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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 an object in it 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 constant velocity will stay having a constant velocity unless it's affected by a net force because really this takes into consideration the situation we're not due to 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 gonna 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 so Newton's Newton's second law second law of motion second law of motion and this one is maybe the most famous although they're all kind of famous actually I won't I won't pick favorites here but this one gives us the famous formula force is equal to mass times acceleration an acceleration is a vector quantity and force is a vector quantity and what it tells us because we're saying okay if you apply 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 Newton's second law tells us 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 in the universe actually dealt with pretty simple mathematics what it tells us is is if you apply if you apply a net force 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 then have zero net force then the object won't 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 or supplied 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 that is an object's of 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 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 it's 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 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 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 our feet wet a little bit with computations involving force mass and acceleration let's say let's say that I have a force and then D and the unit of force is appropriately called the the Newton so let's say I have a force of so let's say that the force I have a force of 10 Newtons and just to be clear a Newton is the same thing so this 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 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 want to know the acceleration I want to know the acceleration I want to 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 would be the acceleration well we just use F equals MA you have on the left hand side 10 Ukiah I could write 10 Newton's 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 2 kilograms times the acceleration 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 byte or 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 let me just do it 10 divided by 2 is 5 and then you have kilograms cancelling with kilograms your left hand side you get 5 meters per second squared and then york that's equal to your acceleration now just for for fun what happens if i double 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 kilogram meters per second squared is equal to i don't have to color-code this 2 kilograms times the acceleration divide both sides by 2 kilograms 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 double the force we went from 10 Newtons to 20 Newtons the acceleration doubled went from 5 meters per second squared and 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 and 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 would be 5 and there would be meters per second squared so if you make the mass larger if you double it then your acceleration will be half as much so the larger the mass you have the more force you need to accelerate it or go for a given force the less that it will accelerate it the harder it is to change its constant velocity