hello and welcome to another chapter and another first lecture of that chapter if you've been following this lecture series you first of all know a bit about this book what to expect and you know that i've mentioned momentum many times in the previous lectures well we're finally there we're finally introducing momentum perhaps the reason i mentioned it so many times was because it's such a fundamental idea and we just hadn't got to it yet we had to cover of course motion velocities accelerations and all that we had to cover forces of course we couldn't really move on we covered gravity which could have weighted but is so fundamental to an understanding and gets the definition of a fundamental force out of the way and then we talked about our first amazing accounting tool because we talked about energy and the conservation of energy if you recall when i talked about energy i said that energy isn't new physics it's not fundamental laws in the way that newton's laws of motion are all it tells us is that energy is conserved the only law is the conservation of it so in a sense we only care about energy because it's conserved well it's still incredibly useful all right and we talked about how it's a more modern development a more modern way of thinking about physics which of course makes us wonder what's in store 150 years from now how will they fundamentally think about physics and approach analytical problem solving using mathematics to solve problems in a whole different way that we didn't even anticipate because i guarantee you that people in newton's time never anticipated the way that we solve physics problems today and i'm not just talking about computers i mean even solving them by hand all that aside why do i bring all this up well because momentum is exactly like energy wait no not really at all energy is measured in joules momentum is measured in well newton seconds or kilogram meters per second so no it's not at all like that why did i say that because it's conserved okay so that actually is a big similarity in terms of how momentum and energy are used in problem solving and not just you know the problems that are assigned in homework but really just thinking about the world conceptualizing things building models whether those are computational or conceptual or analytical you know that's how we solve problems so momentum is a conserved quantity okay now i'm kind of jumping ahead by telling you that right giving away one of the big reveals of the chapter but we saw a conserved quantity already we saw that energy was conserved so i think it's so key to recognize that that's what momentum is all about now momentum is interesting in fact i find it and this could just be me i find it less intuitive than energy for some reason this is the concept of energy even the interesting equations maybe strange equations but somehow very easy to get kind of stuck in your brain like the formula the equation for kinetic energy one-half mv squared one-half times mass times the velocity of that thing that has mass squared one-half mv squared right that's this is such a iconic formula for me and momentum i don't feel like it has that momentum is mass times velocity maybe just because it's it's such a simple concept just mass times velocity that it almost belies on the the the usefulness of it it seems like there that you wait that at least again this is me that i'm waiting for something more that's all it is momentum is just mass multiplied by velocity it's the product of mass and velocity okay so if something's moving it has momentum okay because it has velocity if something's not moving if its velocity is zero okay which would be the same as its speed being zero well it doesn't have momentum so objects at rest have no momentum okay objects in motion have momentum also since mass is involved that implies that something needs to have mass to have momentum turns out that the one thing we know that doesn't have mass which is photons particles of light actually still have momentum despite not having mass so wow that complicates things but that's relativistic momentum and totally not what we're talking about here it's great to go there eventually but here we're talking about classical momentum okay so let's take a look at our sections in this video i want to cover sections 7.1 right because we're in chapter seven which is momentum and impulse some definitions i haven't talked about impulse yet but it's important definition okay and then the law of conservation of momentum okay so let's take a look at our slides so this introductory slide here isn't actually introducing collisions if you see collisions aren't covered until the next video or you know a section later in the chapter collisions won't be covered until 7.4 so why start with collisions because that's one of the things that we really can use momentum for is studying particular types of phenomenon particular types of situations that lend themselves to tracking momentum instead of using a purely newton's law approach okay i'll get back to that i actually said something very similar for energy so hopefully we can quickly make that connection let's look through this slide so how can we describe the change in velocities of colliding football players or balls colliding with bats right how do we you know solve for that system how do we you know have a predictive model that says you know these two things are hit together and this is how fast they're both going to be going after the collision maybe because they have different masses or they they came in with different initial speeds right how do we anticipate what will happen because i guarantee you we know how to do that right that's you know built into so many systems people there's so many you know kind of weight you hear about people you know knowing how something's going to work out right you know up to a certain amount of randomness in the real world but think about billiard balls right there's certain shots where the result is very expected for an expert level player right how how do they know that right because of momentum all right that's like the best way of thinking about a collision of anything especially building balls or maybe billiard balls included here's another way another kind of open question of why we care about momentum okay how does a strong force applied for a very short time affect the motion right so if something you know is is applied for just like a tiny fraction of a second a millisecond right a nanosecond how do you how do you quantify that how do you calculate it how do you deal with you know the the resulting acceleration what does that mean right because you have such such a small segment of time can you actually make a meaningful measurement because aren't you limited however you're making your measurements think