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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 is affected by some type of net force. Or you actually could say that something with constant velocity will stay having a constant velocity unless affected by a net force. This takes into consideration the situation where an object is at rest. You could 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 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? That's what Newton's second law gives us. So Newton's Second Law of Motion. This one is maybe the most famous. (They're all kind of famous. Actually I won't pick favorites here) This one gives us the famous formula...Force is equal to Mass times Acceleration. Acceleration is a vector quantity and Force is a vector quantity It tells us...If you apply a force, it might change the constant velocity but <i>how</i> does it change that constant velocity? Say I have a brick 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 the classical sense before Einstein showed up) The laws of the universe actually dealt with simple mathematics What it tells us, is that if you apply a net force, let's say on this side of the object and we talk about <i>net force</i> because if you apply two forces that cancel out, and they have 0 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 would have a net acceleration going in the same direction and what Newton's second law of motion tells us is that the acceleration will be proportional to the force applied or the force applied is proportional to that acceleration. and the constant to proportionality...or to figure out what you multiply the acceleration by to get the force, or what to divide the force by to get the acceleration... ...is called mass. that is an object's mass DO 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 (we'll see in the future that there are other things we normally don't consider "stuff" that does start to have mass) but for our classical, or first year physics course, you can really just imagine: how much stuff there is As we'll see in a future video: weight is how much that stuff is being pulled down by the force of gravity. 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've lived in a universe where F=(m^2)<i>a</i>sqrt(a) which would've made all of our math much more complicated but it's nice, because it's just a 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 it's kg*m/(s^2) because that's exactly what you get on this side of the formula So let's say that we 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 Once again, these are vector quantities If I have a positive value here, we are going to make the assumption that it's going to the right If I had a negative value, 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 am saying it is "to the right", because it is positive So what would be the acceleration? We'll just use F=m*a You have, on the left hand side, 10 Newtons... or 10 kg*m/(s^2) and that is going to be equal to the mass... which is 2 kg... times the acceleration and then to solve for the acceleration, you just divide both sides by 2 kg So let's divide the left by 2 kg and let's divide the right by 2 kg. That cancels out. The 10 and the 2...10 divided by 2 is 5 and then you have kilograms canceling with kilograms. your lefthand side...you get 5 m/(s^2) and then...that's equal to your acceleration! Now, just for fun, what would happen if I double that force? Then I have, 20 Newtons (I'll actually work it out) then I'll have 20 kg*m/(s^2)... ...is equal to 2 kg times the acceleration divide both sides by 2 kg and what do we get? it cancels out...20 divided by 2 is 10...kilograms cancels with kilograms So then we have... the acceleration, in this situation, is equal to 10 m/(s^2) So when we double the force...we went from 10 Newtons to 20 Newtons...the acceleration doubled! We went from 5 m/(s^2) to 10 m/(s^2) So we can see that they are directly proportional and the mass is that <i>how</i> proportional they are So you can imagine what happens if we double the mass. If we double the mass (let's say in this situation, with 20 Newtons) Then we won't be dividing by 2 kg anymore, we'll be dividing by 4 kg then we will have 20 divided by 4, which will be 5 m/(s^2) If you make the mass larger...if you double it, then your acceleration will be half as much. So the <i>larger</i> the mass you have...the <i>more</i> force you need to accelerate it Or, for a given force...the <i>less</i> that it will accelerate... the harder it is to change its constant velocity.