Newton's First & Second Laws - Online Tutor, Practice Problems & Exam Prep

Intro to Forces & Newton's Second Law

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.

Solving for Forces Using Newton's Second Law

Hey, everyone. So we've gotten some practice with using \( f = ma \). And in this video, we're going to take a look at how we solve for forces using Newton's second law. So we're going to be using the same list of steps and equations. Let's check it out. So we've got this 10 kilogram box, and it's accelerating to the right. It's being pushed by 2 forces. So I've got this box; here is 10. Here, I actually know what the acceleration is, \( a = 9 \). And I got 2 forces. One of them pushes to the left with 30 Newtons. So this is 30 here. And so what I want to do is I want to find the other force. So what does that mean? Well, I've got one force pushing it to the left, but it accelerates to the right. So I know I have to have another force that's pushing it to the right as well. So this is my mystery force here. This is \( f_a \), and I'll call this \( f_b \) just like we have before, and I'm trying to figure out what this \( f_a \) is. So I know I'm going to have to use \( f = ma \), but first, what I want to do is I want to choose the direction of positive. And just like we have before, we're going to usually choose the right direction. So the direction of positive is going to be to the right like this. And now we get into our \( f = ma \) here. So we have \( f = ma \). And remember that when we are expanding the sum of all forces, we have two rules. Forces along our direction of positive are written with a plus sign, and against our direction of positive, are written with a minus sign. So, for example, here, we've got our \( f_a \) which is positive even though we don't know what it is, and then we got our negative \( f_b \) here because it points to the left, and this equals \( ma \). Now we just replace the values that we know, right? So we have \( f_a + (-30) = 10 \times 9 \). So when we move the 30 to the other side, what you solve for, you're going to get \( 90 + 30 = 120 \). And so that's your answer. You've got 120 Newtons here. So now let's take a look at our answer choices. Well, because all of our answer choices are positive, then we don't have to worry about any signs or anything like that. And we could just go ahead and choose answer b. That's going to be our correct answer. Let's move on to the second one. Here, we have a very similar scenario here. The 10-kilogram box accelerates to the left this time. So we've got this 10 kilogram box. Now we know the acceleration is to the left. Even though it points to the left, we're still going to write it in our diagram as 6, but we're going to indicate it with the correct direction. And we have 2 forces. We've got one that's to the left, oh, sorry. One that's to the right. This is \( f = 70 \). We want to calculate the other force. So we have another force just like we had before that accelerates to the left. There has to be a force that's pushing it to the left. So this is our mystery force here, and I'm going to call this \( f_b \) and this is \( f_a \). So now we want to figure out \( f_b \) in this scenario. So we got to choose our direction of positive. We actually don't need to because we're going to assume the direction of positive is to the right; that's given to us in the problem here. So now we write our \( f = ma \). So now we just expand the forces that we know; remember, along the direction of positive is written with a plus sign, and then we got our negative \( f_b \) here, and this equals mass times acceleration. Now we just replace the values that we know. We know this is \( 70 + (-f_b) = 10 \times (-6) \). Well, remember, assuming the direction of positive is to the right, our acceleration actually points left. So this actually brings us to an important point here. Whenever we write \( f = ma \), we're always writing the letter \( a \) as positive, meaning you would never write \( m \times (-a) \), for example, if you knew that it pointed to the left. However, when you actually know the value of the acceleration and the direction, you're going to plug in the correct sign. So for example, here, we've got 6, but it's actually going to be negative 6 because our acceleration points to the left. Alright? So now what we've got here is we're going to rearrange and solve for this force. So we've got we're going to move this over to the other side and this is going to be \( 70 + 60 = f_b \) which is 130. So if you take a look here, we've got \( f_b \) is 130 Newtons. So let's take a look at our answer choices. We actually have two. We have 130 and negative 130. So which one is right? Well, one of the things you might have noticed here is that in previous videos, whereas when we solve for \( a \), we get a positive or negative, which is basically just the direction. Our final answer gives us the direction. When you're solving for forces, however, you actually always get a positive number. Notice here how in these examples, when I solve for a right-pointing force, I got a positive, and a left-pointing force, I still got a positive number. I always get positives because, basically, you're solving for the magnitude of these forces. So what you do here is there's actually a couple of ways to solve this. You could indicate the direction by actually writing it into your answers so your professor knows that you know the direction of the force. Another thing we can do here is look at the problem itself. We're going to assume the direction of positive is to the right, which means if we get a left-pointing force between these two answer choices, it's actually going to be negative 130 Newtons. That's it for this one, guys. Let me know if you have any questions.

