 All right off we go we're If you haven't noticed make sure that you have we're skipping chapter 9 chapter 9 is covered in physics 2 It's one of the things to make sure that we do so that we can take a sequence with at least RPI if not some of the other schools since that's where most of My students tend to transfer so we decided better to cover gravitation chapter 9 in physics 2 So we're gonna We're gonna take an awful lot of what we've already got and just extend it a little bit In fact, we already have a little bit in some ways We're gonna look not just at particles and all the particle motion that goes on with those But we're gonna look at systems of particles Kind of a fancy name for Any problem that has more than one thing in it so far mostly what we've looked at is one ball of dropping or one car accelerating or the the most we had in terms of a system of things was we might have had a Ball with some elastic thing attached to it But we didn't worry about the the mass of the spring or its velocity or any of that kind of stuff It was just still a Particle is all we had in the problem. So now we're going to look at what can happen with a system of particles If I had made nothing more than we might have two or more things in the problem They might be connected In that whatever one does it affects what the other one does That's certainly what we'd have we had a couple things attached by Pulleys and ropes and the like when we want to see how those go Could be there's electrostatic forces of some kind between them But for the most part what we're looking at here To start with at least our separate distinct Particles, but there's more than one of them in the problem So we'll take the the simplest one most of you'll notice Samantha is not here today because she Knows what was coming up. We're going to look at car crash as two cars in a collision as our system of particles and since she's the only one mad enough at me all the time to Chase down my car and hit it There's my car and I know what that what she drives what she's probably a pickup truck a blue pickup truck like a baby blue pickup truck It's probably think I think she's probably done. She probably drives There's there's there's there's there's Samantha's car So I'm gonna take real good. No. Oh, she can see the video So we're gonna this this is as simple as this can be this is our system of particles and we want to see what happened when one of them Has a greater velocity than the other I mean keep keep the same notation the book was using now that will do Such that V1 is greater than V2. Otherwise, they wouldn't collide and that also works If V2 happened to be the other way and they still collide this relationship V1 has got to be greater than V2 just Kind of be in name all about it make sure that they collide if they have the same velocity or V1 is going slower They wouldn't collide It's not a terribly interesting problem though. There's still some things we could do with it So we're interested in that that possibility when Our two cars become one We're going to start with the Condition that as they do this as a client this way they do so such that they stick together So we'll call the single velocity. They now have now. They're not really a system of particles now They're a particle. It's a bigger one than was before But essentially, it's just one particle, but they have a single velocity and we'll call that velocity v-prime Now for what we've got right now Analyzing this type of situation is is a little bit problematic if we look at her car and What happened to it? Because we do not have to analyze a single particle. We've spent weeks doing that now What are we about nine weeks into the nine ten weeks into the course and that's all we've done is looked at single particle problems So you think we'd be able to do something with this and we can to a point Her car starts with some velocity v1 It's got some mass m1. We haven't talked Too much about well certainly we haven't said what that kind of thing has to do in this particular situation But mass has had a lot to do with things as we've been going along here for a couple weeks Some little bit of time later She's got a brand new truck Had a little body work done Now her truck is m1 going some velocity some new velocity In fact, there's been clearly for her a change in velocity. In fact, it's a I don't think you even need to have been in a crash like this to figure out that The velocity she came in with is going to be less than the velocity She's got now. That's just what happens when you hit the car in front of you I think most everybody knows that by the way, we're assuming neither one is on the gas All these velocities as pictured at any time are constant velocities So this is the constant velocity all the way into the collision. She's not accelerating Just constant velocity. Then there's this collision and we have what will take as an instantaneous change in velocity almost instantaneous very short time crashes don't take long and Her velocity will then be reduced to this So so we she has she has something like that type of situation We understand that for there to be a change in velocity an acceleration There must have been a force Friends of yours, I want let's know for what For her to have lost speed For her to a de-accelerated there has to have been a force Opposite the direction of her velocity to affect that We don't know how big that force was We sure know what caused it What did the car in front she hit it? Exerting a force on it it hooded her back. That's an action reaction pair. That's Newton's third law Anytime one thing as exerts a force on another the second thing exerts the same force and magnitude back on the first so She felt some force even if even if we don't know that those are an action action pair We do know there have to be a force like this in this direction to cause her velocity to drop It just wouldn't happen any other way. We know How to do acceleration we've learned that for weeks now That had to have been the case had to have happened in some little amount