welcome to our second section inside of our Newton's Laws unit. In this section, we're gonna be talking about free body diagrams and how to handle it when we have environmental effects on objects or when we have multiple objects interacting with each other. What can we do to draw effective, free body diagrams Now? Drawing effective free body diagrams may sound like a simple thing toe have several videos on, but it really is somewhere where I students see students mess up again and again. So I'm going to allude to several classic problems in physics throughout this section. And it will help you a lot to pay attention to them because they will show up later. They're almost certain to show up in your course. Eso. We've been talking a lot about the concept of the block on the ground, and I've already said that we control the forces on this when it's holding still as being a force of gravity down and then being a force due to the floor up. And we'll talk more about this forced to the floor and future videos. But and the reason is so important to draw free body diagrams effectively is because once we draw this picture, that's what's going to allow us to write out our net force. Remember we generally speaking, we'll divide it into a net force in the X and the net force in the UAE. That then will be equal to acceleration in the X Times mass or acceleration in the UAE Times Mass. So we definitely need to be able tohave an effective drawing that will give us an idea here. So there's a few things we can do with our free body diagrams that can make life simpler. First of all, we definitely want to try to draw things in X and y directions. If it all possible, because when we have perpendicular vectors, it's easier to distinguish what's going on. But if you need a vector to be at an angle, it could be really helpful to put the angle into your free body diagram. So if we have an angle of 30 degrees here, you just write it in. Sometimes that means you have to go back and re draw your free body diagram larger so you can actually tell what the angle is. But it could be a big help to put that angle into your free body diagram. Speaking of angles, occasionally your box isn't sitting on a flat surface. Occasionally, it's sitting on one of these inclined planes that we considered in one dimensional Kinnah Matics. In this case, we need to think about something about our forces a little differently, because while we still have gravity pointing straight down the force of the floor instead of pointing straight up, it's actually gonna The floor can only point perpendicular to itself. It can only apply a force perpendicular to itself, which means it's gonna be that direction. So when we draw the free body diagram, we're gonna have an F G down and then we have a normal force. Now it's hard to tell whether this is actually in the right direction or not. So I prefer when I have a when I have a inclined plane like that actually draw a dash line that shows me more or less what that inclined plane is doing. If you wanna add in a little more detail, you can even add in some dash lines down here and put in your angle so that you can tell what's happening. Um, Interestingly, when you do this, it creates an immediately an immediate right triangle using the's gravitational force, and it will help when you want to draw the forces. For example, if I wanted to say, Well, if I want to extend this and say, You know, I could say Look at this, here's Here's another right triangle Kind of like the one that we talked about when we looked at our in our math review at our geometry. And there's another right triangle right here. So there's right triangles everywhere, which will help to break things up into pieces. In fact, the technique with this incline plain problem, as you'll find out soon enough, is that we're going to flip our axes to have the X axis be parallel to the inclined plane, and then R y axis will be parallel to our normal force. And this can make life a lot easier when it comes to figuring out how this box is going to move. Remember, this is the same trick we did when we talked about one dimensional Kinnah, Matics and inclined planes where we tilted are axis so that it was parallel to the inclined plane. We're just doing the same thing here, but we're taking the Y axis along for the ride. Okay, so that's Ah, word on environmental effects. What if we have multiple body? So we're gonna come back to our box here, but then we're gonna put another box next to it. We could even put a third box afterwards. We'll do this exact example in when the later videos, but when we put these boxes together, we don't need one free body diagram. We need 35 free body diagrams. So we're gonna label these boxes 12 and three, and we'll have one to three free body diagrams. So when we go to do this, of course, they'll all still have gravity pushing on him. So we'll have forced due to gravity. Except if these boxes air different masses. Thes f GS will all be different, too. So I like to put labels here. So I have f g for box one F g for box two and F g for box three, and kind of putting an additional sub script on the sub script. And then we'll have the force due to the floor on one, and we'll have the force due to the floor on to, and we'll have the force due to the floor on three. Okay, so we've got three forces. One for each box now. What if I come up and I push on this thing? I'll say I push on it with a Force F one. Well, of course, Box one feels the Force F one and then it's gonna push on box to. But that won't necessarily be with the same force. What box to is going to feel as we'll call this the force of box one on box too. So F 12 means the force of box one on box, too. And then Box three here will feel a force on box three due to box, too. But we have to take into account here the Action Reaction Law. Newton's third