 We've looked a little bit at some equilibrium problems, so let's come back and look at the more general case where we have non-equilibrium. So in that case, what we know is that the acceleration is not equal to 0. We're going to have an acceleration. And that's because the vector sum of the forces is not equal to 0. Now, it doesn't really tell us immediately just by saying it's non-equilibrium what we have in terms of fx and fy. There could be equilibrium in one of these two, but there isn't equilibrium in both of them. So in general, there will be an ax and an ay. But it's possible that one of those cases might be 0. So let's look at a problem here where we have our forces and we're figuring out what the acceleration is going to be. If I've got a basic diagram where let's just say I've got two forces, let's use some vertical ones this time just to sort of shake things up, I'm going to call it f1 and f2. Well, the sum of the forces in y is equal to minus f1 plus f2. And in general, that's going to be equal to sum may. Well, if I've got actual numbers, I can start solving for different things. There's four different unknowns, so if this is the only equation I'm working with, I need to have three of these things in order to be able to solve the problem. And it could be any of these three things that you're given. In this case, let's say we know that f1 is equal to 20 newtons. f2 is equal to 30 newtons. And the mass is equal to 2 kilograms. If we come through and work out this equation, well, what are we then solving for? Well, we're trying to find out what is my acceleration. One method is to come in and plug in all my numbers first. The other method is to do all my algebra first. In this case, since the equation's laid out pretty well, I'm going to go ahead and plug my numbers in. Well, I'm going to have negative 20 newtons plus positive 30 newtons equals 2 kilograms times my unknown Ay. As I'm working on this, then, what I can see is I do the addition subtraction here. And that gives me 10 newtons equals 2 kilograms times my unknown Ay. Since these two things are multiplied together, in order to separate them, I'd have to divide through by my 2 kilograms. And I see that 5 newtons per kilogram is equal to my acceleration. Now, the units look a little weird at first until we remember that a newton is equal to a kilogram meter per second squared. So a newton per kilogram would have those 2 kilograms cancel each other off. And this is really just 5 meters per second squared for my acceleration in the y direction. So in this case, we knew all the forces, and we were trying to find the acceleration. Let's take a look at a similar situation, but where I'm trying to find one of the forces. So I might have a problem where, again, I've got an object, mass 1. That mass 1 might be 4 kilograms this time. And let's say I've got forces acting on it, a weight and a tension. So this is an object which is hanging from a rope, perhaps. Now, let's say I'm actually told that this box hanging from this rope is moving downwards. And not only is it moving downwards, it has an acceleration downwards of 2 meters per second. Well, I've got to figure out how to draw my diagram. Well, no, I've got my diagram. How do I construct my equations from this so I can start solving different things? This is a little bit trickier equation because we're actually bringing into place several things here. Let's start with our equation, though. Some of the forces in the x, for this particular case, is 0. There's nothing in that direction. I don't have to worry about that. Some of the forces in y is equal to plus t minus weight equals m Ay. I'm going to write this equation one more time just to kind of clarify some things. One thing I'm going to remind you of is that weight is equal to mg. And g is equal to 9.8 meters per second squared. So I can actually find my weight here. I've got plus t minus mg. And that's going to be equal to m. But notice I've got an acceleration that's going downwards. Well, I can handle this in two ways. I can either say my acceleration is negative 2 or I could say my acceleration is in the downward direction with a value of a. You can work this either way and just make sure that you're being very careful on how you're treating your signs. If I had to do the algebra on this particular equation, I would say that my tension is then equal to mg minus ma. And I can plug in my exact values here. Could simplify it a little more by pulling my m out as a factor. m is g minus a. And if I actually plug my numbers in at this point, now I haven't left myself much room, so I'm going to slip over to a different sheet here. That means my tension is equal to 4 kilograms 9.8 meters per second squared minus 2 meters per second squared. I wasn't being careful up here at the top, but I caught myself. I said my acceleration was 2 meters per second. That's got to be 2 meters per second squared. I can't have an acceleration that has units of meters per second. Simplify my algebra a little bit here, and then I have to actually come and plug this into the calculator. 4 times 7.8, that tells me. Now, if we want to actually compare this to a broader problem, I could have actually figured out what is my weight up here at the top? My 4 kilograms times 9.8 meters per second squared and see that I've got 4 times 9.8, that would give me a weight of 39.2 newtons. So as a check back here to reality, what I'm saying is if my object is accelerating downwards as it's being held up by the rope, the tension of the rope doesn't have to support the entire weight, as would be the case if it was in equilibrium. Instead, the tension only has to support part of the weight, and the other part of the weight is causing a downward acceleration.