of time Delta t Let's see we could even say let's see Minus f because we'll take going to the right positive just because we always do anyway So we know that minus f has got an equal m1 times here, I'll put in the Intermediate part as we go Delta v over Delta t M1 Her Delta v was something like well what v prime minus v1 Well remember v1 is Not necessarily the first lesson that's velocity of her as car number one That's the other subscript system we're using for today And that had to take place in some amount of time Delta t God forbid you've ever been in a crash, but you know those Delta t's are pretty short they happen real quick Crash it. You know sometimes on TV. They slow it down So they get the skidding and they get the glass shooting across and it's very dramatic and all and really drag It's Delta t out for a while. That's not what happens The crashes are bang quick and then you sit there trying to figure out what happened Then you're trying to figure out. How can I blame the other person? Quick I've got to think up an excuse So that I don't know I'm not guilty for this so The analysis is there's nothing here that we haven't been working on for a couple weeks other than the fact We're not going to have a very good idea what this is And we're not gonna have very good idea what that is oh we might have an idea But if we come upon some crash or if you're even in a crash You're not going to be able to estimate for me what Delta t was You're probably not going to be able to estimate what this is because don't forget after you do this crash And this is the velocity instantly after the collision but instantly after a Little bit more than instantly after a collision people put on their brakes and get out and see if everybody's okay This is the velocity that instant after collision because after that the brakes go on the skidding happens that the Panic the heartbeat the adrenaline all the stuff's going on the flashing lights the people driving around you laughing at you You sucker. I'm going home. I'm gonna get home in time you jerk I I've been the first person on the scene three times that car crashes in Clifton Park I was I was right there saw the whole thing was the first person there my my immediate Response was I gotta see if I can help I gotta pull over see can I go help make sure nobody's bleeding to death? But I couldn't because everybody else who wasn't first person there had to go by They wouldn't let me across the road so I could go see if these people were okay. They were all in such a hurry I had to wait there for them Before I could go see if somebody's bleeding up because they wanted to get home Wait a second. I recognize the car now All right, so that's the situation we got here Nothing here in the physics. We've never dealt with before except we've just got a lot of things the F and the Delta T Very hard to know what those are it'd be great if we could get rid of those be done with them get them out of the way Since they're so hard to find we could There are ways to instrument cars that we can measure forces and we can measure forces that happen in very quick times But who goes into a car crash with a car monitor? I don't some cars have a black box type things nowadays and they may do some of this type of stuff Especially the Delta T But how many cars have that today just the on-star cars. I don't know what I Don't but then I'm gonna get crashes when Amanda's out on the road so So let's let's look at the other car. Let's see. We've got my car Dang, that's a nice car. This is my car. It's a Red candy apple red the best car color there is Oh, I know Good luck passing this court I So I'm driving along I check my rear-view mirror every seven seconds like a good driver does But in that six point nine seconds, I wasn't looking she came and got me And so I also got a new car now and I also underwent a Delta V in fact What was the nature of the change in velocity of my car most likely? I'm gonna speed up you get hit from behind you. There's a sudden jerk for in fact That's why we have head rests on the back of cars nowadays So when you get hit from behind and your head starts to snap back as your body in your car jam forward Your neck is protected from that very quick snap back called whiplash Very painful very hard to get rid of after even a long time of therapy and That braces and all kinds of ugly things So I underwent a Delta V as well and in fact Are these two Delta V's the same? Is my change in velocity the same? Well, they're not even the change sign because she slowed down I sped up But would the magnitudes be the same? Not likely not like they might be but if anything I would think that even might be Coincidence if they did so We better do something. Let's get we'll call hers one and Mine two because I was car two. She was car one Just to highlight the fact those might not be the same and could be but Might be very Coincidental if there are No doubt I Not hit from behind. I fell the force from behind We know that anyway because there was a change in velocity. So there had to be a force Blue cars get pink forces pink cars get blue forces Are those two forces the same? the Delta V's aren't Are those two forces the same? Well, clearly not the same direction, but are they the same magnitude Are those two forces the force she feels slowing her down and in the collision the force I feel speed me up in the collision and remember we're only talking about the time of the collision We're not talking about all the skidding to a stop afterwards that can go on Are those two forces the same in magnitude? I've got a what yeah Yeah, I thought I heard a no from over here from here From yeah, they're the same. No, they're not Yeah, they are Yeah, so we'll take it away. Yeah You know this this is you know just vote like this was a presidential thing. Don't even think about it You know he's handsome. I'll vote for him Something like that. Yeah So we had a couple of those Joey, did you vote? I hope not because I don't want you to talk to the mouthful carrot pieces all over my feet Yeah, those forces