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# Newton's second law of motion

AP.PHYS:
INT‑3.B (EU)
,
INT‑3.B.1 (EK)
NGSS.HS:
HS‑PS2‑1
,
HS‑PS2.A.1
,
HS‑PS2.A
,
HS‑PS2

## Video transcript

Newton's First Law tells us that an object at rest will stay at rest, and object with a constant velocity will keep having that constant velocity unless it's affected by some type of net force. Or you actually could say an object with constant velocity will stay having a constant velocity unless it's affected by net force. Because really, this takes into consideration the situation where an object is at rest. You could just have a situation where the constant velocity is zero. So Newton's First Law, you're going to have your constant velocity. It could be zero. It's going to stay being that constant velocity unless it's affected, unless there's some net force that acts on it. So that leads to the natural question, how does a net force affect the constant velocity? Or how does it affect of the state of an object? And that's what Newton's Second Law gives us. So Newton's Second Law of Motion. And this one is maybe the most famous. They're all kind of famous, actually. I won't pick favorites here. But this one gives us the famous formula force is equal to mass times acceleration. And acceleration is a vector quantity, and force is a vector quantity. And what it tells us-- because we're saying, OK, if you apply a force it might change that constant velocity. But how does it change that constant velocity? Well, let's say I have a brick right here, and it is floating in space. And it's pretty nice for us that the laws of the universe-- or at least in the classical sense, before Einstein showed up-- the laws of the universe actually dealt with pretty simple mathematics. What it tells us is if you apply a net force, let's say, on this side of the object-- and we talk about net force, because if you apply two forces that cancel out and that have zero net force, then the object won't change its constant velocity. But if you have a net force applied to one side of this object, then you're going to have a net acceleration going in the same direction. So you're going to have a net acceleration going in that same direction. And what Newton's Second Law of Motion tells us is that acceleration is proportional to the force applied, or the force applied is proportional to that acceleration. And the constant of proportionality, or to figure out what you have to multiply the acceleration by to get the force, or what you have to divide the force by to get the acceleration, is called mass. That is an object's mass. And I'll make a whole video on this. You should not confuse mass with weight. And I'll make a whole video on the difference between mass and weight. Mass is a measure of how much stuff there is. Now, that we'll see in the future. There are other things that we don't normally consider stuff that does start to have mass. But for our classical, or at least a first year physics course, you could really just imagine how much stuff there is. Weight, as we'll see in a future video, is how much that stuff is being pulled down by the force of gravity. So weight is a force. Mass is telling you how much stuff there is. And this is really neat that this formula is so simple, because maybe we could have lived in a universe where force is equal to mass squared times acceleration times the square root of acceleration, which would've made all of our math much more complicated. But it's nice. It's just this constant of proportionality right over here. It's just this nice simple expression. And just to get our feet wet a little bit with computations involving force, mass, and acceleration, let's say that I have a force. And the unit of force is appropriately called the newton. So let's say I have a force of 10 newtons. And just to be clear, a newton is the same thing as 10 kilogram meters per second squared. And that's good that a newton is the same thing as kilogram meters per second squared, because that's exactly what you get on this side of the formula. So let's say I have a force of 10 newtons, and it is acting on a mass. Let's say that the mass is 2 kilograms. And I want to know the acceleration. And once again, in this video, these are vector quantities. If I have a positive value here, we're going to make the assumption that it's going to the right. If I had a negative value, then it would be going to the left. So implicitly I'm giving you not only the magnitude of the force, but I'm also giving you the direction. I'm saying it is to the right, because it is positive. So what would be acceleration? Well we just use f equals ma. You have, on the left hand side, 10. I could write 10 newtons here, or I could write 10 kilogram meters per second squared. And that is going to be equal to the mass, which is 2 kilograms times the acceleration. And then to solve for the acceleration, you just divide both sides by 2 kilograms. So let's divide the left by 2 kilograms. Let me do it this way. Let's divide the right by 2 kilograms. That cancels out. The 10 and the 2, 10 divided by 2 is 5. And then you have kilograms canceling with kilograms. Your left hand side, you get 5 meters per second squared. And then that's equal to your acceleration. Now just for fun, what happens if I double that force? Well then I have 20 newtons. Well, I'll actually work it out. Then I have 20 kilogram meters per second squared is equal to-- I'll have to color code-- 2 kilograms times the acceleration. Divide both sides by 2 kilograms, and what do we get? Cancels out. 20 divided by 2 is 10. Kilograms cancel kilograms. And so we have the acceleration, in this situation, is equal to 10 meters per second squared is equal to the acceleration. So when we doubled the force-- we went from 10 newtons to 20 newtons-- the acceleration doubled. We went from 5 meters per second squared to 10 meters per second squared. So we see that they are directly proportional, and the mass is that how proportional they are. And so you could imagine what happens if we double the mass. If we double the mass in this situation with 20 newtons, then we won't be dividing by 2 kilograms anymore. We'll be dividing by 4 kilograms. And so then we'll have 20 divided by 4, which would be 5 and would be meters per second squared. So if you make the mass larger, if you double it, then your acceleration would be half as much. So the larger the mass you have, the more force you need to accelerate it. Or for a given force, the less that it will accelerate it, the harder it is to change its constant velocity.