 Hi, I'm Zor. Welcome to Unisor education. I would like to start a new chapter called statics and in particular we will talk about equilibrium today. Now this lecture is part of the course called Physics for Teens and it's presented on Unisor.com website. It's a free course. No financial strings are attached, no advertisement. So I do suggest you to go to this website for this lecture and all others because all the lectures are arranged in logical sequence because sometimes you can find it just by accident on YouTube but anyway just I have to tell you that this is part of the course. So take the course. And by the way there is a prerequisite course for this which is called Mass for Teens and it's also on the same website. In particular it's very important to have a very good knowledge of vectors and calculus to really be comfortable in the course of physics. So if you are not that comfortable I do suggest you to take the Mass for Teens course first and then go to the physics. Alright so let's talk about equilibrium. Statics is I would say more ancient kind of mechanics than dynamics. Dynamics is all about motion. Statics is about bridges, buildings, about different aspects of life of the people even before they started thinking about what exactly kind of forces are involved in in our everyday life and what kind of quantitative measure of their movements that we can introduce. So all these Newton's laws etc. they are all subsequent to this. In the beginning people had to build buildings and that's probably one of the most important stimulus to think about statics. And obviously in particular they were concerned about equilibrium. So what is equilibrium? Well equilibrium is a state of all the forces combined together which result in no movement basically. So if you have let's say one particular object let's talk about point object and you have many different forces applied to this. If as a result of this the object does not move we are saying that the forces are balancing each other and altogether this is a state of equilibrium basically state of rest so to speak. Now an example for instance if I'm standing right now on the floor within the frame reference associated with earth let's say I'm not really moving anywhere right so I'm standing still and why because I have two major forces applied to my body which is my weight which goes down and the reaction of the floor which basically goes back up and these two forces are equal in magnitude and opposite in direction which means they balance each other. So obviously we all understand that the forces are vectors because they have magnitude and direction and the combined action of all the forces obeys to the laws of vector algebra. So if every vector is associated with every force is associated with a vector and these vectors of all the forces applied to one particular object sum together giving the null vector that is the condition of equilibrium. Now another condition of example of equilibrium is actually the building for instance the building stands now what kind of forces are acting on each brick for instance well there is a pressure from above there is its own its own weight and there is again a reaction from the from the bricks underneath. If you have a bridge for instance and there is some weight on the top of the bridge a car let's say again the car presses down to the bridge with its weight but the bridge has certain elasticity because it's probably built of steel. Steel has certain elasticity and it actually supports the car and it doesn't fall down. So again the car standing on the bridge is at equilibrium. All right so we will basically learn about equilibrium by considering certain examples and that's exactly what I would like to do. So example number one is you have the following construction. So this is the weight of this particular point object and it's hanging on two threads. Now this thread, thread A is horizontal now the thread B is at angle phi. So this is some kind of a knot which ties together all these threads. The thread which leads to the weight the thread to which leads to one support one wall or whatever and another one. Now my question is what kind of tensions of these two threads actually can be observed based on the weight of this particular object. So there is a tension which goes this way and the tension which goes this way. This is TA, this is TB and the combination of three vectors this one, this one and this one should give me a zero vector, null vector and that's the condition of equilibrium. So now this point is not moving. In this and many other cases we actually can do this not moving condition we can express it in different ways as equations, equality of the forces. So what I'm going to do is first I'm going to project all my forces to a horizontal line. Now this force on the horizontal line has no projection because it's perpendicular, right? So the weight doesn't really contribute to movements left or right. Now the force TA therefore must be balanced by projection of TB on the horizontal line. TA is already completely horizontal, right? So TA is the magnitude of the vector which goes to the left, magnitude. TA is not in this case, now if I will put the line on the top that would be a vector but this is just the magnitude of the vector. So magnitude of this vector should be able to the magnitude of projection of the TB and the projection of TB is TB times cosine of phi. So this is a result of this particular point not moving horizontally. It's also not moving vertically. So what are projections of all my vectors onto the vertical line? Now this is 0 so TA does not contribute to any vertical movement since it's a horizontal vector. Now this is definitely down and this is up and the up would be now this is also phi so this is TB times sine of phi is equal to W. Again W in this case is not a vector it's a magnitude of the vector. This is a vector. Now these are two equations with two unknowns TB and TA which I can find and knowing the magnitude of these vectors and knowing their direction basically I have solved the problem right? Alright so how can I solve? Obviously I can find TB from here TB is equal to W divided by sine of phi and now I can find TA which is TB times cosine which is W cosine divided by sine phi or if you wish cotangents of phi. So this is now the problem is solved. Now let's consider another problem. So I would like to use these examples to basically illustrate what the equilibrium is and how conditions of equilibrium can be basically calculated. Now in this case I have an inclined plane with big object here with the thread goes around the pulley down and the smaller object here and I know that masses I know masses but I have to find out is what is the angle when these are balance each other. So this is a state of equilibrium. This is given to me. Masses are given. Question is what's the angle? Okay now let's just do exactly the same thing as before. Now this force is always going down and this is mg. Now this force also down this is capital MG but in this case it's very convenient to break it into two components. One component goes down perpendicularly to the plane and it's very important because there is a reaction of the plane which is equal to in magnitude. Let me just make it really equal. Something like this. So this is mg times sine phi right? This is phi and this is phi. Now and this one no this is cosine I'm sorry this is mg cosine phi and this is mg sine phi. So the mg cosine phi is completely balanced by reaction of the force and this force which is mg sine phi. Since we are in balance in equilibrium is completely balanced by tension. So mg sine phi is equal to tension. On the same hand the tension is balancing this force. It's the same tension. This is the same thread the same tension. Obviously assumed that there are no friction etc and this is ideal. All ideal conditions obviously. From which we can very easily find sine phi is equal to m over capital M and phi is equal to arc sine m over capital M. That's it. We found the angle where everything is in balance. If this angle will be greater then the bigger mass would just pull to the left. If the angle is smaller there is no friction right? Now this smaller mass would go down and if we are in equilibrium this is the condition of equilibrium. So basically these are a couple of very simple examples of the state of equilibrium. A state of rest when all the forces acting onto the same object are nullifying each other. So basically if you have a bunch of forces of i where i is one two etc and so you have n forces applied to the same point object. So talking about point object and all the forces it's at rest if sum of all these vectors is equal to null vector. So that's the condition of equilibrium and these are a couple of examples which kind of illustrate it. Okay that's it. I would suggest you to read the notes for this lecture. Every lecture for this and every other course which is on the Unisor.com. It has notes. It also has exams. So I do suggest you to go through the website to have a complete course at your disposal. That's it. Thank you very much and good luck.