are the same Alan you said yeah, they were why are those two forces the same at least same in magnitude They're opposite in direction clearly, but same in magnitude I already told you that's an action reaction pair This is this is a Newton's third law and it's glorious full Display here, so that I'm not going to put a subscript on those apps because they are the same I'll handle the direction, but I did that this one's going left that one's going right, so this will be m2 Delta v2 over Delta t Same Delta t or not do I need a little subscript on the Delta t's Sorry John Well, they don't even exist otherwise outside of that moment of the collision those forces don't even exist They're not there. They're gone Once the velocity has changed and the two are no longer changing in velocity Well, we're we're We're not letting any time go by here after the collision because so much other stuff goes on all the skidding and the Mass is changing because parts are flying all over the place and all kinds of things are going on so But Maybe everybody dies so nobody can hit the brakes and then they continue like that velocity for a long time So if you feel better with that I know I know see oh good thing. I don't have a green a green a green piece of chalk because there's a tree out there called aren't I? Just to make things even worse anyway Are these Delta t's the same? Or do they need a little bit of Delta t1 and their Delta t2? Yes, the same crash. They're both in the same crack It couldn't be the case that that one of them is Out of the crash and the other one isn't they crash they stick together That's That's their past present and future as far as we're concerned now So those Delta t's are the same The f's are the same It's the masses and the Delta v's that are different. So let's Let's do this. Let's do this. I'm going to take the first equation there minus f Just multiply through by Delta t that way. I've got the f. I don't know I've got the Delta t. I don't know and I put them together the two troublesome things are put together To separate them from the rest is what your elementary school teacher used to do with you and the guy you talked with all the Time you said channel both out in the hall Oh Joey, that's not familiar. Were you a talking turtle? See they they don't do that anymore because it's a self-esteem issue But when I was a kid man, you talk too much you're out in the hallway with a sign on your back says I'm a talking turtle Sitting out there in the hallway. Everybody's walking by. Oh, what's on your back today, man? Yeah, high school All right, so that leaves equals m1 V prime minus v1. Oh I didn't finish this because we know what and we know what Delta v2 is Well, I do what is Delta v2? I didn't quite get this finished. I won't take it over. What's Delta v2? What's our rule with Delta? What's it always mean? The ladder minus the earlier which one of the velocities came later Be prime. So this is v prime minus v2 That's v prime minus v1 So those Delta v's aren't the same Should the v primes be different? What was v prime? The velocity of the two now stuck together. This is not a bounce-off collision. This is a collision where they stick together I knew she was coming I had a bumper made out of bubble gum Came in that way because I knew she'd leave the scene in the accident So this way she was captive And I could then call my lawyer and the police they'd come in they got I like it looks man It's not the class I'm not going up this video all right, so so We've we've got that there for her that's her that's her Collision equation if you want to call that Then we can do the same kind of thing with my collision equation. I was plus f Delta t Right same f Delta t for both of those we don't need subscripts there, and I was m2 V prime minus v2 The f and the Delta t the two things we don't know they're very difficult to find real hard to know about The the mass of the car that's no trouble to know that's right there on the registration sticker We could get the v1 the v2 and the v prime maybe from a Closer to television if they happen to crash in front of we could estimate the speeds off the velocities If both cars had a black box, we might be able to do that. So these these are possible to know That's not that big a deal In fact, we could do stuff in the lab that does just that we could figure out you might have done that kind of thing in In high school physics lab done some cart collisions either on air tracks or with kind of roller skate carts They smash into each other and you measure their times in the line It's not that big a deal So let's let's do the easy thing. Let's add the two equations together Minus that Delta t plus f Delta t that's That's zero in my book. We need a calculator for that side. This side then is m1 V1 prime of the v prime minus v1 and I'm adding them together M2 v prime minus v2 Let's do a little algebra because that's not all this workable Let's make this minus m1 v1 Plus no minus m2 v2 m1 v prime plus m2 v prime I'll take the v prime out. I get m1 Plus m2 Is that all right? Just a little bit of algebra there. Just what I'm doing is collecting the terms Because notice now I have here terms before the collision only Here terms after the collision only and in fact, I've got a minus sign on both of those So I'll take them over to the other side and I get m1 v1 Plus m2 v2 equals m1 plus m2 V prime that's pretty neat Because those are things those are all things that aren't all that hard to come up with maybe maybe maybe the camera Saw my car. So we got my velocity Then the camera saw our velocity From that then I could calculate her velocity Which of course she would have lied about anyway, but now we can nail her Couldn't I do that pretty easily? If I had my velocity before and after I can figure out what her velocity is no matter what she claims in court We could come on an accident scene analyze the accident scene and Testifying court as an expert at 300 bucks an hour There's a lot of engineers out there making this kind of money as Forensic accident analysis engineers. They're