one of the great basic tools with analyzing motion is high speed cameras especially because they're incredible availability in the modern world so could you do that with you know really high speed collisions no but turns out that the video analysis would be great if you took the momentum approach that we're leading to okay so can we apply newton's laws to collisions okay so i'm not going to tell you no but i'm going to say that it's impractical to do so okay instead we plot apply a different technique we use momentum okay it's the better technique for things like collisions okay what exactly is momentum well i told you right i gave that one away as well i said that it's mass multiplied by velocity it's p equals mv okay how is it different from force or energy well it doesn't have the same units so i'm not sort of almost flipping away i'll be like oh well it doesn't have the same units but listen it's not units are super important they certainly help me understand physics but if if you just want kind of to think about you know how you would visualize momentum i mean it's you could think about something that is moving with with a certain velocity right and has a certain mass and then maybe compare that to objects that have more or less mass or slower or faster velocities how then would their momentums compare right consider two things moving side by side right consider a you know an apple being dropped from a hot air balloon and then consider a bowling ball being dropped from a hot air balloon and then consider a cow being dropped from a hot air balloon which one would have more momentum on impact right because when they all pick up the same amount of velocity air resistance ignored yeah so the only thing that would be different would be the mass and so of course the cow would have way more momentum okay and the cow colliding into the ground right is going to be a case where it's very fast all right a lot of release of energy so it turns out kind of fast things also would apply to a conservation energy approach right not a coincidence there these two you know kind of conserving momentum conserving energy there's a lot in common but again different quantities right and and and they have their their own key focuses okay not saying they're interchangeable okay so what does conservation momentum mean okay well that i have not clearly defined and we'll get that i'll actually wait till we get to that section because that'll be the second section later half of this video in a few minutes okay so we're gonna answer these questions within this chapter so let's just think about a situation everyday situation dropping a ball that bounces okay so we've got the iconic bouncer ball bouncy ball hitting the ground coming back up by the way we know it doesn't come all the way up one of the reasons we know it doesn't come all the way up is because of energy right because you know clearly bouncing a ball is not a perfect mechanical system you lose some mechanical energy you lose it to heat right well really like the ball like heats up well not exactly it's because sound and heat behave basically the same it's all about kind of this random motion of trillions of individual particles in the case of sound air particles transmitting energy so you could call that you know a form of heat energy or you could actually and people do you could call it sound energy right because you drop a ball bouncy ball whether it's a tennis ball or or a children's bouncy ball right like a rubber ball it makes a good good loud clunk sound when it hits the ground right that's indicative of energy that's lost okay now there's energy lost on the way down on the way up because of a little bit of air resistance but you know because it's not exactly a streamlined shape like an airplane wing or something it's what's called a bluff body by the way this kind of spherical shape okay not maximum drag but fair amount of air resistance all that aside the energy is really lost in that impact and that's interesting because that's what we're talking about we're going to be focusing on momentum and the change momentum on an impact like this the sudden change in velocity okay but it turns out that it ties so nicely and back with energy because we could then you know say there's a certain amount of mechanical energy before right that we could just quantify as say the gravitational potential energy that the person you know has when they open their hand and let the ball fall we know that that energy is more or less enough completely convert to kinetic energy on the way down obviously i still have energy on my mind from the previous chapter so you know very little loss of mechanical energy but then i said there will always be a significant loss here so if you just track the kinetic energy right before impact to the kinetic energy right after impact you would have very different speeds right just looking at the magnitude of the velocity obviously one would point down the other one point up but that non-withstanding there would be a big drop you would lose a lot of kinetic energy right because there's a sudden loss of energy at the very fact they're very fact that the the way the ball bounces is momentarily stores a lot of that what was initially gravitational kinetic energy then became energy of motion kinetic energy well it stores it for a split second in its own elastic potential energy because i mean it compresses right if you had a fast enough camera you'd actually see it especially a tennis ball right you may have seen videos like this you can actually see them get deformed like significantly become like ellipsoidal instead of spherical okay so then let's read the bullet points because i think it clarifies something i've been i'm kind of hinting at a lot this idea of how momentum is well suited to certain situations things that happen fast okay this textbook is called the physics of everyday phenomenon this chapter should be the physics of quick everyday phenomenon okay so every day because we're not talking you know like atomic fast or something or nuclear fast or even you know um you know chemical fast right but this is you know in terms of everyday phenomenon this fast so ball reaches the floor it's blocked its velocity quickly changes direction all right it goes from one way to completely the other way 180 degree change okay so there must be a strong force exerted on the ball all right for a very short time right so in this case you know split second that force is exerted this force provides an upward acceleration necessary to change the direction of the ball's velocity so you know that's good to point out because if this whole time you've been you know screaming at your screen and saying like you know this is why why are we talking about this we already saw this back in the chapter when