Newton's 1st Law

Hey, guys. So now that we talked about Newton's second law, we want to make sure we go back and cover Newton's first law. So let's go ahead and talk about that in this video. I'm going to just skip ahead. We're going to come back to this bullet point in just a second here. I actually want to start with the example because it's something we know how to do. We've got a force or a box that's pushed to the right with 20 and then 20 to the left. So we know this box has a mass of 6 kilograms. I just want to draw that real quick. This box here, we've got 2 forces. This f equals 20 and this f equals 20. So I'm going to go ahead and label these. Let's call this one fa and this one fb. And what we want to do is to figure out the acceleration. So I want to stick to the steps. I know I'm going to have to write f = ma, but first, I want to choose the direction of positive. So remember, that usually that's to the right like this. And so now we're going to write f = ma here. We've got to expand all of our forces and when we're doing this, any forces along our direction of positive get a plus sign and anything against gets a negative sign. So that's going to be our fb. This is our ma. Now we just replace our values. This is positive 20 plus negative 20, right? That's because this points backward, and this equals 6a. So the 20 and the negative 20 cancel out to 0, which means that the acceleration is 0 over 6, and that's 0. So let's talk about Newton's first law. Newton's first law is sometimes referred to as the law of inertia. And basically, what it says is that if your net force is ever equal to 0, like just we had in our example here, our net forces were 0 because 2020 cancel each other out, then our acceleration is 0. And if you ever have an acceleration at 0, your velocity is constant. So basically, what inertia means is that objects resist changes to their velocity unless they're acted upon by a net force. The way you might have seen this written in your textbooks is that objects keep doing whatever it is that they're doing unless you have a net force. Let me go ahead and show you some examples and situations here. So here we've got a box that's at rest. Right? It's velocity is 0 and there's no forces acting on it. So there's no net force. Here, we have the same block at rest, but now we have these forces that perfectly balance out just like we did in our example. In both of these situations, the net force is equal to 0. So therefore, our acceleration is 0. And if this box is at rest, then that means it's just going to stay at rest. So these objects just keep doing whatever it is that they were doing. So now let's talk about what happens when objects are moving. This is slightly less intuitive. Now you have this box that's moving at 5 meters per second, but there's no forces acting on it. Here, we have this box that's moving at 5 meters per second, but you do have some forces 55 that perfectly cancel each other out just like we had in our example. In both of these situations, just like we did on the left, the net force is 0. So that means that the acceleration is 0. And that just means that this object keeps moving at a constant velocity. So this box is just going to keep moving with v equals 5. That's going to be its velocity. Right? So what happens is moving objects in which their velocity is not equal to 0 actually don't require a force to keep moving. This is kind of something that is a little bit counterintuitive. Right? If you push a box and it's moving, eventually, it's going to stop. But that's because we have friction. So if matching this box was basically floating in space and you push it with 5, it would keep on going forever unless something finally stopped it. So without net forces, these objects would just keep on moving forever. That's what Newton's law basically tells us. Alright. I've got one last point to make here, which is we talked about inertia as the resistance to changes in velocity. And basically, mass is kind of like a quantity or an amount of that resistance to change. What do I mean by that? Well, imagine we had these 2 blocks here. Right? They're both 2 kilograms and you pull 1 with 12 newtons. If we wanted to calculate the acceleration using f = ma, you would have the acceleration is 12 over 2. Right? Force divided by mass. And that would give you 6 meters per second squared. Now imagine that you had a 3 kilogram block instead of 2, you pulled it with the exact same 12. So now we want to calculate the acceleration and this is just going to be 12 over 3, right, because that's the mass, and you would get 4 meters per second squared. So really, for the same exact net forces, a heavier object, right, in which the mass is heavier is going to accelerate slower. You can actually just see this from f = ma. Right? If you have the same exact net force but your mass is higher, then that means your acceleration is going to be lower which means it's going to resist changes in velocity more. It's going to change velocity slower. Alright. So that's it for this one, guys. Let me know if you have any questions.