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# Newton's second law of motion

Newton's second law of motion is F = ma, or force is equal to mass times acceleration. Learn how to use the formula to calculate acceleration. Created by Sal Khan.

Video transcript

Newton's first law tells us that an object at rest will stay at rest, and an object with a constant velocity will keep having that constant velocity unless it's affected by some type of net force or you actually can say that 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 gonna 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 the state of an object? And that's what Newton's second law gives us- 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- 'cause we're saying ok if you apply force it might change that constant velocity but how does it change that constant velocity? Well say I have a brick right here and it is floating in space Newton's second law tells us that 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 it's constant velocity. If you have a net force applied to one side of this object then you would have a net acceleration going in the 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 accleration And the constant of proportionality 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 normallyconsider stuff that does start to have mass but for our classical or at least 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 have made all of our math much more complicated. But it's nice that 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 10Newtons - and just to be clear, a Newton is the same thing - so this is the same thing as 10kilogram.metre per seconds squared and that's good that a Newton's the same thing as kilograms.metres per second square 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 -it is acting on a mass, let's say that the mass is 2 kilograms and I wanna know the acceleration. And once again in this video, these are vector quantities. If I have a positive value here I'm going to--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 will be the acceleration? Well we just use F=ma You have-on the left hand side 10 - I could write 10 Newtons here or I could write 10kilograms.metres 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'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 cancelling kilograms. Your left hand side you get 5 metres 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 20Newtons--I'll actually work it out-- 20 kilograms.metres per second squared is equal to --I'll actually color-code this-- 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 metres 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 metres per second squared to 10 metres per second squared. So we see that they are directly proportional and the mass is how proportional they are. And so you can imagine what happens if we double the mass. If we double in, let's say 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 will be 5 and it'll be metres 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 it's constant velocity.