we talked about newton's you know second law you know we have a force we have an acceleration why don't why not just give us the force well the force acts for a very short time and it also essentially acts like a big spike so if you if we go over here i'm gonna catch up on the same slide okay so and i had it um smaller for a number of reasons but now anyway so what i want to just point out is if we were to look at this right if we were to look at a little graph that will squeeze in down here underneath our person's feet that just showed force okay and this is the force applied from the ground all right the force applied from the ground on the ball it's the only force we care about right and then we had time well and you know when we started the time here we said hey this is time equals zero right and then there's some you know certain time of free fall so after a certain amount of time we get down to this point which we'll just call t1 right and we know how much time that would take if air resistance is negligible or reasonably it would be right as i said you know really you know that's fine to assume it's just don't assume energy isn't lost in this collision um because you can actually quantify exactly how much is lost because the floor is essentially immovable but i'm getting ahead of myself here though what we do care about is that we know there's a certain amount of time okay but then do we know how much time the force is applied that really quick force that changes the direction of the ball no because it would look really rough we'd essentially have this spike right so let me put it right at t1 it wouldn't it wouldn't have like a well-defined delta t it wouldn't be like the force from the you know from the floor you know started you know a little bit before t1 you know kind of went up and then went right back down right that is not what the force from the floor is going to look like no way okay instead it's going to be this incredibly steep spike right it's going to have like you know some like you know curvature to it right because it's like you know it's got a shape so then you know how would you actually meaningfully quantify that because the different the difference between you know saying that you know this slope right here is linear and it's like a like a more like a spike like this versus like you know it's like two parabolas that meet at a point those are going to make very different predictions depend because it is so steep and you're and you're trying to get so little data to actually you know want to actually quantify this area because what is this area right here right what does the area like under the curve represent well it's force multiplied by time okay well the force multiplied by time is precisely the change in momentum okay so this very difficult to practically calculate area under this you know ill-defined little spike we can actually well calculate using the concept of momentum okay because we don't have to actually try to figure out that area instead we just use a law we just rewrite newton's second law right and that's a workhorse of a law right so let's go through this okay i think i've laid the groundwork enough let's move move through these steps okay so force like like these are difficult to analyze okay i've definitely stressed that point right strong forces that act for a very short time are just not good candidates for calculating acceleration okay the forces may change rapidly as i talked about that difficult to analyze curvature all right it will help to write newton's second law in terms of the total change in velocity over time instead of acceleration okay acceleration impractical to calculate here we're going in a different direction we're trying a different strategy all right and in that process we're actually going to like define momentum separately okay which is so interesting because it's it's like we're rewriting newton's second law in terms of momentum the very thing that i was stressing we care about because it's conserved so it's actually that's actually a remarkable use of newton's second law that it that it can be so directly applied to momentum right because it can't be directly applied to energy in the same way okay so let's go to the next one here so a little bit about the steps of it okay because again newton's second law i'm assuming you know it fairly well f equals m a right right over here okay so we're just going to multiply both sides of newton's second law by the time interval over which the force acts okay so we've rewritten a by its definition because acceleration after all is meters per second per second it's the change in velocity per time okay that's all we've done the thing in parentheses is the acceleration okay delta v change in velocity over delta t divided by delta t delta t is change in time okay all right so we want to make sure we're clear on that so all we all we're doing is what's called rearranging the equation which is a common thing we need to do these types of physical science derivations okay so we multiply both sides of the equation by delta t okay so where we're at we're at right here is we're at the next step where we have exactly over here actually we've got to this step right here okay and we got there by multiplying as i said both sides of the equation by delta t so what i mean by that is this is one side of the equation the far left side and then the far right side is the other side of the equation this doesn't count that was just an intermediate step so multiply this side by delta v or excuse me delta t as well look look how that would affect both the left hand side where the force term is and the right hand side well over here it's just going to make a new expression force multiplied by change in time okay but over here the delta t's will cancel so all we're going to have left on the right hand side is m times delta v okay so this is cool because this rewriting of newton's second law which is often called you know newton's second law in momentum form specifically in translational momentum form because it turns out there's another kind of momentum that applies to rotational systems called angular momentum we'll talk about it really briefly in the next chapter where we go through all the angular topics all at once but that's neat that we've done that but the two terms i'm referring to are impulse and momentum itself right we're seeing it all officially in equation form right here okay what do i mean by that well the left side of the equation the the part that's just the product of net force i kept saying force but it's net force because just like when we use um you know the the work energy law it's network right with newton's second law is important remember it's not just one force it's the total sum of forces acting on whatever object you're