momentum and impulse going to be the topic of this lesson in my brand new General Physics playlist which will eventually cover a full year of University algebra based physics now most students associate this chapter which is going to be on momentum impulse and collisions they really focus on the collisions it's the hardest part of this chapter before we can talk about it we really got to talk about momentum and impulse which should be the point of this lesson and then in the next one we'll cover the collisions my name is Chad and welcome to Chad's prep where my goal is to take the stress out of learning science now if you're new to the channel we've got comprehensive playlists for General chemistry organic chemistry General Physics and high school chemistry and on chatsprep.com you'll find premium Master courses for the same that include study guides and a ton of practice you'll also find comprehensive prep courses for the DAT the MCAT and the oat all right so we gotta have a little discussion about momentum and uh what if I told you that you know yesterday uh someone was out for a ride and uh they hit me doing 40 miles an hour uh that would sound terrible and I'm just going after sympathy votes for her and uh what I didn't tell you is that the somebody was an amoeba uh and they were out for a ride because they were riding on the back of a mosquito and they hit me doing 40 miles per hour uh and obviously you're like wow that's one fast mosquito I know that's what you were thinking uh no you're thinking okay facetious here and the key here is that such a small mosquito with an amoeba on it don't forget that part it doesn't have a whole lot for momentum associated with it and so colliding with me is not the biggest deal in the world like it would be if a person was out for ride on a horse or in a car or something like that so if we look at the definition of momentum here and it's uh symbol is the lowercase letter P it is a vector FYI so it has both magnitude and Direction but it's just equal to mass times velocity and so the mass matters so I told you that you know so somebody was out for a ride and hit me doing 40 miles per hour and I only hinted at the velocity and it sounded terrible because I made it sound like it was a car accident or something like that so but the key is if it was the mass of a mosquito with an amoeba on it who cares it doesn't have a whole lot for momentum and so it colliding with you is not the biggest deal in the world so momentum has both those components both mass and velocity so and momentum is directly proportional to both of them you double the mass you've doubled the momentum you double the velocity you've doubled the momentum you double them both and you have quadrupled the momentum so but that's momentum and again it's a vector and it has the same direction as the velocity as well which is also obviously a vector all right so that is momentum and again it's a vector which means we're going to have to worry about potentially breaking it up into X and Y components and things about sorts sometimes we're going to deal with two-dimensional problems as we'll see with collisions and stuff like that so but sometimes we're gonna deal with just one dimensional problem so and more properly we'll just call this linear momentum and a one-dimensional problem there's only one dimension and we have to worry about components but as we'll see we're going to be working our way up towards these two dimensional problems now the second thing we'll talk about is what we call impulse an Impulse is also a vector turns out it's equal to force times the duration of time so and it turns out if you want to change something's momentum or change its motion so to speak there's an Impulse that is required and ultimately means there's a net force that needs to be applied cool now notice the impulsive proportional to force but it's also proportional to delta T so let's say you know you get in a fight and you give somebody a quick push you know uh there's an Impulse associated with that but instead of giving them a quick push what if you put your shoulder down and you just drive into them and you just keep pushing keep pushing so that's going to be a greater impulse and you might have only hit him with the same Force neither case either the quick push or you gotta push where you're just driving into them but with the longer duration there's going to be a much greater impulse and you're going to get a much bigger change in their motion as we'll see in just a second so and again we said there's going to be a connection here between impulse and momentum and we call that the impulse momentum theorem so in that impulse momentum theorem here says that the impulse F delta T is going to equal the change in an object's momentum that's the connection here so if we look at the units for both of these there's no special SI units for momentum we're just going to use the base the combination of Base s i units that represent it so mass is kilogram velocity is meter per second so it's simply just a kilogram meter per second well if you look at force times time that's going to be a Newton's second well a newton is a kilogram meter per second squared times a second cancels out one of those seconds and you're just left with a kilogram meter per second so interestingly enough these have the same units the SI unit of impulse is also kilogram meters per second and so now is not so surprising that we have