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Concept #1: More 1D Equilibrium

Transcript

Hey guys so in this video I want to go over a bunch of examples of equilibrium problems and we're going to do this in the mix of X. axis and Y. axis but it's still going to be one dimensional equilibrium as I'm going to show you I'm also going to introduce pulleys and spring scales Let's get started so here I have that both of these systems are at rest or not moving and I want to draw free body diagram and find all forces on all objects So first things first this is a pulley it has a cable around it and the idea here is that if one of these mass was heavy the other then this thing would not be at equilibrium lets say if this was a 3 This would accelerate this way OK but because these two masses are the same masses and this thing was not originally moving it's not going to move it's going to stay as it is right so the first human to do is draw the masses of the weights of all of these There's 3 objects this pull is a mass of 3 so it has an mg pulling it down OK This force is a 19.6 because it's just two times nine point eight these are the mg's. This is 19.8 as well but this one is a 3 kilogram so this is going to be 29.4 okay. what else this is an equilibrium so there has to be a force pulling it up OK There has to be a force pulling up I'm going to call this.T1 and this T1 has to be 19.6 here I have to have a force holding this up as well I'm going to call this T2 T2 going to be has to be 19.6 as well I wrote this wrong here 19.6 okay. And it should actually make sense this is the same rope This is the equivalent of the rope has the same tension throughout OK now let's look at the pulley the pulleys being pulled down by the pulleys being pulled down by this T1. So the same thing T1 19.6 The pool is being pulled down by T2 19.6 as well and it's been pulled down by this so the force that holds the pulley in place is this tension here I'm going to call this T3 and I can say the T3 has to go against it's going against this this and this so T3 is just the addition of all these forces and if you do that that gives you a 68.8 Now this is me drawing all the forces into the picture itself it's not technically free by the diagrams so I want to do those real quick Here's the first object right here the block on the bottom on the left rather So I'm going to go there's an m1g here and their is T 1 here and they have to be the same for the second one there's an m2g and there's a T2 and these two have to be the same and on the pulley those three forces going down in one going up so to draw a big dart.So that I can fit all these arrows I have T1 m3g and then I have T2 and then pull holding it up I have T3 and I can see that the force up cancels with the three forces down OK so I want you to try this one here the pulleys massless which was the only thing that that means that it's not going to have mg pulling down on it so this one's a little tricky I want you to give it a try and see how far you can get I'm going to keep going and hopefully tried so first I want to do is draw all these forces here this guy's an mg pulling down it and mg of 29.4 So this tension here has to be 29.4 because this whole thing is inequilibrium right notice that. This mass is heavier so this system would accelerate this way except that it's already hit the floor so it's already sort of stabilized and it's back in equilibrium OK so I can see that these two forces will balance here I have another mg going to be 39.2 I have a tension going up.

And I might have a normal go in up. So this this problem this block is far more complicated or not far more complicated but a little bit more complicated than the three so it's a good thing that we started with the three if you weren't sure which one of the two to start with maybe you would have drawn these forces and seen that this guy has two forces and this guy has three forces therefore you should start in the one with two forces only because it's a little simpler and because the system is an equilibrium this tension here is the same Ok this tension here is the same so that allows me to figure out that this tension is twenty nine point four I can fit it there which allows me to find my normal OK so now that I have tension I can find normal how all the force is going up have to cancel out all the forces going down so I can write tension plus normal those little forces going up equals mg That's the force going down there for normal equals mg minus tension and mg is 39.2 tension was Same here 29.4 And if you do this you get that normal is simply 9.8 Newtons. Normal is 9.8 Newtons rights so I got all these forces again just to be clear this tension here is29.4. In that said if you want to draw free body diagram. by the way there is technically one more. Force here right the pulley is being pulled down by a tension of 29.4 here the pulley is being pulled down by a tension of twenty nine point four here so there has to be a force that holds this pulley up right now here don't draw any strings or whatever you can see there's a lot this means that this pulleys like fixed on a wall or something so there's like a nail here some like that and I can say this is usually not important usually don't get asked what the force there is but if I want to know the force on this layer here this force is going up against these two tensions so you just have to add up those two tensions in whatever that is so here I gets around as to what's actually fifty eight point eight.Right so that's what this is so it's a little messy would be drawing free body diagram so here's my3 kilogram it's been pulled out my mg and it gets pulled up by the tension and I can say that they are.