paying attention to right maybe the ball right so it's net force times delta t that ex that whole thing that product is called impulse okay so it's kind of like we defined work as the product of force and displacement here we're defining something called impulse which is the product of force and time okay you know or elapsed time and if we go back over here super fast i'll point out that we should have a letter for it a lot of textbooks actually kind of hesitate to introduce an extra letter i don't know why i think you know we're used to seeing a letter for every named variable and there is one that is you know widely used and it's j uppercase j by the way so we have then that j is impulse by definition okay that's what you know the letter is for impulse and j is equal to f times delta t okay so the product of net force and elapsed time okay that's what is impulse okay why are we introducing a whole another thing if we're already talking about uh momentum because impulse and momentum are the same they actually they actually have the same units okay um which i always think of as a odd exception because i can't think of any other example in physics where two quantities that have the same units that are both translational you know so neither one's applying to like a different kind of coordinate system so they're both buying the same coordinate system have their own names right it'd be like if we gave a name to change in velocity because you know we gave a name to change in velocity over change in time that's acceleration but what if we actually name just the change in velocity itself right we don't have a name for that it's just called change in velocity but impulse is by definition the change in momentum you know or it's defined to be equivalent to it but what's interesting is it's also defined as force or multiplied by time so force applied over some time okay sometimes i start to say force over time but that if you just say that then you're saying force divided by time but if you say a force applied over some time then you're talking about the situation it's probably better just to say force multiplied by time right so but let's look at this real fast because this next bullet point our next paragraph talks more about impulse so impulse is how a force changes the motion of an object or rather related impulse how a force changes the motion of an object depends on both the size of the force and how long the force acts okay so this product of force and time impulse okay it can be big if you have a big force over a short time or it could be big because you have a small force that you push really gradually although honestly if you had a small force that you pushed over a long time so gradually applied then you'd probably be in a situation where you might as well just you know go back to using acceleration because don't get me wrong there are plenty of situations where using newton's second law or you know the equations that apply to uniform acceleration are completely the best way to go like any free fall situation or any projectile situation right because yeah gravity is a pretty strong pull but it's gradual and often the you know the the time we spend um exposed to it is many seconds right or minutes even so you know that's great for using the approach of acceleration right but that's not what we're talking about here so the right side of the equation right so going back to the equation that i've been keep drawing your attention to the part that is just m times delta v that is by definition change in the momentum because momentum which has its own letter uppercase p okay that's that's what we use for momentum i know it doesn't match the first letter of the word but uppercase p is momentum okay is equal to right defined as mass times velocity every object that's in motion has a momentum okay that's what momentum is it's just the product of mass and velocity and if we're going to look at its units real fast a good time to do so all right we see then right so momentum by definition represented by the variable uppercase p has units put those in parentheses to make it clear that we're talking about units not variables what would be the kilogram for the the variable m and then for the variable v right here shown as an uppercase v which is not typical we usually use uppercase v for volume but it's just drawing attention to this is the big thing you care about this is the thing that's going to change right because then you're you're never that you're rarely going to have a case where you care about changing momentum there's kind of one special case that we talk about very conceptually remember this is after all a conceptual physics class which is a little little hint of math right right we just spend most ideas yes presenting the equations but more about their proportionalities more about understanding them like a balance but all that aside when when we look at you know this equation m is usually not going to change but it does for one particular case that we touch on that's called the rocket right because the rocket is a case where the rocket's using up fuel a significant amount and that fuel was a big part of its original mass so there's a big change in its mass over time okay but usually doesn't change right certainly not for a collision of a ball right the ball stays intact it's the same mass right before and after it hits the floor all right so then i was saying the units of velocity are meters per second so then the overall units of momentum are kilogram meters per second okay that's fine you can write it that way but there actually is a more intuitive way to write it which ties it in nicely with impulse because if you look at this kilogram meters per second is an awful lot like a newton because a newton by definition right i'm not saying that you know momentum is a newton i'm just pointing out what a newton is a newton is you know defined by newton's newton's second law right on the opponent's ponious newton um well when you look at when you look at newton's second law it's mass times acceleration so it's kilograms times right kind of like this right but instead of velocity it's acceleration what's acceleration meters per second squared right because meters per second per second well then the only difference between this you know expression for momentum and the already hopefully well-known expression for you know force the newton is just the difference of having an extra second in the denominator so that means that momentum right the units of momentum the kilogram meters per second can be correctly expressed as the newton second because if you multiply a newton by a second things are thinking what would happen right you'd cancel out one of the seconds one of them in the denominator leaving only one behind making it look exactly