Newton's Third Law & Action-Reaction Pairs

by Patrick Ford
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Hey, guys. So up until now we've been dealing with Newton's 1st and 2nd loss. Remember that the first law is the law of inertia, and the second law is F equals M A. And we use F equals ma. We're usually just looking at all the forces that act on one particular object. Now we're gonna start to see what happens when objects exert forces on each other. So to do that, we're gonna need Newton's third law. So let's go ahead and get into it. Newton's third law is otherwise known as the Law of Action Reaction. And basically, what action reaction means or says is that every action or, more specifically, every force is going to result in a reaction force. And there's a couple things you should know about this reaction. It's of equal magnitude, meaning it's the same size or the same strength. But this force acts in opposite directions in the opposite direction. What do I mean by that? So imagine your person A You go up to a block and you push unblocked, be so we're gonna have a force here and let's just call this forest 50 Newtons now, because this is the block and this is a force of you on the block. I'm gonna label this F A b. So this is an action. This is a force. So Newton's third law says, is that there is an equal magnitude, but opposite opposite direction. Reaction force, meaning it's the same 50. But now it's gonna point backwards. So how do we draw this? Do we draw this like this? And do we call this F B A is equal to negative 50 because it points to the left? Well, no. Because if every 50 Newtons was countered by an equal and opposite 50 on the same object that nothing could ever move because everything would always be at equilibrium, every 50 would be countered by a negative 50. So it's really, really important about Newton's third law is that all forces exist in action reaction force pairs and these four spares always act on different objects, meaning you person a push on the block with 50 Newtons, the block pushes back on you with an equal but opposite Newtons. So this is F B on a the acts on you and this is gonna be negative 50 Newtons that takes care of the fact that it goes backwards. So in general, what this means is it F of A and B is the negative of f of be on A. That's how you'll see this written in your textbooks. So what this means is that this F A B is the action, and the reaction is the negative. F b A. There's a couple of real world examples that we've been really familiar with. For example, the normal force, which is a response to a surface push, is actually an action reaction pair. So if this block here is a and the floor here is B the weight force of a pushes down on the floor. So the weight force is the action, and in response, the floor pushes back on block A. That's the reaction, and that's the normal force. Now these things actually don't have to be touching another example of this is the weight force. So the earth is going to pull on you towards the Earth Center. This is the weight force. This is M G. This is the action. But you also pull back on the earth with an equal and opposite reaction force. So this is a reaction. So you actually pull on the earth just as hard as it pulls on you. The only difference is your mass compared to the earth is way, way smaller. So you're going to accelerate more than the Earth does. All right, so let's get into the example here. So you're 80 kg. You stand on a frozen lake with a 40 kg ice block, and you push it with 20 Newtons, so I'm gonna draw this out real quick. This is 80 and you're up against a 40 kg block. You're going to push it. We know this is F which equals, uh, this is going to be 20. All right, So what I'm gonna do here is I'm gonna call a you you're 80 kg person and I'm gonna call be the block. So what that means is that this force here is actually f A B. And that's 20 we want to do in this. First part is we want to figure out the force that the bloc exerts on you. So what does that mean in this first block? In this first part here, we want to figure out not f a B. We want to figure out F b A. So to do that, we're gonna have to stick to the steps. We know the first thing we're gonna do is draw a free body diagram. But now that we're talking about multiple objects, which you have to do is you're gonna have to draw a free body diagrams for each of these objects. Remember, we have to now in this problem. So I'm gonna go ahead and do that over here. I've got the 40 kg blog. I've got the weight force. That's what I checked for. This is the weight. Then I have any applied forces, which I know I have. This is my f a B. And I know this is 20 and then I also have I don't have any tensions, so I've gotta wait. I've gotta apply force, but I have no tensions. I do have a normal force because you're on the frozen lake. So this is the normal force, and I've got no friction. So if these are the only two vertical forces, my normal and my weight, that means that those things have to be equal to each other because the block isn't gonna go flying into the sky or crashing through the ice. Right? So those things have to balance. So really, the only horizontal force is f a B. Now we want to do is we want to figure out the free body diagram for you. So you're gonna be over here, you have a weight as well. This is w equals mg. And so what we said from Newton's third Law is that if you push on the block with a force of 20 Newtons, then the action that's the action. Then the reaction is the block pushes back on you with an equal but opposite force. That means there's this force over here that points to the left. This is negative, F b A. And so what does that equal? Well, if F A B is 20 then that means that negative f b A is negative. 20. And so that's the answer. So I'm just going to finish off the free body diagram over here. So that means that F B A by Newton's Third Law is equal to negative Newtons. All right, so let's keep going now. Now we want to calculate the acceleration of the block. So now we want to calculate a be someone to call that. So what we wanna do is if we want to figure out the acceleration of b of the block, we're gonna have to use f equals Emma. But remember, we're gonna do f equals m A. And so when we use f equals M A, you're gonna have to do all the forces that act on A. So all the forces that act on that object equals the mass times the acceleration of that object. So if we want to figure out the acceleration of the bloc, which really just goes right here, this is a block. We're gonna have to look at all the forces that act on the block. All right, so that means we're gonna use f block equals mass of the block times acceleration of the block. And so the only force that acts in the X axis is going to be f A B. So that's F A B equals And then I've got 40 times the acceleration of the block. I know this is going to be 20. So therefore, my acceleration is equal to 0.5 m per second squared. That's the acceleration. Sorry. That's the acceleration of the block now going to do the exact same thing. We're gonna do the acceleration of you. So now I'm going to calculate not the acceleration of the block with the acceleration of A which is you. So where to do the exact same thing? If we want to figure out the acceleration of you, right, The acceleration. We're gonna have to look at all the forces that act on you and in the horizontal direction, there's really only one. It's the reaction for us. So we're gonna we're gonna use f equals m A. And so now we're going to use someone to use f A e equals m A. So this is gonna be negative. F b A. That's the reaction force on you equals 80 times a. So this is negative. 20 equals 80 times a and so therefore you're going to get the acceleration of a is equal to negative 0.25 m per second square. So let's talk about that for a second. So what action reaction actually doesn't mean does not mean that two objects that have the same acceleration we just saw that we have 0.5 versus 0.25 here. Because remember that acceleration is inversely proportional to mass. So if you have two objects with different mass, then they're going to accelerate differently for the same force. All right, guys. So that's it for this one. Let me know if you have any questions.