Anderson Video - Free Body Diagrams

Professor Anderson
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>> Hello class, Professor Anderson here. Let's talk about free-body diagrams. This is something that's going to be important when we analyze force problems. And the idea with a free body diagram is very simple. The first step is to make the object of interest into a dot. And the second is identify the forces acting on it. All right, so let's see if we can do that for a very simple example. Let's say that we have a box hanging from a wire. So here is our box. It's hanging from a wire. That's it, okay? The object of interest is the box, so we're going to make that into a dot. What are the forces that are acting on my box? What's one of the forces that's acting on the box? Christian, I know you have a thought there. >> (student speaking) So, you have gravity, so the mass of the object. >> Okay, we have gravity. And gravity is in fact equal to MG, right? All right, what else do we have acting on it? Yeah, Christian? >> (student speaking) Tension in the wire? >> Tension in the wire. Which way is the tension in the wire going? >> (student speaking) Upwards? >> Upwards. Okay, now if the box is at rest, then I want to draw my two arrows to have the exact same magnitude. And if they have the same magnitude, then they're going to perfectly cancel out, and there's going to be no acceleration of the box up or down. So whenever you draw force diagrams and your object is at rest, try to draw those arrows the same length. This will help you visualize it. All right, let's make it a little more complicated now. Let's hang it from two wires. And let's say that it looks like this. Now, I need to draw my free body diagram for that box. I still have F gravity going down. But how should I draw the tension in the wires? What do you think, Samantha? >> (student speaking) At half of the magnitude of the line for the gravity? >> Okay, half a magnitude of that. Maybe. Should I draw it like this? >> (student speaking) No. >> No? You don't like that. All right. How shall I draw it? >> (student speaking) Out to the sides? >> To the sides? Okay, like that? >> (student speaking) At an angle. >> Okay, I'm not following directions very well, am I? Okay, at an angle. Any particular angle you like? >> (student speaking) Like the one in the original problem? >> Like that one? >> (student speaking) Yeah. >> Yeah. Absolutely. Maybe something like that, okay? Tension has to act along the wire, right? As you pull on something, the tension has to act directly along that wire. So that looks pretty good. Now do I think that these arrows are about the right length? What do you think? Have I drawn those arrows about the right length? >> (student speaking) Yeah. >> Maybe, right? They're certainly not half of gravity, but they can't be half of gravity because they're at some angle. What we want to know is, is the vertical component of tension going to be enough to combat gravity? And so, that's the section that has to be half [inaudible]. Which means that this section has to be longer than that. All right, let me ask you a follow-up question. Let's say we hang our box from two wires, like so. What are the forces that are acting on the wire? Well, it's still gravity going down. But now tension we said is along the direction of the wire. So we need tension in this direction, then we need tension in that direction. And now let me ask you a question. Can these wires be horizontal? In other words, you have a wire going from one side of your dorm room to the other, and you're going to hang your physics textbook on that wire then use something with that to shoot darts at it, right? Sean, what do you think? Can these wires be horizontal? >> (student speaking) I don't think so because there is no force to counteract to the downward force of gravity. >> That's right. The tension here is perfectly horizontal. We've got a problem, right? We can't make the net force here equal to zero. We don't have anything to combat gravity. And so, the answer is no. That wire cannot be horizontal. And in fact, it can't be horizontal, no matter what the tension is in the wire. So even if I take a giant steel cable and I crank on it at one end with a winch, and now I hang something like a textbook on it, it sags -- a little bit. Okay? Not a lot but a little bit. It cannot stay perfectly horizontal. You have to have some angle associated with it which gives you a slight vertical component [inaudible]. Kind of weird to think about, right? When you think about those giant cables which that are holding up the Golden Gate Bridge, right? Those things are pretty big. But if you stand at one end of those cables and look along the cable, it sags. It certainly sags. It always sags a little bit. Okay, any questions about the stuff that we've talked about so far? Anything else that you guys want to talk about before we call it quits for today? Okay, hopefully this stuff is clear. Certainly, if it's not, come and see me during office hours. Cheers.
