Hey, guys. So up until now, we've been dealing with motion and motion equations. Now we're going to get into something a little bit different. We're going to 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'll 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 they're vectors. Now, what forces do is they change an object's velocity. Imagine I had this block here and it was at rest, meaning v=0, and you walk up to this block and you push against it. I'm just going to 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.

By the way, the unit that we use for forces is called a Newton, named after Isaac Newton. And we write this with the symbol, or the letter capital letter N. So, imagine we were pushing this thing with 10 newtons. Well, there's 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 ma,f=ma. Again, one of the most important equations that you'll 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 10 newtons here, then it's going to accelerate in the direction of that net force.

So again, I want to talk about the net force really briefly here. Basically, the net force is like the resultant or like the vector addition. Basically, just arrows. Once you add up all the arrows 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 3 of these arrows. So like 30 newtons like this, and then you had 20 newtons that was backward. The net force, once you add up all those things together, that's 10, much like our example here. Alright.

So what if you wanted to actually calculate the acceleration of this block? Well, we can do that using f=ma. Remember, this equation says as long as you know 2 of these variables, you can always solve for the 3rd. So we can actually rewrite this equation and solve for a. a=fnet divided by the mass. So what that means is that you have your net force of 10 divided by the mass of 2, and you get an acceleration of 5 meters per second squared. Alright. So that's how we do these kinds of problems. If you always have 1 if you always have 2 to 3 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 kilogram 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 going to 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 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 going to be really important when you're expanding f=ma. 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. This we're going to choose to be up and to the right and so now brings us to the second step. If we want to calculate the acceleration and we have forces, then we're going to have to write and expand f=ma. So now we just do f=ma like this and now what we have to do is when you're going to expand your forces remember you're going to have to add up together forces and so here's the rules. When you're expanding the sum of all forces, forces that point along your direction of positive get written with a plus sign. So for example, our fa 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 our Fb points to the left that's against our direction of positive. So it gets sign like that and that's ma. Now we just replace all the values that we know. So this is plus 70 Plus negative 20 remember because it points left and this equals 10 times a So when you go ahead and solve for this you're going to get 50 equals 10a and so therefore a=5m/s². 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 going to be like this. This is our a here. So we know that a=5. One way to think about this is that if you have 2 forces 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. Alright. Let's get to the, the second the the second problem here. We're going to follow the same list of steps. First, we want to choose the direction of positive. So we want to do up and to the right and now we just run right f=ma. So we've got f=ma here and now we're going to expand our forces. Forces along our direction of positive are going to be written with a plus sign just like before and the ones against get written with a negative sign Now one thing you should keep in mind is that when we write a here, we're always going to write the letter a as positive. We'll talk about that in just a second here. And so now we just replace the values that we know. So we got plus 70 plus negative 100 equals now you've got 10 times a. So here what we're going to get is negative 30 equals 10 A, and so A=-3m/s². So let's talk about this. Now we actually got a negative number. So what does that mean? Well, negative just means direction. And if we get a negative number, it just means our acceleration points against the direction of positive. So here our acceleration is actually going to point to the left a=3. Now we're always going to write, letters in our diagram and numbers to be positive oh, 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 got a positive a here and it points to the right. We got a negative 3 here and it pointed to the left. So we always write the letter in f=ma as 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.