called upon by one party of the other usually their Insurance company saying here's the data Can you tell us who's at fault so we can go to court? So the other insurance company And the engineer will take it good. We could we could come up with this Based on the skin marks If we knew how far they skidded and we knew the coefficient of friction We could back out of that the velocity just after collision, couldn't we? That's no different than the stuff. We've been doing for a couple weeks now People can't hit us and lie anymore. We're too smart now Because we can look at the data. I don't know what the skid marks were I know what the coefficient of friction of those tires on that kind of pavement are I Know how fast we're going after the collision. I know our two masses. I know what my velocity was I Know what you were doing when you hit me. I Want compensation? I want a new candy apple red car pink I want a candy apple red car And and red chalk to go with it to shut up the mace airs over there You're so far away you can't see that's pretty useful The two things we couldn't deal with the force and the time are out of the problem And just some things that are pretty easy to deal with are in the problem now We also what maybe you notice there's a there's a combination of variables. We haven't had before That's recurring here. It's mass times velocity mass times velocity mass Times velocity Just about any time we have recurring variables. We asked ourselves. Do we have something here? That is important enough as a combination That it's a good time to throw in a new name a new variable letter To screw with the students heads a little bit more. That's what we think in physics meetings We've got this combination M times V. Let's call it something give it a new letter that doesn't make any sense piss off the students That's the essence of teaching that stuff you hear about the light bulb going off. That's bullshit, man It's it's when when your eyes start to cross spin around the blood dripping out of your ears. That's teaching That's That's one of you. That's one. Oh, man. I live for those moments. So we've got this combination Recurring of M times V. We know V is usually a vector Should it be here? You think? Are we dealing yet because we could have had the possibility that they're going one way or the other and we might Need to account for that especially if it was a head-on collision. We were going towards each other We need to account for that. So this this is a vector quantity. In fact, it kind of makes sense You know, there's something fundamentally different between you and a Prius going 60 miles an hour and One of those lumber trucks coming down from Quebec going 60 miles an hour There's just something fundamentally different about those two things on the highway That makes us feel both mass and velocity are indeed important Especially in how crashes play out That lumber truck could go right over the top of that Prius and he'd go come on. There was a little bump in the road That's all you know So So that's not that's kind of you've that kind of makes some sense that there's a mass Times velocity that makes some sense and in fact There's got to be a big difference between Two cars going the same way and hitting Going head-on and hitting hitting at a 90 degree angle or any other possible angles in between So it makes sense That this is some kind of vector quantity Because we know that the direction Can have a big thing to play in these and a lot of these type of problems We've been looking at for several several weeks here So we define that that product mass times velocity as Who's got it somebody knows it I bet Tyler Who remembers it from high school physics? Phil does Phil is momentum Momentum a term you've all heard and so of course we need to give it a symbol Because it's way too much work for us to write m times v all the time We need just a single letter we could write because we don't want to work this hard So what do you think? Well, it'd be a good symbol for it. You know, he he would be a great symbol for it he Momentum until you get to dynamics, then it becomes a G unless you use a different book then it becomes an L Well, I I'm okay with it not being an M. We've already got an M here I Can write a big M different from a little M, but half of you couldn't so it'd be disastrous if we used an M So we'll use a piece Momentum is defined as the mass times the velocity the vector of a lot the full vector velocity of a vehicle Oh, I have a particle but not to give it all the particles so So let's see. What have we got here then? M1 times V1. Well, that's That's P1 and 2 times V2 that's P2 Len thanks for paying attention today. I appreciate it any time Okay Almost caught you there Equals what's this then maybe p3 it is different than either one of these isn't it? We'll put it into words then and we'll worry about a symbol. What is that? Is that a momentum? And if it is a momentum, it's the momentum of what? It's the momentum of the two vehicles together because that's what we've got after the crash So we can call this people will call it P prime. That was our symbol for after the crash Remember immediately after the crash not time for skidding and deceleration and panic to go on immediately after the crash Could be a vector This was a one-dimensional problem, but we we were concerned with whether it was left or right when we set up the whole thing In fact, that's that's where all these minus not all the minus signs But the that's where this came from the fact we could do this is because we are concerned with the direction of things and how It was going on we're paying attention that so this this we we're not losing anything by calling that The vector if it's one-dimensional we just use plus and minus if it's two-dimensional We'd have to use i and j three-dimensional. I have to do it i j and k, but it's all still all still fundamentally the same In fact, not only can we say that What more could we say about p1 plus p2 as a quantity itself? No There's there's nothing to integrate here because