 But here's one problem that he had. And this is statics, torques, forces and stuff like this, right? Yeah, one problem Where you have a plank and it's being held up with a couple of strings There's a robot here. This is Gijo's robot. Okay, there's a robot here and And You've got the plank and the question is What's the tension in this string and this string given the following information? Okay, the mass of this guy, let's say it's 10 kilograms the mass of the beam is I Forget what they are. We'll just come up with the wrong 75 kilograms Okay kilograms The total distance Of the beam let's say at six the distance here Is 0.5 And this is 0.5 as well 0.5 as well The distance of the robot is let's say two meters And is there anything else? Is there anything else? Is there anything else? Um No, that would be it, right? So you're given this information. Hopefully I'm not missing anything. Hopefully this is coming out Let's see. Is this better? That's a little bit better six Two meters and these are meters all of it, right? 0.5 0.5 10 kilograms 75 Kilographs Oh, we do need this distance too. The distance That's probably oh, no, no, we got that figured out. Okay, cool. So the question is what's the tension here? At t1 and what's the tension at t2, right? So the way we laid down this problem the way we ended up doing this problem I like this problem. Okay, because it involves torques right so There's there's two types of static equilibrium problems you end up getting Usually in physics that you have to think about right one of them is You try to balance out the forces, right? So if you have here, let me show you this If you have an object, right? And there is like a force acting on it like this Okay, this pen is done. Let's grab a different Blue pen So if you have a force, let's say you have a box. There's a force one acting on this box here. There's another force Acting on this box here too. Let's say there's another force Acting on this box here, right? And this box weighs let's say 20 kilograms and it's not moving You ask yourself, okay, what? you know What's one of these forces, right? They'll give you this one They'll give you this one. They'll give you this one. They'll say if this thing isn't moving static What's this force here, right? And all you do with this type of problem is you say all the forces have to balance out So you break up this one Into its components, right? So this is f1 y F1 in the x direction you break up this one Into these components, right? And you say this is f3 x f3 y and this one, let's say it's just horizontal, right? Then all you say all you do you say All the y forces f1 y must equal to f3 y Oh, you got this guy too. Sorry my bad And you got mg here, right? And that's acting straight down. So you say f1 y Plus mg has to equal f3 y, right? Because that's one force acting now. That's another force acting now And that's the only force acting up. So they have to balance This plus this has to equal that if this thing is not moving If this thing is not accelerating let's rephrase because if it's moving at constant speed, this is also true But let's say it's static, right? And in terms of the x direction The weight doesn't come into play because that's acting straight down Then f1 x plus f3 x have to equal f2 in the x direction, right? The forces have to balance out When it comes to torques, right? They come into play when We're not treating everything As a point source, right? There's distances involved when there's distances involved You do the same thing the forces In one direction have to equal the forces in the other direction, right? But It's not just the forces. They have to equals the torques of them. They have to equal, right? So the force times the distance of this times force times the distance of this Have to equal each other, okay? So over here Let's erase this What you do with this is you say, okay, what are all the forces Acting on this object Right on this system So there's This guy here acting up. That's t1 There's this guy here acting up All right, this is t2 There's the robot's mass Weight acting down Which is this guy And the only other thing we have here Is the plank Acting down on this, right? And what we do with the plank is we take the plank as being a Point source and we say that's in the middle Acting down Okay Now consider this Which one of these t1 or t2 is going to have a more of a tension? Right because if we had this let's assume we had this model Instead of all this stuff on it. Let's say we had a plank And it was laid out the same way and this was a string and this was a string What would t1 and t2 be what could you say about t1 and t2? right If this is a plank t1 And t2 they would be equal Right if this is a homogeneous plank That it's not heavier on one side or anything These two would bear the Same amount of weight to hold this guy up, right? That's why you know I'll use gloomy reference But when people are carrying coffins You put three people on one side in general and three people on the other side So no one's really carrying too much weight unless they're different heights, right? You try to when you're getting people to carry something heavy You want everyone to be approximately same height. So the weight distributes evenly, right? Unless they're willing to either bend down or lift up and that could create some problems But if you have a homogeneous plank and you got strings holding it up The tensions in the strings will be the same. However, let's assume we had this thing What would happen if you put a weight here? right Wherever you put the weight whichever string is closest to That string is going to carry more weight The tension in here would be more than the tension in here now, right? That would make sense So for the system t1 Is a bigger force than t2 Okay now if you notice we have Two unknowns here to a certain degree. We want to find both of these and we don't have any specified pivots when it comes to torque and pivots are Basically in torque type of problems are you basically put something as a hinge And everything else can rotate around that. So if you have a plank Here if you have a plank And if this thing's sitting against the wall This would be your pivot and then you could have forces hitting here hitting here And you would try to see if it's an equilibrium then this has to equal this times the distance has to equal this Times the distance. That's what the whole principle of torque is, right? So if this