this equality here because they have the same units so but we can derive this from Newton's Second Law let's take a look so Newton's second law says f equals mass times acceleration but we know acceleration is change in velocity over the change in time so and then we can move this over delta T get F delta T equals m Delta V so in the case it's typically the velocity is changing not the mass and so we could look at this one further away and make this Delta MV which is momentum and so we now get the impulse is equal to the change in momentum so we've just kind of derived this impulse momentum theorem so we're now just going to kind of tackle some problems we're going to deal with some impulse problems some momentum problems and then some application of the impulse momentum theorem as well all right so we'll start easy and work our way up first question says a 1200 kilogram car is traveling with a velocity of 20.0 meters per second what is its momentum and again momentum is just mass times velocity and both of those are given we can plug and chug as long as they're SI units and they are so a 1200 kilogram car it's traveling 20.0 meters per second so we could probably do this in our head so 1200 times 2 is 2400 but times 20 add another zero is going to be 24 000. so and in this case again kilogram meters per second is the unit that's the magnitude of the momentum and it's in the same direction as whatever Direction the velocity was in all right so second question here a 1200 kilogram car traveling at the velocity 20.0 meters per second that should sound familiar uh hits a cow that's new so you should also know that the cow gets up and walks away no cow is injured in this question uh the cow applies an average force of 90 000.0 Newtons for 0.20 seconds to the car in the direction opposite to its motion what is the impulse caused by the cow on the car and what is the velocity of the car after hitting the cow so two-part question and the first part again is just what is the impulse of the cow on the card here we've got the definition of impulse right here and so impulse just equals f delta T and those numbers are given and so here we're told that the force of the cow on the car is 90 000 Newtons and that's 90 000.0 Newtons so and then delta T here we're given as 0.20 seconds now before we move on so in all likelihood we're going to be defining the velocity of the car as the positive direction and this Force right here is in the opposite direction and so technically this would be a negative 90 000 Newtons kind of in that Paradigm and that's why the impulse is going to come out negative as well super important that we keep in mind the directions here and the signs that that affects on on our different Vector quantities all right so if we work this out so you probably do this in your head good time to pull out your calculator anyways but do it in your head uh multiplying by 0.2 is same thing as dividing by five and my personal favorite way though is just to multiply by 0.1 and then double it because multiplying by point one is same thing dividing by 10 and we just move it back a decimal place and that's negative nine thousand and then doubling that would be negative 18 000. and that's going to be not Newton seconds I mean technically it is Newton seconds but more properly kilogram meters per second that is the impulse of the cow on the car now the second part of that question is what is the velocity of the car after hitting the cow and this is where the impulse momentum theory is going to come into play now we've written it as F delta T equals Delta P but we can technically write this as just I equals Delta P since we've already solved for the impulse in the previous part of the question we don't have to actually substitute in F delta T we'll just substitute our value here of negative 18 000 kilogram meters per second and so we can say negative 18 000 kilogram meters per second is going to equal here and again change in momentum is going to be P final minus P initial which would be MV final minus MV initial technically it's the same mass either way of that car and so we could factor that out as well so but I'm going to leave it out just like that we're going to get Negative 18 000 kilogram meters per second equals that 1200 kilogram car the final velocity is what we want and the initial velocity was that 20 meters per second all right so in this case we can see that 1200 times 20 well 1200 times 2 would be 2400 so 1200 times 20 add that extra zero is 24 000. and so we're subtracting 24 000 kilogram meters per second but we'll add it to the other side and so adding a 24 000 to a negative 18 000. so It's Gonna Get Us six thousand kilogram meters per second is going to equal 1200 kilograms times that final velocity and we'll divide through by 1200. to figure that out and in this case we could just look at that as being equivalent to 60 divided by 12 those two zeros are going to cancel and 60 by 12 is 5 and that is indeed the final velocity and with the appropriate number of sig figs like we need two based on the time that was given above to Sig fig so it's 5.0 meters per second and it is positive which means the car is still moving in the same direction it was traveling it hits the cow and slows down tremendously but is still moving in the forward Direction with a velocity of 5.0 meters per second so another one with yet again this 1200 kilogram car a 1200 kilogram car is traveling with a