like you wanted to so a newton's second is a kilogram meter per second and is the units or they are the units of momentum and i said it draws attention back to the whole fact that change in momentum and impulse are equivalent and this whole idea that impulse and momentum have the same darn units because you know we use these units for momentum newton seconds and then look at the definition of impulse its force times time well that of course is also newton seconds as it should be okay so again you know what's the difference then between you know momentum and impulse it's just how you come about it right if you're told the average force right the average net force and you're told how long it applies right maybe you know that information from some estimate you know um i you know i said that's the harder thing to know but maybe you know that right well then from that information then you could get the change momentum right or maybe more likely you know the velocity before and after something by going back to the ball drop right you know v1 and v2 right immediately before and after the collision okay here they're kind of showing like you know pretty far before and after the collision but again assume there's no air resistance but what we have then is we have you know we know those two velocities if you know those two velocities right well then you've got your delta v right because it'd be v2 minus v1 okay that's all delta v is v2 minus v1 okay v final minus v initial okay but here we're using two two and one okay so you know that you know the mass of the ball check out what you know then you know the actual impulse value you know the change in momentum so that's cool because then if you know say like the the net force right then you can you know then you can calculate the time it was applied or maybe more likely just based on maybe some you know the frame you know right before you like going back to video analysis but you know you you see this you know high speed camera you see the ball right before it hits the ground and you see it right after it's obviously not in contact with the ground anymore so you get a good estimate of delta t right that's more likely what you actually measure now you actually have a way of calculating force so it may be very hard to measure directly okay so another use of momentum now comparing momentum i mentioned this before and this is the figure i was thinking of like visualizing visualizing it or rather comparing momentum between things is a good way good way of visualizing it a good way of making sense of what it really is so here we have a case right it's the it's the it's like i said it's the cow it's the dropping the cow out of the hot air balloon dropping the you know um the ping-pong ball out of the hot air balloon that one's hard not to imagine having air resistance um okay so um let's say you know dropping the cow versus dropping the bowling ball which one has more momentum when it hits the ground clearly the cow because they both have the same velocity but could you have a airborne cow and an airborne bowling ball have the same momentum sure right yeah the cow is a lot more a lot more massive but what if it wasn't moving as fast right so what if you had a cow moving at you know two meters per second right and you had a bowling ball moving at 75 meters per second well that that significant extra velocity could make up for it right now what's interesting is it's just directly a product it's a linear linear relationship it's just mass times velocity so you know if you want to have if you know the bowling ball is you know 1 100 the massive of the cow then you would literally literally have to have the bowling ball go 100 times faster for the two objects to have equal momentum okay so that's the idea and here it's showing with a bowling ball and a tennis ball right no cap okay so we've said this but it's good to call extra attention to it so this equivalence between impulse and momentum is the impulse momentum principle okay it's actually a similar principle to the work kinetic energy principle right it's like these it's we define these separate things they're not really different right they have the same units but we we have a you know we could calculate them practically in different ways so you know so yeah we define them individually but we remember that they are equivalent to each other so we might go back and forth so here's a case where like i was saying you might you might know some some aspects of impulse like the you know the change in time but not the force and then you might know you know everything about the change momentum and then you can calculate your one unknown because really this equation has has four things you could potentially not know right so if you if we think about this real fast and just i'll write right over at the four things okay so so the basically the four things that we don't know about this equation or that we could solve for algebraically right on the impulse side would be the force all right i want to write this in a permanent pin so f net okay that's one of the things we could solve for the other thing would be delta t okay and you would solve for that not as two separate values it's just a single thing right because it it really is right it's just some amount of time in the past okay so think of that as a single variable and then on the right hand side the delta p here okay remember p is you know our new letter that represents momentum but when we expand it out what what's inside of that p an m and a v right so we just have an m and then instead of the delta v here you could actually you kind of have two more things so i guess there's a sum of a five i lied because you think about it really here you have v final minus v initial and here you really could you know again often you might solve for delta v collectively right so just like i was saying you always would for delta t right you just the difference in the velocity was five meters per second because before it hit the ground it was traveling at three meters per second downwards after it hit the ground it was traveling at two meters per second upwards okay so the difference is five right not one because you might think three minus two is one well how'd you get five because it was negative three okay think like a number line here right so we had negative three as the initial velocity right so v initial okay negative three meters per second over here we'd have zero right continuing on the number line and then over here we'd have positive two meters per second what's the dis the distance between those okay and this is the final right well the delta v here is five meters per second okay so yeah you might just solve for that value or maybe given that value right but other times you might know either the initial v