law, which says if Box one pushes on the box to in Box two is going to push back on box one, which means we need to draw second vector here, pointing backwards on box one, which is the force of box to on Box one. See what I've done here. I've got force of one on two and then force of two on one, and I know that these have to be equal and opposite to each other because of Newton's third law. So this is Newton's third law showing up inside of our free body diagram. Sometimes we'll call these reactionary forces similarly because box to pushes on box three and that means box three will push back on box, too. We'll have to put in a force here. We'll call this the force of box three. I'm box too. And as before, we'll have the force of box three inbox to has to be equal to the negative of box to Unbox three. Now, Box three is is fortunate in that it doesn't have 1/4 box pushing it backwards, so it doesn't need a new additional vector here. But this is how we're going to draw free body diagrams for multiple objects. Notice that the forces that show up in the free body diagram for Box one our Onley forces affecting the acceleration of box one. They're things that are pushing on box one, not the forces that are being applied by Box one. If we want the force that's being applied by box one, we have to look over here. This is the force of box one on box, too. And so this is the force applied by Box one. Box two is pushing on both Box one and Box three because it's physically touching them. So we see the force due to box to hear showing up in three body diagram for the first box and the force from box to pushing on Box three, showing up in the free body diagram for Box three. Now this takes a lot of practice to really be able to do proficiently, but it's really, really key to getting these correct, Because once you draw your free body diagrams correctly, like I said before suddenly riding out, Newton's law becomes really, really simple. We just say, Well, it's the sum of forces on box one. So all the forces on box one. If we looked in the horizontal direction, we have F one minus force of box to on box one, and then that be equal to the massive box one times the acceleration of box one. In this case, if each box were to move together, we would know they would all have the same acceleration and we'd be able to say that acceleration of one is equal to the acceleration of to which is equal to the acceleration of three. In that case, I'll generally just give them a generic acceleration A and that similar variable. There will be what we use to connect our equations because each of these will get their own equation. Will also have force of one on two minus force of three on two equals, M two times A and the force of box two on box three. I wrote this down on box to on Box three will be equal to the mass of box three times its acceleration.

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## Video Transcript

welcome to our second section inside of our Newton's Laws unit. In this section, we're gonna be talking about free body diagrams and how to handle it when we have environmental effects on objects or when we have multiple objects interacting with each other. What can we do to draw effective, free body diagrams Now? Drawing effective free body diagrams may sound like a simple thing toe have several videos on, but it really is somewhere where I students see students mess up again and again. So I'm going to allude to several classic problems in physics throughout this section. And it will help you a lot to pay attention to them because they will show up later. They're almost certain to show up in your course. Eso. We've been talking a lot about the concept of the block on the ground, and I've already said that we control the forces on this when it's holding still as being a force of gravity down and then being a force due to the floor up. And we'll talk more about this forced to the floor and future videos. But and the reason is so important to draw free body diagrams effectively is because once we draw this picture, that's what's going to allow us to write out our net force. Remember we generally speaking, we'll divide it into a net force in the X and the net force in the UAE. That then will be equal to acceleration in the X Times mass or acceleration in the UAE Times Mass. So we definitely need to be able tohave an effective drawing that will give us an idea here. So there's a few things we can do with our free body diagrams that can make life simpler. First of all, we definitely want to try to draw things in X and y directions. If it all possible, because when we have perpendicular vectors, it's easier to distinguish what's going on. But if you need a vector to be at an angle, it could be really helpful to put the angle into your free body diagram. So if we have an angle of 30 degrees here, you just write it in. Sometimes that means you have to go back and re draw your free body diagram larger so you can actually tell what the angle is. But it could be a big help to put that angle into your free body diagram. Speaking of angles, occasionally your box isn't sitting on a flat surface. Occasionally, it's sitting on one of these inclined planes that we considered in one dimensional Kinnah Matics. In this case, we need to think about something about our forces a little differently, because while we still have gravity pointing straight down the force of the floor instead of pointing straight up, it's actually gonna The floor can only point perpendicular to itself. It can only apply a force perpendicular to itself, which means it's gonna be that direction. So when we draw the free body diagram, we're gonna have an F G down and then we have a normal force. Now it's hard to tell whether this is actually in the right direction or not. So I prefer when I have a when I have a inclined