The same the four a little bit more complicated and for four make a little bit bigger dark dark the four is pulled up by a T. and this is pulled up by an N.. Has an N pushing it up and then it's got a mg going down so this is the free body diagram for the three This is a free body diagram for the four and then the pulley is pulled down by the two tensions C. and T. so in it's to get pulled up by the force of the nail or whatever.We're going to call this force up this is the this is the cylinder right here OK that's it for this one let's talk about spring scales so a spring scale is a small little device that you can use to find the weight of different things or any kind of force so you measure a little device and you're going to hook something onto it right there's a little hook you attach an object to it. That's going to cause the spring to stretch in the spring inside of the device and you'll be able to read the weight of this object you can also just pull it yourself and see the magnitude of that force OK So spring scales measure tension OK we're going to measure tension So imagine that I have a little rope holding on to something and if I have a spring scale here the reading of the scale is the same that tension would be OK So let's do some problems here so the really scales that what tension would be on the chord spring scales are almost always massless in if they are massless the tension on both sides is the same so for example. I have a spring scale here to draw on.Kind of like that if the tension on the left is ten that means that the tension in the right will be ten as well the tensions are always the same now the reading on the scale the scale would be reading oops the scale would be reading ten as well right so it's pulled ten to the left ten to the right it doesn't even scale reads twenty it just reads ten because you can think of it as a rope right a rope has a tension of ten would be everywhere it's the same tension at that point right there so you can think of the spring scales a point on the rope so let's do this for examples real quick and then we'll be done so also use them as your rest are at rest I want to draw free by the diagrams and calculate all the forces in all these pictures the pulleys and the spring scales are masses so we don't have to worry about the mg of those so here first force mg is nineteen point six So there has to be a tension up I'm going to call this T1 and it is also going to be nineteen point six because this is at rest and it's also an equilibrium How do I know that because well unless the string breaks it's going to stay where it is. Right so there's this is all the same rope right here so it's going to have the same tension OK which means that this tension here is nineteen point six which means that if you're a three kilogram block you're being pulled to the left with that nineteen point six So tension one equals nineteen point six notice that the tension changes direction depending which object you are right or you're looking at. What else while this object sits here at equilibrium the acceleration of this object is zero it's not moving right the whole system is at rest and it's not accelerating so all the forces have to cancel if there's a force pulling to the left there has to be a force pulling to the right T2 equals nineteen point six I call this T1 in this T1 because the same road I called is T 2 because it's a different world segment but the tensions have to be the same so that this thing cancels and it doesn't move OK if I wanted to draw free body diagram it would be I have an mg down this way.

This is for the two and I have a T1 this way and there are the same if I were drawing for the three I have T1 to the left T2 to the right and they are the same as well. OK those are the two three body diagrams let me do this one this thing here is a spring scale. All right in let's let's start so here I have an mg. of thirty nine point two which means this tension one right here it's thirty nine point two. if you are the spring scale right here this tension goes all the way to here so if you are the spring scale you are being pulled to the left with eighty one of thirty nine point two and because your acceleration is zero just exactly like before your attention to the right is T2 thirty nine point two as well because the forces have to cancel right now another thing that I want to know here is what is the reading. On the scale what would the spring scale show in the answer is simply thirty nine point two Newtons remember that the tension on the spring scale tension on the left and the right will be the same always and Remember also that the reading on the scale will be that tension OK so it's not both of them it's just one of the two tensions and they will be the same OK if I want to draw free by the diagram I have this is my four it's kind of it's kind of mg going down.

Only has a T1 going up and this is my spring scale it has eighty one to the left T2 to the right in they are the same.

Right when you see real quick I have five kilograms here some being pulled down with an mg of forty nine and here I am an mg of forty nine as well.

So I have a tension here T1 equals forty nine because this thing is at equilibrium by the way the system is not going to move because even though there is two blocks they are of the same mass so if they started rest there and it's never going to break the bounce right notice that this is one continuous string so this tension has to be the same everywhere which makes sense because here you would expect that this thing to be for this thing to be equilibrium this tension would be.

A forty nine as well so this is all one string so it's all the same tension if you were a little dark here you're being pulled to the left with T1 equals four nine and you're being pulled to the right with T1 equals forty nine that does not mean however that the tension of the top rope is forty nine times to the tension at the top of the Rope the top segment of the rope is still forty nine OK so it's forty nine everywhere let's do one more and here I have an mg of fifty eight point eight fifty eight point eight This means that the tension one here is fifty eight point eight this tension this is a different wire segment right because I have an object in between here this tension two is fifty eight point eight So if you are the spring scale you are being pulled to the left with the same tension here fifty eight point eight and you are being pulled to the right with the same tension tension two fifty eight point eight Now what is the reading on the scale the really on the scale is not fifty eight point eight times two but it simply fifty eight point eight because if you remember spring scales the tensions on both sides are the same in the scale will read that tension right it's going to read what tension is on the rope which is the same on either side and not double just because people in two ways so that tends to be tricky people get confused by that but remembered spring scale is going to read the tensions of the two sides which are the same not all of those tensions OK that's it for this one hope makes sense let me know if you have any questions.