final and just have to find the other one in that case you would know everything else here you know the net force you know the um change in time or maybe you don't care right because maybe which what you know maybe you're just given the impulse value okay so just to call attention to the things that you might be actually applying this equation to okay so right expanding on a little bit so here we have nice pictures right we've got the ball coming down it has some initial momentum okay see how they're really they're you know the whole momentum here right because that's that's it's that's what we care about right a lot of times i'll kind of i'll draw the picture with the velocity because you know as i pointed out the mass isn't changing i can bring the mass in later to my calculations but it's also good to call attention to that is after all momentum that retract that we are tracking okay so then there is some change in momentum okay that change momentum happens during a very short time where an impulse is applied okay by the time that's all over there's a probably much greater time for it to gain just this this amount of extra airborne height but again airborne height we're ignoring because it takes place in an approximate vacuum right or negligible air resistance but what we do care about is that p final right so the whole thing is that the p initial went to the p final and it happened in some practically unmeasurable small amount of time where a impulse was applied okay so what do we got then all right so we know in this case that it was traveling at negative mv on the way down and it was traveling at positive mv on the way up how is that different from the example i just did right well in my example i had to go at negative three and up on two why did i do that well because i keep talking about how realistically it loses a lot of energy that's on my mind because when i do labs with my students i always see this happen right there's a big measurable loss of energy and even the best bouncy ball right even the best tennis ball even the best ping pong ball there's just no way is it just the process inherently involves a lot of energy loss you just can't have a collision like that with an unmovable floor right total energy loss yeah insignificant so it's you're never going to see a case where it's it was negative you know it was negative mv on the way down positive mv on the way up you can't you can't you know preserve the momentum that well all right so regardless you know that's what's happening here now is that totally impossible because i just said oh it can't happen well i mean no there'd just be something else that is in the system that that is kind of outside of what we're paying attention to because we just we just care about the change of momentum of the ballots all we're trying to quantify maybe it was able to you know completely seemingly recover its momentum you know but going in the other direction without any loss of momentum therefore without any loss of energy because by the way if you lose momentum you lose energy how do i know that because the only way that this ball would lose momentum is lose velocity it's not going to lose mass right if it loses velocity what will happen to its kinetic energy kinetic energy is one half mv squared v goes down so does kinetic energy so losing momentum is also losing kinetic energy every time okay right because even if you lost mass that's also in the kinetic energy term so every time all right now here's the thing though now could this you know kind of retention no loss of momentum come from somewhere sure it could come from the fact that maybe there was a an extra little kick on the floor right it was um you know a floor with like a already some stored elastic energy in it right so there's certainly situations where it could have okay all right so then let's finish with a few slides to cover conservation of energy and then we'll leave off on recoil that's that'll be covering the next video if you're wondering what the heck the recoil that's like shooting a cannon or like a musket or something right honestly a gun as well right but and then what's gonna happen is it's gonna have a kickback right called a kickback also called a recoil that's absolutely conservation of momentum momentum it's a just a textbook example of conservation of momentum all right and as are collisions especially things like billiard balls or in this case people right when people crash together i mean we have an intuition of what happens right if they if they had exactly equal mass right if these two football players have exactly equal mass and they came in with exactly equal velocity then they came in with exactly equal momentum okay but equal in magnitude because is momentum a vector sure is right look right here right momentum is a vector right it has direction it has the same direction as velocity so if you have two equal magnitude momentums that are coming together and colliding then you could end up with a case where what happens i bet you know right they would just both come to rest right now it's an idealized case right but you know under the just the right circumstances maybe it happens right they just happen to have the you know make you know maybe one was more one player was more massive than the other but then you know that player was moving slightly slower than the other so they came together with exactly identical momentum in a perfectly straight line and they just stopped right so that's actually what conservation momentum momentum tells us should happen so it's matching our intuition okay so does newton's third law still hold holding this situation okay well absolutely okay and students and myself you know often sometimes will will be musing or sometimes all students kind of say well what's the heck this is we should solve this with newton's third law why are we using momentum and you actually sometimes can totally choose this is the case where sometimes there isn't a clearly better way of doing it because newton's third law we get the force pair we can then you know solve for things like you know the the final velocity afterwards right because we can just you know consider a situation where we can ignore acceleration and just go straight straight to the forces okay all right so if the net external force acting on this system okay of objects is zero the total momentum of the system is conserved okay this was the thing i was holding out for because there's a question early on i basically answered all the other ones but in a sense that i i knew we'd have to revisit them but i never answered that what what actually means or what what has to be true for momentum to be conserved because all the conservation laws are not universally applied right like mechanical energy isn't always conserved because