 Let's talk about static equilibrium. I've got a mass here supported by two strings. We say this is static equilibrium because it's static, it's not moving, it's at rest. And equilibrium because all of the forces here acting on that mass are balanced. In fact, it's a great application of Newton's first law, which tells us that an object at rest will continue in a state of rest until a net force acts on it. And sometimes students think that means that there's no forces acting on this object, but there are lots of forces acting on it. It's just that there's no net force. That means if I add all the forces together that are acting on this mass, they'll all cancel out, or they'll add up to zero. So how can we go and determine what forces are acting here? One of the common things you get asked is what is the force of tension in these two strings? And we can solve for that by doing a free body diagram. The first force I'd put in my free body diagram is the force of gravity acting downwards on this mass. Then there are two forces of tension as well. There's one here for that horizontal force of tension and one for this diagonal force of tension. After I've made my free body diagram, I can redraw those forces into a triangle. And it's going to make a right angle triangle. We can measure the angle the string makes with the vertical. I measured that earlier to be 38 degrees. And I can put that into my diagram. Lastly, I can calculate one side of that triangle because I know the mass. In this case it's 500 grams or half a kilogram. So I can use Newton's second law. Force of gravity equals m, the mass of the object, times g, the acceleration due to gravity. I can put in one other side of the triangle. Now all that's left is to do a little bit of trigonometry to go and work out the other two sides of the triangle. The horizontal side of the triangle will be the force of tension from the horizontal rope. And the diagonal or hypotenuse of that triangle will end up being the force of tension in the diagonal rope. Here's another situation and it's a little bit trickier. I've got the same mass, it's 500 grams, and it's suspended by two strings. And each of them make the same angle. In this case it's an angle of 40 degrees from the horizontal. So what's the force of tension in these two ropes? We're going to start off in the same way. Let's make a free body diagram. The force of gravity going downwards, acting on that mass. And in this case there's two forces of tension going in the same direction as each of those ropes. They'll have the same magnitude, but they'll be going in opposite directions. So once I've got my free body diagram drawn out, I can go through and make that into a triangle just like I did before. Now it won't be a right angle triangle, but I can still solve it to find out what each of those forces of tension are. So if you've got a ruler and protractor, you can go through and make that diagram and solve that vector addition really easily just through graphical analysis. And I've got a video showing you how to go through and do that. If you don't feel like busting out the ruler and protractor, there's another way you can do it as well. Think about just one of those two ropes. I'm going to think about this one here. I know I have a force of tension acting in the diagonal. And I can break that force of tension into kind of like two components. One component here going horizontally and one going up vertically. Now that component that's going up vertically is going to take half of the weight or half of the force of gravity of this mass. So what I could do is I could take the force of gravity of the mass and I could divide it by two and make that equal to this upwards pulling y component of the hypotenuse of that triangle. Then I can go through and solve for the hypotenuse using some simple trig. I don't have to go through and draw that with a ruler and protractor. I like that method. It's a little faster, but you have to remember that you have to divide the weight by two. Reason being that each of those two strings are going to take half of the overall force of gravity on that mass. And sometimes students forget to do that. So make sure you're comfortable with one of those two methods. For more help with static equilibrium, check out this old video that I've got dealing with the same sorts of concepts. Or check out my website, ldindustries.ca.