but that means that there is a tension. Right? So there's gonna be a tension along the rope going upwards, and we actually know what that tension force is. This tension force is 90. So again, because we know the 90 here, because we know the magnitude here, then we have to draw this arrow as being a little bit bigger than the weight force. Alright. So that's the tension force. And what about any normal forces or friction? Remember that only happens when you have 2 surfaces that are in contact, but if this rope or this box here is just sort of like suspended in air, there's no surfaces in contact, so there's no normal force and also no friction. Okay? Alright. So that's basically your free body diagram, just these two forces here. So if we want to calculate the acceleration, we just have to stick to the very same step that we did before. If we want to figure out a, we just have to do the sum of all forces. Right now we're just gonna look at the y axis equals ma. Okay? So what I'm gonna do is I'm gonna choose upwards as my direction of positive. So I've got my 90 plus my 50, which picks up my minus sign is gonna equal, and let's see, the mass is 5 kilograms, so this is gonna be 5a. Okay, so this is just gonna be 40 equals, 5 a. And so last but not least here, what you have is that the acceleration is equal to 8 meters per second, And because again we've got a positive number that just means that the box is gonna accelerate upwards like this. And that makes sense. Your force is 90 newtons. You're pulling on it higher harder than the boxes weight, so it's just gonna go upwards. Alright folks, that's it for this one.
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