mechanical energy can become other forms of energy now is energy absolutely unequivocally conserved well no actually there's a broader law that says that there's an energy mass equivalence so saying that energy is conserved you could you know you'd be caught saying that's wrong because you're not looking at the system in a broad enough way because you're not considering einstein's equals mc squared that mass can become energy and energy can become mass right that's a big idea so so why do i bring that all up because right all momentum conservation the law of momentum conservation also only applies to certain situations does that make it kind of like a corner case like you know we have to be really careful to make sure that it applies this situation well not really because it turns out that all the situations that we've been highlighting the ones like collisions you know fast collisions um explosions and recoils essentially that's what's happening in a gun right our cannon it's a controlled explosion and there's a recoil right so a very fast release of energy and also a very fast release of our you know our objects very quickly going from zero momentum to large momentum right zero velocity the high velocity right in case of launching something what those what those cases have in common is that they happen quickly right that was why we i said that we shouldn't try to solve for acceleration right it's too messy but that's also why it turns out the conservation law is so well suited so the fact that it happens fast simultaneously discourages us from using newton's second second law and encourages us from you to use conservation momentum now that's probably the way this field has been developed over you know centuries but it's still cool because having conservation of momentum only apply to situations where the external force is zero okay is perfect for things that happen fast right so if you have two people crashing together really fast two billion birds billiard bars billiard balls crashing together right the gun exploding and you know so the gun recoil down here right all those things they happen so fast that external forces like gravity right that's a big one don't have time to make a difference on the outcome right because once the the shot in this case because it's like an old-fashioned shotgun or something right so a bunch of little pellets once those pellets have been you know moving for a while well then it's completely naive to say they're still moving in a straight line or that they even still have the original momentum because gravity's going to cause an arc downwards right absolutely so that is an external force that's momentum not being conserved right but that's later on so momentum is what we use for the the fast sudden effect and then we can actually track the results of that because one thing we can do is we can have something like launching a cannonball or launching little pellets from a shotgun or a musket and then tracking them finding out how far they go what's their range as a projectile so what's cool is that would be a two-part problem where you use conservation momentum for the fast part the explosion right then you use you know newtonian laws and uniform acceleration in the in the corresponding kinematic equations to deal with the the slow mini second phenomenon that follows okay so two separate tools for two separate parts of an overall process all right so now let's go back to our players okay so that's the idea momentum is conserved as long as there's no as long as there are no external forces okay so the impulse on both are equal and opposite okay that's this special case the changes in momentum for each are equal and opposite okay yeah that's everything's conserved okay the total change of the momentum for the two players is zero what does that mean well because they they both had momentum coming in right they had some amount of initial momentum right now how much initial momentum did each of them individually have non-zero okay but how much momentum did the two of them collectively have as a system because you know taking the two players and saying this is a two-body system is exactly the kind of thing that physics likes to do that physicists like to do okay three body systems we don't like so much but two body systems are great okay because then we just use all the same tools that we would for a single body system okay we just say okay we got these two things right they now have each their own momentum vector they're each equal in length but opposite in direction so if we sum them the sum is zero so that means that the initial momentum of the two players collectively was actually zero even though they each individually had non-zero momentum which means that afterwards when i said that intuitively we know they both just come to rest right entangled in each other well in that case the final momentum is clearly also zero because there's no leftover velocity but that works because the initial momentum was also actually zero okay for the two of them so it's a cool demonstration of conservation of momentum all right so now let's look at the case though where the final result won't be zero because although that's so neat it doesn't i don't think highlight the process of solving it very well so we're actually going to do the next few slides is something that the slides don't do all that often actually work through a numerical problem which saves me the work so a 100 kilogram full back moving straight downward downfield at five meters per second collides with a 75 kilogram defensive back moving in the opposite direction at four meters per second okay so we've got um so we have 100 times five is going to be the momentum of one of them so i'm looking that's always going to give us a 500 and then so yeah the bigger person is moving faster and then the smaller person all right is moving slower yeah so that it's really going to drive them apart right so this this this player this one here the one in green is you know shown smaller too it will have significantly less momentum because they're both lighter and slower okay so the defensive back hangs on to the fullback and the two players move together after the collision okay so this is um in collision terminology this is called and you'll see this come up here in section four an inelastic collision okay now we'll define that again when we get to that section okay that's just any collision where they stick together all right so what is the initial momentum of each player okay so let's start there all right so go ahead and calculate these okay great practice to do so pause the video right okay so now i'm going to show you the results of the calculation for the individual momentum for the full back and the defensive back okay so with the fullback its momentum is mv