>> Hello class, Professor Anderson here. Let's talk about free-body diagrams. This is something that's going to be important when we analyze force problems. And the idea with a free body diagram is very simple. The first step is to make the object of interest into a dot. And the second is identify the forces acting on it. All right, so let's see if we can do that for a very simple example. Let's say that we have a box hanging from a wire. So here is our box. It's hanging from a wire. That's it, okay? The object of interest is the box, so we're going to make that into a dot. What are the forces that are acting on my box? What's one of the forces that's acting on the box? Christian, I know you have a thought there. >> (student speaking) So, you have gravity, so the mass of the object. >> Okay, we have gravity. And gravity is in fact equal to MG, right? All right, what else do we have acting on it? Yeah, Christian? >> (student speaking) Tension in the wire? >> Tension in the wire. Which way is the tension in the wire going? >> (student speaking) Upwards? >> Upwards. Okay, now if the box is at rest, then I want to draw my two arrows to have the exact same magnitude. And if they have the same magnitude, then they're going to perfectly cancel out, and there's going to be no acceleration of the box up or down. So whenever you draw force diagrams and your object is at rest, try to draw those arrows the same length. This will help you visualize it. All right, let's make it a little more complicated now. Let's hang it from two wires. And let's say that it looks like this. Now, I need to draw my free body diagram for that box. I still have F gravity going down. But how should I draw the tension in the wires? What do you think, Samantha? >> (student speaking) At half of the magnitude of the line for the gravity? >> Okay, half a magnitude of that. Maybe. Should I draw it like this? >> (student speaking) No. >> No? You don't like that. All right. How shall I draw it? >> (student speaking) Out to the sides? >> To the sides? Okay, like that? >> (student speaking) At an angle. >> Okay, I'm not following directions very well, am I? Okay, at an angle. Any particular angle you like? >> (student speaking) Like the one in the original problem? >> Like that one? >> (student speaking) Yeah. >> Yeah. Absolutely. Maybe something like that, okay? Tension has to act along the wire, right? As you pull on something, the tension has to act directly along that wire. So that looks pretty good. Now do I think that these arrows are about the right length? What do you think? Have I drawn those arrows about the right length? >> (student speaking) Yeah. >> Maybe, right? They're certainly not half of gravity, but they can't be half of gravity because they're at some angle. What we want to know is, is the vertical component of tension going to be enough to combat gravity? And so, that's the section that has to be half [inaudible]. Which means that this section has to be longer than that. All right, let me ask you a follow-up question. Let's say we hang our box from two wires, like so. What are the forces that are acting on the wire? Well, it's still gravity going down. But now tension we said is along the direction of the wire. So we need tension in this direction, then we need tension in that direction. And now let me ask you a question. Can these wires be horizontal? In other words, you have a wire going from one side of your dorm room to the other, and you're going to hang your physics textbook on that wire then use something with that to shoot darts at it, right? Sean, what do you think? Can these wires be horizontal? >> (student speaking) I don't think so because there is no force to counteract to the downward force of gravity. >> That's right. The tension here is perfectly horizontal. We've got a problem, right? We can't make the net force here equal to zero. We don't have anything to combat gravity. And so, the answer is no. That wire cannot be horizontal. And in fact, it can't be horizontal, no matter what the tension is in the wire. So even if I take a giant steel cable and I crank on it at one end with a winch, and now I hang something like a textbook on it, it sags -- a little bit. Okay? Not a lot but a little bit. It cannot stay perfectly horizontal. You have to have some angle associated with it which gives you a slight vertical component [inaudible]. Kind of weird to think about, right? When you think about those giant cables which that are holding up the Golden Gate Bridge, right? Those things are pretty big. But if you stand at one end of those cables and look along the cable, it sags. It certainly sags. It always sags a little bit. Okay, any questions about the stuff that we've talked about so far? Anything else that you guys want to talk about before we call it quits for today? Okay, hopefully this stuff is clear. Certainly, if it's not, come and see me during office hours. Cheers.