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# Introduction to momentum

## Video transcript

welcome back I will now introduce you to the concept of momentum momentum and the letter 4 momentum is in physics and or at least in mechanic's is the letter P P for momentum and I assume that's because they the letter M has already been used for mass which is I guess an even more fundamental idea so P for momentum so what is momentum well you probably have a a general idea of it being people if if you see a big guy running really fast I'll say he has a lot of momentum and if there's a big guy running really fast and a small guy running really fast most people would say well the big guy has more momentum without maybe maybe they don't have a quantitative sense of why they're saying that but but they just feel that that must be true and if we look at the definition of momentum it'll make sense the definition of momentum is equal to mass times velocity so something with say a medium mass and a huge velocity is going to have a big momentum or something with maybe a medium mass but with the other way around I forgot what I just said so a medium mass and big velocity huge momentum or the other way around huge mass medium velocity you have maybe the same momentum would still have a big momentum or another way of viewing momentum is how little you would like to be in the way of that object as it passes by how little would you how how unpleasant would it be to be hit by that object that's a good way of thinking about momentum so momentum is mass times velocity and since well let me let me so so what how does it relate to everything we've been learning so far so we know that force is equal to mass times acceleration right and what's acceleration well acceleration is just change in velocity right so we also know that force is equal to mass times change in velocity per unit of time right per change in time T for time so force is also equal to well mass times change velocity mass let's assume that mass doesn't change right so that could also be viewed as the change in the change in mass times velocity in the unit amount of time right in this little trick here I said you know the mass times the change in velocity that's the same thing as the change in the mass times the velocity assuming the mass doesn't change and here we have mass times velocity which is momentum so force can also be viewed as change and momentum per unit of time now I'll introduce you to another concept called impulse and impulse kind of means what you think it means and impulse is defined as force times time and I just want introduce you this to you just in case you see it on an exam or whatever so it's not a difficult concept so force times change in time or time if you assume time starts at time zero but force times change in time is equal to impulse I actually don't know after I should look up what letters they use for impulse but another way of viewing impulse is if force times change in time well that's the same thing as change in momentum over change in time times change in time right because this is just the same thing as force and that's just change in momentum so that's impulse as well impulse and the unit of impulse is the Joule and we'll go more to the Joule when we do work and all of that and if this confuses you don't worry about it too much the main thing about momentum is that you realize it's mass times velocity and since force is change in momentum per unit of time if you don't have any external forces on a system or want to say on a set of objects they're their combined or their net momentum won't change and that comes from Newton's laws the only way you can get a combined change in momentum is if you have some type of net force acting on the system so with that in mind let's do some momentum problems whoops invert colors okay so let's say we have a car it's a car we use some more interesting colors a car with a magenta bottom and it is let's see what is this problem say it's a thousand kilograms thousand kilograms so a little over a ton and it's moving at nine meters per second east so it's velocity is equal to nine meters per second east or to the right in this example and it strikes a stationary two thousand kilogram truck so here's my truck here's my truck and this is a two thousand kilogram truck and it's stationary so the velocity is zero and once when the car hits the truck let's just say that somehow it gets stuck in the truck and they just both keep moving together so they get stuck together the question is what is the resulting speed of the the combination truck and car after the collision well all we have to do is think about what is the combined momentum before the collision well let's see the momentum of the car is going to be the mass times the call mass of the car Matt well the total momentum is going to be the mass of the car times the velocity of the car plus the mass of the truck times the velocity of the truck and this is before they get they hit each other so what's the mass of the car that's a thousand what's the velocity of the car it's nine meters per second so as you can imagine a unit of momentum would be kilogram meters per second so it's a thousand times nine kilogram meters per second but I won't write that right now just to keep things simple or so I save space and then the mass of the truck is 2,000 and what's its velocity well zero it's stationary initially so the initial momentum of the system this is 2,000 times zero is nine thousand plus zero which equals nine thousand kilogram meters per second that's the momentum before the car hits the back of the truck now what happens after the car hits the back of the truck so let's go to that situation so we have the truck I'll draw a little less neatly and then you have the car and it's probably a little bit well I won't go into whether it's banged up and whether it released he'd and all of that let's just assume that that that there was nothing this is a simple problem that we can do so if we assume that there would be no change in momentum because we're saying that there's no net forces acting on the system and when I say system I mean the combination of the car and the truck so what we're saying is this combination this this new vehicle called a car truck its momentum will have to be the same as the car and the trucks momentum when they were separate so what do we know about this car truck object well we know its new mass right the car truck object it will be the combined mass of the two so it's a thousand kilograms plus two thousand kilograms so it's three thousand kilograms and now we can use that information to figure out its velocity how well its momentum this this three thousand kilogram object's momentum has to be the same as the momentum of the two objects before the collision so it it still has to be nine thousand kilogram meters per second so once again mass times velocity so mass is three thousand times the new velocity so we could call that I don't know new velocity V sub n that will equal nine thousand because momentum is conserved that's what you always have to remember momentum doesn't change unless there is a net force acting on the system because we saw a moment-- force is change in momentum per time so if you have no force in it you have no change in momentum so let's just solve divide both sides of this by three thousand and you get the new velocity is three meters per second and that kind of makes sense you have a relatively light car moving at nine meters per second in a stationary truck that it smacks the truck and they move together the combined object and it's going to be to the east the combined and we'll do more later but you know we assume that a positive velocity is East if somehow we ended up with a negative it would have been west but it makes sense because we have a light object and and the stationary heavy object and when the light object hits the stationary heavy object the combined object still keeps moving to the right but it moves at us at a relatively slower speed so hopefully they give you a little bit of intuition for momentum and that was a not too confusing of a problem and in the next couple of videos I'll do I'll do more momentum problems and then I'll introduce you to momentum problems in two dimensions I will see you soon