force is one, this is force two And this distance is d2 and this distance is d1 And if this thing is in equilibrium, it's not moving what you would say is F1 d1 has to equal F2 d2 right And always keep in mind if you want to know how torques come to play Just imagine if you have to move a gigantic boulder, right? Now you could sit there and try to lift it up and throw out your back You could try to push it this way if it's sitting on a hinge or On a on a on a slope you could maybe push it over, right? But if it's all flat ground is large, you're gonna have a hard time So how do you move something heavy large? If you can't do it physically just manually yourself without any tools Well, you go grab another rock you put it in front of it You go grab a metal rod or something like a lever and you stick that thing in the Into this under this big rock and you go use the little lock rock as a hinge Why am I doing this? I could draw it, right? So if you have this gigantic rock you want to move you put another rock here You bring a hinge here, right? And you stand here and go pull the sucker down and you can move that, right? If this thing's longer, it's easier to do if you try to pull down here Right, that's going to require you giving a lot more energy, right? It's one of the basic tools that we have That we've known about humanity forever, right? So this would be your hinge So if you want to think about in here, this would be your hinge This is your hinge So if these two If this is not moving, if this is in equilibrium, this has to equal this Then the force here would be bigger than the force here, right? Because this is further out So it's sort of thought process as well You want to know how the system operates, right? So you're going to keep all this in mind The more problems you do this way The more little nuances you remember about specific types of systems Like there's a whole mindset behind people who are inventors, right? It requires to give the same amount of energy but a different amount of force Yeah, right? And the torque is what we're talking about, right? The torques have to equal each other to a certain degree So take a look at this So for us over here One of the things we do when it comes to physics types of problems We try to simplify problems for ourselves, right? We try to make things easier The way we try to make things easier We either label things in a certain way where they make sense Or we label things in a certain way on a drawing to eliminate the unknowns, right? So we try to get rid of the unknowns and solve this A more simplified system than the one that's being presented And one thing we can do when we're trying to solve the system To find out what the tension is here and what the tension is here Is we specifically eliminate either T1 or T2 But putting in an imaginary pivot at one of these locations So all of a sudden, if you have a drawing, if you have a pivot If you're applying force on the pivot Nothing's going to happen with this, right? So what we do is for the first problem We're going to eliminate T1 And we're going to try to solve T2 And we're going to put a hinge here Okay, so we say, you know what? Just imagine that this system was exactly this But this point was locked, right? We're making it a hinge And we're going to reference everything to this point Then what we have, I'm going to redraw this down here Let me bring out a green I'm going to redraw this thing here Just with the forces that we're dealing with, right? So we're making this a hinge, right? Here's a hinge This is going to be difficult to erase, I think Here's a hinge And then I'm going to draw the plank here, right? Here's our plank So we have T1 going up like that Oh, sorry, T2 going up like that We've got the weight of this guy coming down And we've got the robot And it's the center of gravity is here But we're just going to put it on the plank Working down like this So the torques These two torques That the torque that is being applied at this point, at this point Has to equal the torque at that point For this thing not to move Right? So all we need now is the distances here So this distance, that was 0.5 From here to here is 2 So this is 1.5 The distance here If the whole thing is 6, right? And this is 0.5 Right? Well, if the whole thing is 6 Well, we can't do the middle at 3 Right? Because we've got to account for this So that's 0.5 So the distance here is I should have made the numbers easier To here And there's 0.5 there So actually we have to account for this as well Here, let me erase this Let me put it down here so we see So if we go from here to here Right? Because the plank is going up there That's 6 minus 0.5 Which is 5.5 meters The center of gravity of the plank Is going to be in the middle of this plank Excluding the weight here Because that's on this side of the hinge Right? So 5.5 divided by 2 Well, 5 divided by 2 is 2.5 0.5 divided by 2 is 0.25 So it's 2.75 meters So this distance here is 2.75 meters And this distance here Starting from here, that's 0.5 So that distance there is 5 Right? I hope you see that That's okay I'm just going to erase this So this distance here Here, let me draw it here Is 5 meters Okay We're almost finished laying down this problem So the equation for this Is going to be Let's call this r for robot Let's call this plank for the plank And that's t2 Right? So the torque on r plus the torque on the plank Has to equal the torque on t2 So the torque on r is force times distance Right? Well, the force on this is mg The force on this is mg as well But the m varies So this is the mass of the robot Mass of the plank Mass of the robot Here, let's write down the formula Mass of the robot Times gravity Times the distance which is 1.5 Plus The force the mass of the plank p Times gravity Times the distance which is 2.75 Has to equal t2 The force at t2 Times 5 Ah, you can barely see that Too light, too light mg 1.5 Plus mg 2.75 Is equal to t2 Times 5 Right? And then all we do is just plug in The mass of the robot is 10 Gravity is 9.8 The mass of the plank is 75 Times 9.8 Those are just numbers You divide by 5 And you got your tension on 2 Right? How do you find this one? You move your pivot from here And you put it there You measure everything from here This way The distances, right? And you solve for t1 Nice problem Really Fun problem to do You gotta love physics You gotta love physics Right? Physics is just It's just brilliant Really Physics is just brilliant