right it's i guess his right their momentum 100 kilograms times five meters per second okay so you take that product and you get 500 kilogram meter per second okay or the units i like to use newton's seconds both are fine okay then the momentum of the defensive back okay well i was talking a lot i was focusing on its magnitude thinking about you know which which person is going to end up getting moved more afterwards obviously the lighter slower person but now not just the magnitude but the negative is so important okay just as it was for the case where everything's zeroed out because otherwise you will not get the correct result right you got to remember that momentum is a vector and this player right although they have a smaller magnitude momentum do have a negative momentum right opposite direction okay so it's 75 kilograms no negative there mass is just always positive but then multiplied by their not speed but velocity which is negative four meters per second right because velocity is the one that has direction so then what you get for momentum is negative 300 kilogram meters per second the negative just means that they're moving to the left how do we know that well that's the traditional direction of negative and right is the traditional direction of positive if we're being a little bit more careful we actually might just draw a the direction of positive x on the figure i tend to do that right some of these books don't because they don't want to like you know clutter up the image and make it look overly complicated but i hope we can agree that that normally the positive direction is towards the right okay at least you know in the united states okay so the total momentum of the system will just be the sum of these two values okay but the negative matters okay so we take the total momentum sum of the momentum of the fullback plus the sum of uh well not the it's just the sum so the the total momentum is the sum of the momentum of the fullback plus the momentum of the defensive back okay so 500 minus 300 200 newton seconds okay or 200 kilogram meters per second all right that's the total momentum of the system okay and there's nothing else in this system there's we don't we certainly don't care about things like the ground because if we did if we included the ground in the system well now we have now you know it's i guess on the one hand we included the ground in the system that we don't have to worry about friction right because the ground otherwise might be a unignorable external force acting on both players right if we included it then now it's part of the system it's not external that was the condition after all for conservation momentum so in some sense you actually can make your system bigger and bigger so it includes everything that you need to so now you don't have to worry about external forces right because if you zoom all the way out until you have the planet then are there any major external forces well unfortunately there actually are because of you know well after all gravity right you know the orbit around the sun so that actually looking at planetary motion that'd be a really bad one for a conservation of momentum okay that's all about momentum constantly changing um but anyway i get off topic the point is that there aren't there we're assuming no external forces a reasonable assumption not for a whole you know run down the football field but for the moment of the collision sure okay and here they come right so we're going to have them crash together all right importantly when you do this and something easy to forget is that since we are going to consider the momentum after the collision in which they'll only be one object because they're locked together now well that new object has the sum of their masses obviously okay so now we have a new object the collective um you know fullback plus the just forgot the term uh defensive back is 175 kilograms okay all right so then what's the velocity well the momentum after the fact the total momentum must be the same as the initial momentum because that's what conservation told us right so right let's go let me show you that real fast and go to our football player right we're just over here okay so okay so the reason that we can confidently say this equation right here because otherwise it might seem like we could just kind of jump to it the reason that this is true is because right because this after all is the velocity of them after the collision right this would be like v you know final or v2 whatever you want to call it right because they both had their own initial v ones okay well the reason that we know that this p total right p total all right equals p final equals p initial right because after all the p total the 200 were plugging in that was the momentum before the collision but that's the whole point that value hasn't changed that's the tool of using conservation momentum that we can find the momentum before something happens and know that that value is going to carry through and that will allow us to solve for other things in this case the final velocity of the players okay all right so afterwards right after the fullback holds on to the defensive back and continues to move you know holding on to him they will continue to move in the forward direction because after all the fullback was more massive and you know we'll just have a bigger momentum because they're more massive and they had a greater velocity so that definitely wins out and we move forward at a rate of 1.14 meters per second if we had changed some of our values what if we you know made um the you know the fullback 125 kilograms instead right really big well then we just get a slightly larger velocity here right so you can think about how tweaking would get the results that you may expect okay so the velocity is in the direction of the fullback okay right so and again it will always be in the direction of whichever player had even slightly more momentum right or in that case the velocity might be really small right because there's no way for it to go the other way it's either going to be completely at rest and where they're exactly equaled out or the final result will be carrying on whichever moment whichever momentum vector in this one dimensional case was slightly bigger okay all right so in the next video we'll talk about more conservation momentum because that's the way we approach recoil so in a sense we've we've laid the rules okay now we're just going to apply them to a few particular situations sounds like fun right well stay tuned for the next video for that much fun i hope this video introducing momentum impulse and the conservation of it and tying it with tying it in with a bunch of other ideas in classical mechanics has been both interesting and informative thank you so much for watching