6. Intro to Forces (Dynamics)

Newton's First & Second Laws

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## Intro to Forces & Newton's Second Law

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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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## Solving for Forces Using Newton's Second Law

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every once we've gotten some practice with using F equals Emma. And in this video we're gonna take a look at how we saw for forces using Newton's second law using the same list of steps and equations. Let's check it out. So we got this 10 kg box and it's accelerating to the rights. It's being pushed by two forces. So I've got this box like, Here's 10 here. I actually know what the acceleration is. A equals nine and I got to force is one of them pushes to the left with 30 Newton's. So this is 30 here, and so 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 for us here. This is f A, and I'll call this FB just like we have before, and I'm trying to figure out what s f A is, so I know I would have to use F equals M A. But first what I want to do because I want to choose the direction of positive and just like we have before, we're gonna usually gonna choose the right direction. So direction of positive is going to be the right like this. And now we get into our f equals m a here. So we have f equals m A. And remember that when we are expanding the sum of all forces, we have two rules forces along our direction of positive, written with a plus sign and against our direction of positive or written with a minus sign. So, for example, here we've got our f a, which is positive, even though we don't know who it is. And then we got our negative FB here because it points to the left and the Sequels. M A. Now we just replace the values that we know, right, So we have f a plus and this is gonna be negative. 30. And this is gonna be, uh, 10 times nine. So when we move the 30 to the other side, where you saw for you're gonna get 90 plus 30 equals 120 so that's your answer. You've got 100 and 20 Newtons here. So now let's take a look at our answer choices. Well, because all of our answer choices are positive that we don't have to worry about any signs or anything like that. We could just go ahead and choose. Answer be. That's going to be our correct answer. Let's move on to the second one here. We have very similar scenario here. The 10 kg box accelerates to the left this time. So we got this 10 kg box. Now you 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 six. But we're going to indicate it with the correct direction. And we have two forces. We've got one That's to the left. Sorry, once to the right, this is ethical. 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 gonna 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 feet was m A. So now we just expand the forces that we know, Remember, uh, along the direction of positive is written with a plus sign. And then we've got our negative FB here, and this equals mass times acceleration. So now we just replace the values that we know. We know this is 70 plus negative f b and then this equals 10. And then do we write six or negative six? Well, remember, assuming the direction of positive is to the right, our acceleration actually points left. So this section brings us up brings up an important point here. Whenever we write f equals m A. We're always writing the letter A as positive meaning you would never write em times negative 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 you plug in the correct sign if you actually know it. So, for example, here we've got six, but it's actually gonna be negative six, because our acceleration points to the left. All right, so now we've got here is we're gonna We're gonna rearrange and solve for this force. So we've got we're gonna move this over to the other side, and this is gonna be 70 plus 60 equals f B, which is 130. So if you take a look here, we've got FB is 100 and 30 Newton. So let's take a look at our answer choices. We actually have to. We have 100 and 30 and negative 130. So which one is right? Well, one of things you might have noticed here is that in previous videos, whereas when we saw 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 saw for a right pointing force, I got a positive and a left pointing force. I still got a positive number. 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 you Professor knows that you know the direction of the force. Another thing we can do here is look at the look at the 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 Newton's. That's it for this one. Guys, let me know if you have any questions.

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## Newton's 1st Law

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Hey, guys. So now that we've 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 gonna just going to skip ahead. We're gonna come back to this bullet point in just a second here. I actually wanna start with the example because it's something we know how to do. We've gotta force or a box is pushed to the right with 20 and then 20 to the left. So we know this box is a massive 6 kg, so I just want to draw that real quick. This box here, we've got two forces. This F equals 20 and this F equals 20. So I'm gonna go ahead and label these. Let's call this one f A. This one FB and we want to do is want to figure out the acceleration, so I'm gonna have to stick to the steps. I know we have to write f equals m A. 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 gonna write f equals m A so f equals m a. Here, we've got to expand all of our forces. And we're doing this. Any forces a longer direction of positive our A plus get a plus sign and anything against gets a negative sign. So that's gonna be our f b c r m A. Now we just replace our values. This is positive. 20 plus negative 20 right? That's because this points backwards and this equals six a. So the 20th negative 20. Cancel it to zero and you get zero equals six A. Which means that the acceleration is 0/6, and that's zero. 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 zero, like just we just like we had in our example here are net forces was zero because 20 and cancel each other out in our acceleration is equal to zero. And if you ever have an acceleration of zero, your velocity is constant. So basically what inertia means is that objects resist changes to their velocity unless they are 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 go two blocks that's at rest, right? It's velocity is equal to zero, 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 balanced out, just like we did in our example. Here. In both of these situations, the net force is equal to zero. So therefore our acceleration is equal to zero. 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 m per second, but there's no forces acting on it. Here we have this box that's moving at 5 m per second, but you do have some forces five and five that perfectly cancel each other out, just like we had in our example and both of these situations, just like we did on the left. The net force is equal to zero, so that means that the acceleration is equal to zero. And that just means that this object keeps moving a constant velocity. So this happens. So this box is just going to keep moving with V equals five. That's going to be its velocity, right? So what happens is moving objects in which their velocity is not equal to zero 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 that's moving, eventually it's gonna stop. But that's because we have friction. So imagine this box was basically floating in space and you push it with five. 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, right? I've got one last point to make here, which 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 have these two blocks here, right? They're both 2 kg and you pull one with 12 Newtons. If you wanted to calculate the acceleration using F equals M A, you would have the acceleration is 12 over to write force divided by mass and I'll give you 6 m per second squared. Now imagine that you had a 3 kg block instead of to you pulled it with the exact same 12. So now we want to calculate the acceleration. And this is just gonna be 12/4 12/3. Right, Because that's the mass and you would get 4 m per second squared. So, really, for the same exact F nets, a heavier object right in which the masses heavier is going to accelerate slower. You can actually just see this from F equals M A right f equals M A. If you have the same exact net force. But your mass is higher than that means your acceleration is going to be lower, which means it's going to resist changes in velocity more. It's gonna change velocity slower. All right, so let's say for this one, guys, let me know if you have any questions.

Additional resources for Newton's First & Second Laws

PRACTICE PROBLEMS AND ACTIVITIES (26)

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- A 4.50-kg experimental cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13...
- A 4.50-kg experimental cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13...
- A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of t...
- A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The...
- A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a hori...
- Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his...
- To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in...
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- Problems 35, 36, 37, 38, 39, and 40 show a free-body diagram. For each: a. Identify the direction of the acce...
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- The 100 kg block in FIGURE EX7.24 takes 6.0 s to reach the floor after being released from rest. What is the m...
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