velocity of 20.0 meters per second if it is hit by a truck and this isn't if it's purely hypothetical again nobody injured no actual accidents here but if it is hit by a truck causing it to move backward with a velocity of 10 meters per second after the Collision what is the car's change in momentum so we want the change in momentum here and again that's equal to final momentum minus initial momentum which in this case is equal to m v final minus m v let's get a big V there V initial didn't want to subscript V cool and this is going to be our calculation the thing we got to be careful with here is signs yet again so in this case the car is initially moving in this Direction with a velocity of 20 meters per second but it gets in a head-on collision with a truck and ends up in the end moving backwards with a velocity of 10 meters per second and we've got to account for that a lot of students will do this calculation a little bit wrong so if we look at this change in velocities change in velocity is not going to be 10 meters per second so if you went down from 20 meter second down to 10 meters per second in the same direction that would be a change in velocity of 10 meters per second if he went from 20 meters per second down to a complete stop that would now be a change and I guess technically of negative 20 meters per second but in this case not only does not come to just a complete stop he's actually heading back the other direction the velocity Has Changed by negative 30 meters per second so and that's what kind of students sometimes Miss on something like this where there's a change in Direction in a one-dimensional problem like this so but if we take a look here so Delta p it's going to equal that 1200 kilograms so final velocity again in the opposite direction is negative 10 meters per second minus again that 1200 kilograms times the positive 20 meters per second all right now we can do a little bit of math here in this case 1200 times negative 10 is going to be negative 12 000 kilogram let's get this right kilogram meters per second uh and then minus 1200 times 20 is going to be minus 24 000. kilogram meters per second and so we got a negative number subtracting another number so in this case your change in momentum is going to end up being negative 36 000 kilogram meters per second foreign just accounting for that change in Direction super important a lot of students would have missed one of the negative signs here so the next question is going to involve a hitter hitting a baseball off a t from rest and if you're completely unfamiliar with baseball those might mean nothing to you I had a friend from India who plays only Cricket play baseball with us this last weekend it was a hoot because he doesn't know any of the rules so if you're completely unfamiliar with baseball a t holds a baseball stationary that you can practice hitting and hit a stationary ball a ball that is still a ball that has no velocity and hit it off the T to kind of work on your form that way hopefully you're better when a ball is actually being pitched towards you later on so that's what it means when a ball hit off a t and so the question says a hitter hits a 0.10 kilogram baseball off of a t i put in parentheses from rest for those who aren't familiar if the average force applied by the bat to the ball is 10 000.0 Newtons and the velocity of the ball immediately after being hit is 40.0 meters per second how long was the bat in contact with the ball so we're wanting duration of time here and so we can see that this ball is having its momentum change because it has no momentum and is going to a situation where it's going to have momentum have velocity in this case so there must be an Impulse involved we're told the forced part of that impulse what we're not told is how long and that's what we're being asked to solve for so it's that impulse momentum theorem yet again [Applause] so we're going to have F delta T equals Delta P which we can write out again as F delta T equals MV final minus MV initial and go from there so in this case again the force is given us 10 000 Newtons time is not given so mass in this case I'm going to factor that out and make it 0.1 oh 0.10 let's get that right for Sig Fig's sake and I'm going to factor that out and just do V final minus V initial and so in this case v final is 40 meters per second and initially was zero so minus zero and there's a problem all we got to do is simply solve for delta T and so in this case delta T is going to equal 0.10 kilograms times 40 meters per second all over ten thousand Newtons and again you can look at that Newton as a kilogram meter per second squared which is why when you take kilogram meters per second and divide it by a kilogram meter per second squared you're going to come out with units of seconds all right so take a look at this so 40 times 0.1 is going to be 4 and 4 divided by 10 000. let's see what that comes out to and I'm going to use my calculator here we could probably do this without but hey let's just use the calculator we're going to get 4 times 10 to the negative 4. in this case we want two sig figs limited by the mass so 4.0 times 10 to the negative 4 seconds so and that's an SI unit this is about 0.4 milliseconds which is not far from the actual truth of how long a typical uh bat is in contact with a ball in a typical swing in baseball and that sums up this lesson if you found it helpful consider giving it a like happy studying