plane like that actually draw a dash line that shows me more or less what that inclined plane is doing. If you wanna add in a little more detail, you can even add in some dash lines down here and put in your angle so that you can tell what's happening. Um, Interestingly, when you do this, it creates an immediately an immediate right triangle using the's gravitational force, and it will help when you want to draw the forces. For example, if I wanted to say, Well, if I want to extend this and say, You know, I could say Look at this, here's Here's another right triangle Kind of like the one that we talked about when we looked at our in our math review at our geometry. And there's another right triangle right here. So there's right triangles everywhere, which will help to break things up into pieces. In fact, the technique with this incline plain problem, as you'll find out soon enough, is that we're going to flip our axes to have the X axis be parallel to the inclined plane, and then R y axis will be parallel to our normal force. And this can make life a lot easier when it comes to figuring out how this box is going to move. Remember, this is the same trick we did when we talked about one dimensional Kinnah, Matics and inclined planes where we tilted are axis so that it was parallel to the inclined plane. We're just doing the same thing here, but we're taking the Y axis along for the ride. Okay, so that's Ah, word on environmental effects. What if we have multiple body? So we're gonna come back to our box here, but then we're gonna put another box next to it. We could even put a third box afterwards. We'll do this exact example in when the later videos, but when we put these boxes together, we don't need one free body diagram. We need 35 free body diagrams. So we're gonna label these boxes 12 and three, and we'll have one to three free body diagrams. So when we go to do this, of course, they'll all still have gravity pushing on him. So we'll have forced due to gravity. Except if these boxes air different masses. Thes f GS will all be different, too. So I like to put labels here. So I have f g for box one F g for box two and F g for box three, and kind of putting an additional sub script on the sub script. And then we'll have the force due to the floor on one, and we'll have the force due to the floor on to, and we'll have the force due to the floor on three. Okay, so we've got three forces. One for each box now. What if I come up and I push on this thing? I'll say I push on it with a Force F one. Well, of course, Box one feels the Force F one and then it's gonna push on box to. But that won't necessarily be with the same force. What box to is going to feel as we'll call this the force of box one on box too. So F 12 means the force of box one on box, too. And then Box three here will feel a force on box three due to box, too. But we have to take into account here the Action Reaction Law. Newton's third law, which says if Box one pushes on the box to in Box two is going to push back on box one, which means we need to draw second vector here, pointing backwards on box one, which is the force of box to on Box one. See what I've done here. I've got force of one on two and then force of two on one, and I know that these have to be equal and opposite to each other because of Newton's third law. So this is Newton's third law showing up inside of our free body diagram. Sometimes we'll call these reactionary forces similarly because box to pushes on box three and that means box three will push back on box, too. We'll have to put in a force here. We'll call this the force of box three. I'm box too. And as before, we'll have the force of box three inbox to has to be equal to the negative of box to Unbox three. Now, Box three is is fortunate in that it doesn't have 1/4 box pushing it backwards, so it doesn't need a new additional vector here. But this is how we're going to draw free body diagrams for multiple objects. Notice that the forces that show up in the free body diagram for Box one our Onley forces affecting the acceleration of box one. They're things that are pushing on box one, not the forces that are being applied by Box one. If we want the force that's being applied by box one, we have to look over here. This is the force of box one on box, too. And so this is the force applied by Box one. Box two is pushing on both Box one and Box three because it's physically touching them. So we see the force due to box to hear showing up in three body diagram for the first box and the force from box to pushing on Box three, showing up in the free body diagram for Box three. Now this takes a lot of practice to really be able to do proficiently, but it's really, really key to getting these correct, Because once you draw your free body diagrams correctly, like I said before suddenly riding out, Newton's law becomes really, really simple. We just say, Well, it's the sum of forces on box one. So all the forces on box one. If we looked in the horizontal direction, we have F one minus force of box to on box one, and then that be equal to the massive box one times the acceleration of box one. In this case, if each box were to move together, we would know they would all have the same acceleration and we'd be able to say that acceleration of one is equal to the acceleration of to which is equal to the acceleration of three. In that case, I'll generally just give them a generic acceleration A and that similar variable. There will be what we use to connect our equations because each of these will get their own equation. Will also have force of one on two minus force of three on two equals, M two times A and the force of box two on box three. I wrote this down on box to on Box three will be equal to the mass of box three times its acceleration.

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