 Hey everybody, my name is Brad Langdill and I'm going to teach you about physics whether you like it or not the topic we're looking at right now is called static equilibrium and You can really break it down into the two basic words and you can figure out what it's talking about here Static means not moving So if you're a static you are still you're at rest. You're not moving and equilibrium means balance So you can really get an idea when a physics question talks to you about static equilibrium We must be talking about an object that is not moving and something about that object must be balanced And as you can see below here, I've written that the net force is the thing that's going to be balanced Remember the net force is the sum of all of the forces all of the forces acting on an object in the x and y directions The sum is zero when these forces are balanced So we're going to work through some problems today where prop objects are at equilibrium and we see these forces being balanced or We see the net force adding up to Zero, so let's take a look at one particular problem like that This one says two cables suspend a 450 Newton engine The ropes are both at 25 degrees from the horizontal and they act in opposite directions and here you can see the ropes There's one there's the other so what's the force of tension in each of the ropes? Well in order to find the force of tension in this particular example We're going to have to work out first of all the net force acting on this on this engine and to do that We're gonna have to make a free-body diagram of all of the vectors acting on this object So we're just gonna make a free-body diagram to start off with the free-body diagram is a diagram that only shows The forces that are acting on the object. We don't have to draw the engine in or anything like that So for my students usually the first force we talk about the easiest one is the force of gravity That's pointing down And in this case the force of gravity is the same as the weight. It's 450 Newton. So that's given to us in the question That's kind of helpful The other two forces that are acting here are these forces of tension from our wires Tension is just a force that's present in a rope or wire So there's one force of tension there. There's one force of tension there So I'll go and draw that out in my free-body diagram like so Here's one force of tension. There's the other force of tension They're both at 25 degree angles and they're both equal because if these two ropes are the same length Then the force is going to be the same that's felt in each of the ropes The tension will be the same and I think the ropes are the same length So this must mean the tension is equal for both of them Now let's see if we can do some work to figure out Oh, I don't know what the net force statement is for this particular Free-body diagram So the first thing I think I would do is I'd realize that because we have two dimensions get rid of that hand Because we have two dimensions here the x and the y dimension We're gonna have to break this tension vector into both x and y components So I'll just draw one of them over here on the side there's one and It is a force of tension we've got a Y component that I write as f y and we've got an x component that I write as f x and The angle up here Was 25 degrees Okay, so that's pretty good So when I go to do a net force statement I've got to do a net force statement in the x and the y direction Notice I said net force statements not statement. So let's do the x direction first. I guess The net force in the x Is equal to let's see. What do we have in the x direction? Well, we've got Forces of tension in the x direction one from the first one from the first wire here force of tension in the x and One from the second wire and you could probably see even from the diagram here that these two forces of tension are Equal and opposite when I add them together They are going to give me zero and that's good because I want my net force statement to be zero if this is static equilibrium Remember net force is always zero in the x and y for static equilibrium. So that works out Now let's look at the y direction. I'm actually gonna erase that I think so I have room to do the y direction What are the forces acting in the Y Collie office, please So in the y direction we have the force of gravity and We've got let's see force of tension in the y one right here From the first rope and then we've got another one actually from the second rope is what well So there's one force of tension in the y There's two forces of tension in the y And they're going to be equal So if I was to simplify this down a little bit here Let's see what I can do the force net in the y direction is zero Again because this is static equilibrium the force of gravity is 450 Newtons and there are two equal forces of tension in the y direction So if I do a little bit of algebra here, I move my 450 to the other side by subtracting 450 Newtons from both sides 450 Newtons is equal to two of force of tension in the y So force of tension in the y direction is equal to 225 degrees degrees, sorry Newtons Well so far so good, but that isn't our answer. We're not looking for the force of tension in the y direction We're looking for the net force of tension. So back to our vector triangle. I guess 225 Newtons, that's the y component if I want to find the hypotenuse here I think I'm gonna have to use sine. I've got my angle here of 25 degrees I've got the opposite side is 225. I'll find the force of tension using sine. So sine 25 degrees equals the opposite side 225 Newtons over the force of tension So the force of tension is equal to, pull up my calculator here, here it comes 225 divided by the sine of 25 degrees So 532 0.39, I guess for significant digits, we're gonna call this 5.3 times 10 to the 2 times 10 to the 2 Newtons Doesn't really look like a 2 There we go. Now it looks a bit like a 2. Newtons. That is the force of tension in the wire It looks like a lot. It's a little sloppy, but as you can see the big ideas are there. The net force in the x and y direction have to be 0 if it's static equilibrium So we have a net force statement in the y direction. We did one in the x, but we found that was 0 as well And then from there, it's just doing a bit of work with vectors So I hope this helped and if you have any more questions or problems check out my website at LDindustries.ca Take a look at the notes for this material Hope that helped. We'll see you guys later