6. Intro to Forces (Dynamics)

Newton's First & Second Laws

# Intro to Forces & Newton's Second Law

Patrick Ford

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Hey, guys. So up until now we've been dealing with motion and motion equations. Now we're gonna get into something a little bit different. We're gonna start talking about forces and Newton's laws, in particular, Newton's second law in this video, which is probably one of the most important things you learn in your entire physics class. So let's go ahead and check this out. So what is a force? A force is really just a push or a pull. And we draw forces as arrows because their vectors now what forces do is they change in objects? Velocity meaning? Imagine, I had this block here and it was at rest, meaning the equals zero. And you walk up to this block and you push against it. I'm just gonna make up a number here. Imagine that that force was 10. So if you've pushed it and the block is at rest, then it's going to start moving, which means you've changed its velocity. In other words, there is an acceleration. So, by the way, the, uh you know that will use four forces is called in Newton, named after Isaac Newton, and we write this with a symbol or the letter Capital letter ends. Imagine we were pushing this thing with 10 Newtons. Well, there is a relationship between how hard you're pushing force, the mass of the block and also the acceleration. And that relationship is called Newton's second law. I like to call this the Law of Acceleration. You won't see it written in your textbooks like that. But basically what it says is that if you add up all the forces that are acting on an object otherwise known as the Net Force, which we'll talk about in just a second, that's equal to M A F equals M A. Again, one of the most important equations that you learn in all of physics. But basically what it says is that if you have a net force that is acting on an object like our Newtons here, then it's going to accelerate in the direction of that net force. So again, I want you. I want to talk about the Net force really briefly here. Basically, the Net force is like the resultant sor like the vector editions, basically just arrows. Once you add up all the Barrows together, the net force is what you get. So, for example, we've got our 10 Newtons here. That's our only force. So that's our net force. But there are other possibilities. Imagine we had three of these arrows. So, like, 30 Newton's like this. And then you had 20 Newtons. That was backwards. The net force, once you add up all those things together, is that you would cancel out two of these arrows like this in which you would be left with is you just be left with one arrow. That's your net force. That's 10. Much like our example here. All right, so what if you wanted to actually calculate the acceleration of this block? Well, we can do that using F equals M A. Remember this equation says, as long as you know, two of these variables you can always solve for the third so we can actually rewrite this equation and solve for a is equal to F net divided by the mass. So what that means is that you have your net force of 10 divided by the mass of two, and you get an acceleration of 5 m per second squared. All right, so that's how we do these kinds of problems if you always have one. If you always have two or three variables you can always solve for the other. Let's go ahead and get some more practice and check out these examples here. So now we've got this 10 kg block. It's being pulled by multiple horizontal forces. We want to calculate the acceleration in these problems here. So you want to calculate a now you're going to be doing this a lot in future chapters. So we have a list of steps here that's gonna help you get the right answer every single time. Let's check out the first step here. Now we know we're going to have to add up some some arrows that point in opposite directions and things like that. So the first thing we always want to do is we always want to choose the direction of positive. So signs are gonna be really, really important when you're expanding. F equals m A. So we have a couple of points here that are going to help you get the right answer. The first one is that we usually choose the direction of positive to be to the right and up, which is pretty much what we're used to, right? So we've got our directions of positive. There's gonna choose to be up and to the right, and so that brings us to the second step. If we want to calculate acceleration, we have forces that we're gonna have to write and expand f equals m A. So now we just do f equals m A like this. And now we have to do is when you're gonna expand your forces, remember, you're gonna have to add up together forces. And so here's the rules. When you're expanding to sum of all forces, forces that point along your direction of positive get written with a plus sign. So, for example, are f A. Here goes along with our direction of positive. So it gets a plus sign. And then when you're expanding, some of all forces forces against the positive direction. Just get written with a minus sign. So here are FB points to the left. That's against our direction of positive. So it gets a minus sign like that and that's m A. Now we just replace all the values that we know. So this is plus 70 plus negative 20. Remember? Because it's points left, and this equals 10 times a. So when you go ahead and start with this, you're gonna get 50 equals 10 a. And so therefore a is equal to 5 m per second squared. So let's talk about our answer here. We got a positive number, which just means that our direction of acceleration is going to be along the positive direction. Right, So this is gonna be like this. This is our A here. So you know, the E equals 51 way to think about this is that if you have to, force is like 70 and 20 and you think about it like a tug of war. The 70 wins. So that means that the acceleration is going to be in this direction. All right, let's get to the second. The second problem here could follow the same list of steps. First, we want to choose the direction of positive. So we want to do up into the rights. And now we just run right. F equals Emma. So we've got f equals ma here and now we're going to expand our forces forces along our direction of positive are going to be with a plus sign just like before and the ones against to get written with a negative sign. Now, one thing you have you should keep in mind. Is that what we write? A. Here? We're always going to write the letter A as a positive. We'll talk about that in just a second here. And so now we just replace the values that we know. So we've got plus 70 plus negative 100 equals. Now you've got 10 times a So here's what we're going to get is negative. 30 equals 10 A and so a equals negative 3 m per second square. So let's talk about this now. We actually got a negative number. So what does that mean? Well, negative, remember just means direction. And if we got a negative number, just means our acceleration points against the direction of positive. So here are acceleration is actually the point to the left A equals three. Now we're always going to write letters in our diagram and numbers to be positive. Sorry to be positive. And then when you get actually get into the math and start replacing all the numbers, that's when you start inserting the signs and I have one last thing to talk about here is that when you're solving for the acceleration, the sign of your answer is actually going to give you the direction of the acceleration. Right? We've got a positive a here, and it points to the rights. We got a negative three here and it pointed to the left. We always write the letter N f equals M. A is positive. But then the answer your sign of the answer is actually going to give you the correct direction of the acceleration. That's it for this one. Guys, let me know if you have any questions.

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