 We can continue our discussion of force diagrams or our free body diagrams by looking at specifically what you have to do if you're given a diagram, but you need to construct your equations. So how do we construct those equations from our diagram? What I'm talking about with a diagram is let's say you're given a particular problem where you've got some mass, let's call it mass one for right now, and then you're given a diagram showing you a series of forces acting on that object. Now in this case we've kept it nice and simple by having all of our forces up and down or left and right. So when we do this we're trying to construct our set of equations. Some of the forces in x and some of the forces in y from this diagram. One approach is to start if they're named F1, F2, F3, F4 just to make sure we're not missing anything, is to start with F1. F1 is over here to the right so that means that's going to be in the positive x direction. Similarly F2 is in the positive x direction. F3 however, well that's down so our up and down direction gives us our y equation and down is negative so we would plug in a negative F3. When we come to F4 that's up so that's going to give us plus F4 and then our last one our force 5 here is in the negative x direction because that's pointing to the left. Now our equations aren't entirely complete because we don't know yet is this object in equilibrium or is this object accelerating. So it's possible that there's an acceleration component in the x direction and an acceleration component in the y direction and this gives us our full force equations for this diagram. Now this was a complicated diagram that I had 5 forces but it was a simple diagram and that they were all either up or down, left or right. So let's take a look at a little bit more complicated diagram. Let's say we've got a diagram where we're given various quantities. Weight, attention, maybe a normal force, maybe a friction and then maybe there's somebody helping it out so we have attention 1 and attention 2. So this is a fairly complicated diagram as well. We still want to come through here and describe our equation. Now this might be the diagram for a box sitting on a table being dragged by two people and there's some friction in the system. So in this situation we would expect that the box is moving, possibly accelerating to the right. It's probably not accelerating up and down. So this is our sort of physical sketch. This diagram over here is our force diagram. We want to use this equation, not our physical sketch, to help us through our equations. So for this particular situation again we want to start with each force and figure out what we have to include in each of these equations. If I start with T1 it's directly to the right and so I've got a plus T1 in the x direction. T2 is a little bit more complicated. It goes to the right but it also goes up. So we could take this and think about it in terms of our trigonometry. We've got an x part and a y part for that equation. So the total tension 2 is not in either equation but a part of that tension 2 is in the x direction and a part of that tension 2 is in the y direction. The rest of our forces are a little bit easier. Normal force points upwards, positive y, weight, negative y, friction, negative x. Always a good idea to come back and check and make sure that you've included each one of the forces somewhere in the equation in terms of making sure that I've got everything in these equations. We're not quite done yet because we still have to consider whether or not it's accelerating. Again for this situation with the box going along a desk in that particular case my MAy becomes zero because it's not accelerating up and down. MAx, it could be accelerating to the right or it could be moving at constant velocity. We'd need a little more information. You're always safe putting MAx and MAy in there as long as you're keeping track and later come back to evaluate what those particular accelerations might be.