And now the physics of helping a friend move. We've all been there, somebody you haven't heard from like a year. And suddenly they're moving and they call you up. And say, hey, remember all those good times we had? Can you help me move? Well, normally I say something like, okay, if I only lift one-third of the weight. I mean, this isn't a 50-50 deal. I'm just going to do, let's go with a number of third to help us solve a problem. And the question is where should I hold something and where should my friend fold something? So let's sort of set it up mathematically, let's say we're carrying a really big carpet. It's rolled up, really heavy, like that. So this is a carpet and it's of a mass big M, because it's heavy. And if we agree that I'm only going to carry a third of the weight, we gotta be smart enough to know how to arrange ourselves to make that happen. because if we both held one end, we would share the weight, we would each have sort of half the weight. But if we arrange ourselves then it's possible to just hold part of the weight. So since there's bodies we want to solve it for two body variant, I'm going to give you one answer. One is you, me, the person holding one-third of the weight wants to be on the end. Okay, so I'll put in myself here with my arm holding on to the end. And we'll put it on an axis. And we'll put one end of the carpet at the origin where I'm holding the thing. And the other is the length L of the carpet. And the question really is where does my friend need to go so that I'm only holding a third of the weight? All the way at the other end, over here, in the middle. So I'll just draw the friend here and he's holding on somewhere, we will call X. He's holding on at position X. All right, and now we just gotta solve it, right? It's a statics problem, so imagine we're not moving it yet, we're just standing there perfectly still. We're holding this and I want this person to be two-thirds of the weight and me one-third of the weight. So statics, we can do the sum of the forces and in x, y and z equals zero, sum of the torques equals zero. So in this case we really just care about moving in on the y, we're balancing our forces on the y. So let's say sum of the forces in the y equals zero. So the forces in the y, you have the force applied by my friend here, Ff and that's up on the carpet. And then you have the force I'm having to apply, Fy, here up on the carpet. And then you have MG down. Okay, so there's two unknowns, one equation. Two unknowns, so we're not there yet, so here's an unknown. How much force am I applying, here is an unknown. How much force is, Wait a minute, this is the friend, and this is y means me, you, yes. Very confusing, you are here and your friends is here. This is an autobiographical story, but I'm applying it if it happens to you. Okay, so we also need to do torques. We also know that we have information based on the fact that we're not letting it pivot. And let's put the pivot point on us, on you, on me. And let's say the sum of the torques equals zero around that axis that I just identified here. So we don't have to worry about my force, about the Fy, about your force. We just care about how gravity is causing a torque because it's off the Axis. And how your friend's force is causing a torque because it's off the axis. So to see the gravitational one is pulling it clockwise, so that's a negative. So it's -mg and it's being applied at a distance L/2, right? Because the center of mass is in the middle of the carpet, so pulling it down -mg L/2. We're not doing all the detailed vector cross product on this one. And then the friend is applying a positive torque because it's pushing it in the counter clockwise direction. And they are applying a force F friend at a distance from the pivot point X. Right there, pushing it that way, those two have to equal zero. And now you say, yay, we got two equations. But we brought in another unknown, we don't know X. We don't know X, we don't know the force of the front. So we need a third equation. X isn't going to help us, Fx, know their torques help us. What we've forgotten is we have one more piece of information from the problem. Remember, I only want to lift one-third of the weight so we know our relationship between F friend and F you. So that is that, the force of the friend has to be twice the force that you apply, Fy. That's the part of saying one-third, right? So now we have three equations and three unknowns. So now we can get it, and what was that we want know? We want to know where, what we're actually solving for is X. We want to know where do I want my friend to be to make sure that I'm only carrying a third of the weight. So it's just three, it's just algebra here. Probably put this into this and say, because we want to get in terms of Ff here, so I'll replace Fy. So Ff + Fy is one-half Ff, is that what it did? Equals Mg, right, so that's, Yeah, so that's three halves, so Ff is two-thirds Mg. How did I screw that up? Let's see, [LAUGH] Ff + Fy, I'm writing this in terms of Fy. Yeah, let's just go with that, that looks right. So the force of the friend is going to carry two-thirds of the weight. Yes, of course yes, we knew that, yes. And I'm going to carry one-third of the weight, Fy is one-third Mg. Sorry, we don't edit here, I just talk, okay. Yes, that is correct, there's the requirement, is that I carry one third, he carries two-thirds. Okay, what we want is X, now I'm with us. Okay, so -Mg L/2 +, and now let's write Ff in terms of Mg. So it's two-thirds Mg + two-thirds Mg at X = 0, so now we just cancel the Mg's and we bring that over and get two-thids X = L/2. So times three-halves and we get that X = three-fourths L. So in this scenario, if you end up in this situation, you're back here and you're watching your friend over here. Make sure he's at three-quarters L and then he's caring twice as much as you. And it kind of physically makes sense. If he goes all the way to the end, then the numbers would be half, we would each be doing half the weight. The further back he comes, the more he's having to carry. So you could say, hey, why don't you come back a little bit? Pull it back, and they can carry little bit more.