Free-Body Diagrams

by Patrick Ford
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Hey, guys. So now that we've covered Newton's laws and the most common types of forces that we're gonna see in this chapter in this video I want to show you how to draw a free body diagram. Free body diagrams are really useful because they help us organize what's happening inside of a problem. And more importantly, a lot of problems are going to ask you specifically to draw this diagram as a first step. So even if a problem doesn't ask you to draw when you're still gonna do it anyways, because going to help you solve the rest of the problem, So let's get started. What is a free body diagram anyways? Well, the symbol or the abbreviation is F B D, and it's really just a diagram that shows the forces that are acting on a single object, and we're gonna draw that single object as either a dot or a box. Some professors will do dots and we'll do boxes. Just pick one double check with your professor and then stick to it. So we're gonna draw all the forces that are acting on this object, and we're gonna draw all those forces as arrows that are coming from the objects center. Now remember, there's a lot of different types of forces. What I've done here is I've given you an order. So we should go down this order here so that you're not forgetting any of those forces. So we've got this complicated diagram here and we're gonna We're gonna go ahead and navigate through all of those forces and come up with a free body diagram. So let's get started. The first one is the weight force. Remember that the weight forces just the gravitational force from the Earth. It's always acting unless it's otherwise stated. So what happens is this box here has a weight force and that's going to act towards the Earth Center. Now, if you don't know where the earth is, you can usually just assume that it's straight down. So this is going to be the weight force like this. So the second one we're gonna look for is any applied force or tension. Remember, you have an applied force. Whenever you have someone or something that is directly pushing or pulling that object, you're gonna have attention. Anytime you have a rope or string or something like that. So what happens here is we have a hand that is exerting a force on this rope here. Now you might think that's an applied force here. But what happens is this Hand is actually doing is exerting an applied force on the rope. But remember that that applied forces traveling through the rope so that the rope is actually the thing that's pulling the box. So, really, what happens here is there's not an applied force. There's just a tension force because the apply force is actually traveling through the rope, so there's no applied force in this problem. But there is attention, all right, so let's go to the third one. A normal force, remember, a normal force is going to be perpendicular or 90 degrees, and this happens whenever you have two surfaces that are touching each other or in contact. So in this case, we've got this box that is touching the table top or the floor or something like that. So those two surfaces are in contact. And remember that the weight force is pulling this object and it's pulling this box down to the ground, and the normal force is going to be a response, a reaction to that surface push. And it's going to go straight up like this because that makes a 90 degree angle with the surface. So that is our normal force. Now, the fourth one we're gonna look at is the friction. So if those two surfaces are now rough, so if you have these things rubbing against each other, that's when you're gonna have some friction. So what happens is this tension right? This hand is pulling this object up into the right. So what happens if this box actually wants to slide this way? Right? It's not actually gonna go up like that, but it is going to go off to the right like this. So you're gonna have some friction for us. It's going to be opposite to the direction that it wants to move for that motion. And so it's going to move to the left like this, so it's gonna be our friction force. So notice how this diagram is kind of messy. So one thing we can do is we can actually just say we're going to just draw this object as a dot like this, with all the forces that are acting on the object. So we've got the weight force like that. Then we've got the tension, and then we've got our normal force. And then finally, we've got our friction force like this. So this is a free body diagrams, just a dot with all the forces in the directions labeled like that. So that's what we're gonna do here. All right, That's really all there is to it, guys. So let's go ahead and take a look at these examples. We're gonna draw a free body diagrams for both of these situations because we're gonna have to calculate the acceleration for the following scenarios. So let's go ahead and get to problem A which is we're gonna push our 2 kg physics textbook to the right with the force of 20 Newtons. And then we also have some kinetic friction. So remember, the first thing we're gonna do is draw a free body diagram, and we're just gonna draw it as a dot or a box. I'm just gonna go ahead and draw this as a dots. Now, we're just gonna go ahead and stick to the order, remember that there is a weight force, so we're gonna label that weight force like this that's gonna be weights. And we also have a A force to the rights. So we're gonna look for anything. Applied forces or tensions were told that you are pushing the textbook to the rights with a force of 20 Newtons, so we know that that's going to be an applied force. This is my f A. And we know this is equal to 20 Newtons and then we also have the force of kinetic friction. Now there isn't any tension or anything like that because we're not told that there's a rope or string or a cable. So there's no tension. But there is a normal force because if you have this physics textbooks that is on a flat table, then you're going to have a normal force. That is a response to the surface push in this case, the weight force like that. So we know that's the normal. And then finally, we have a kinetic friction. We know that that is going to be eight Newtons Now the box is gonna want to be pushed to the right, so friction is going to be opposite to the direction of motion. It's going to go to the left like this. So we know this friction force is gonna be eight Newtons. So this is our free body diagram. So now that we have a free body diagram, we're going to have to calculate the acceleration for both of these objects. So really, what we're looking for is looking for a Now remember that we have to calculate the acceleration by using f equals m A. So we're gonna start off with the sum of all forces equals m A. And now we just have to pick a direction for positive and then use f equals m A. So I'm just gonna choose the right to be the positive direction. So what I've got here is I've got a 20 Newton force that's positive. And then I've got an eight Newton force that is to the left. So that's actually gonna be a negative eight Newtons. And this is going to be equal to the mass, which is two times the acceleration. So what I've got here is I've got 12 equals two a. And so therefore what I've got is that the acceleration is equal to 6 m per second squared, so this is gonna be our acceleration. All right, so let's go ahead and move on to the second one. We've got a rope. We're gonna pull box upwards with the force of 90 Newton's the boxes, we use 50 and the mask is 5 kg. So we're gonna start off with the free body diagram. We know that That's just gonna be a dot like this. The first thing we're gonna look at is the weight force. So when we have this weight force that's acting straight down, we know this weight force is equal to 50 Newtons, so this is gonna be 50 downwards like this. Now we're going to look for any applied force or tensions, so we don't have an applied force. But we are what we are told. They're using a rope. We are pulling a box upwards with the force of 90 Newton's. So now that means that we have a forced upwards like this. This is going to be my tension because we're using a rope and it's going to be 90. Newton's like this now. We're not told that this that this box is on some kind of a surface like a table or anything like that. So there isn't no there's a normal force because there's no two surfaces that are in contact with each other. And so because there's no two surfaces in contact, there's also no friction. So really, these are just the only two forces that are acting on this object. So now that we have a free body diagram, we're going to calculate the acceleration, just using the exact same steps that we did before. So to calculate the acceleration we're gonna use f equals m A. So we're gonna pick the direction of positive, which is going to say upwards as the positive direction, and so are F equals. Emma says that 90 Newton's upwards plus the 50 Newtons downwards, which is gonna be negative, is equal to the mass, which is five times the acceleration. So we've got 40 equals five a. And so once we divide, we're just gonna get that. Um the acceleration is you go to 8 m per second squared and that is going to be 8 m per second squared upwards. Because this this force is the stronger one. That's it. That's it for this one. Guys, let me know if you have any questions