I don't have any any dT's or dV's or anything just the two added together Here's p1 That's the speed the momentum of The blue pickup before crash this is what This is the momentum of that awesome Great-looking car before the crash So it's exactly the two particles are still independent of each other, but we are adding them together. So what is this? Total momentum there's more to it than that total momentum of what when? Total momentum of the system of two cars Before collision this is the momentum before What's this in words? This is the momentum of the whole system before collision this is The momentum of the whole system after collision Not during collision because during collision this change in speeds is going on We don't know exactly what that is because notice v prime Well v prime still in there But but how that happens in that incredibly short period of time. We don't know any of that This is just the instant before collision the instant after collision in a collision The total momentum before Equals the total momentum There's no change in momentum in the system whatever the system momentum was Stays the same now There's there's a little bit of a subtlety to this but not too big a one Remember what the deal was with this minus f and the plus f This was the force on one car. This was the force on the other car, but they were equal and opposite Not only that they're equal and opposite and they're essentially Inside the system those are not forces outside the system It's not the force of the great hand of God Flucking Samantha's car off the highway, which the police should do probably but we may need God to do it's not the force of any air resistance or any skidding on the road or it's the it's only the Interaction of the two cars with each other inside the system because of the collision itself That makes those two forces that are equal and opposite and Internal force they're internal to the system. So if we look at the system as a whole Those two forces add together cancel each other We don't even care what they are Collision is Is an interaction between particles such that all of the forces doing all of the changing because there's a lot of Change going on here speeds are changing cars are crumbling all kinds of nasty stuff is going on the forces are Internal and they cancel there are no external forces At least as we see it If we let the if we let the post collision period stretch out of it Yeah, there's lots of forces. They're skidding and there's always wind resistance We let off time and go by in the real world, but that instant collision for our purposes all those forces are internal and they cancel No external forces Yeah, because if there's more cars in the collision if it's a multi-car collision and We take them all as a system all those forces are still inside Now yeah, things are a lot different if it's a if it's a chain event of crashes like like they always have in the I-5 in California where they plow and each other and 60 cars are going in that crash that That takes a long time actually to develop that's that's several seconds make 30 seconds for that many cars to be in a crash An awful lot can go on remember. We're talking about the instant before collision the instant after collision and So for our purpose we'll only do two particle collisions here But if three have to hit at the same instant there'd be no change in this before hitting an instant, I mean man to go down get some friends And chases me down with all of them I mean Oh, don't tell her please don't tell her I said that this bow I'm at it in this table. I Know I'm a man is her friend the other driver. They're all women drivers. Oh No external forces If there are no external forces as there are in the collisions, we're going to look at the momentum before equals the momentum after or Delta key of this system Equals zero It's not changing we add four and a half together zero in the absence of external forces on a system Momentum is conserved. Maybe you've heard of conservation of momentum. There it is right there one of the most important ideas in Physics, it's a conservation of momentum If you go into the study of fluid mechanics Fluid dynamics especially This will be one of the most important things you'll ever look at conservation of momentum. All right, let's uh Let's put some numbers to it just just so we can see how it deals out Just For funsies because there's nothing more fun than looking at car accidents Also get used to some of the numbers and some of the Magnitudes that we might say you might see who would who was em one was a was a Samantha's car right the little blue pick up. I don't have a small pickup my car My car was 1100 kilograms Mostly that's because of the metal flake paint I Used it kind of looks pink sometimes, but when you look up close It's really candy apple red with a gold metallic flake in it. It's just his head So that's why my car has a lot of mass In case you were wondering I'm insulted that even needed to be brought up 32 meters per second go over the speed limit probably texting at the time 17 meters per second so find out for me in this situation Just to work through the numbers a little bit real simple Double-check your units. So let's see. Let's just make sure we understand what the units are on Momentum nothing more doesn't calculate the momentum before We know that'll equal the momentum after The instant after collision we can use that to find out what the prime is But you coming on the accident situation you probably know what the prime is yet first thing they do in an accent Well first thing after they make sure it was okay. They bring out the tape measure measure the skid marks record the Ambient conditions was a raining or snowing Is that a gravel road or a pavement asphalt or concrete? They write down all that stuff? Because they're going to go back into their car open up their laptop and put all that in and out comes the Well internally it does the coefficient of friction calculates all this stuff for They'll have laptops in there now talk about who's texting while they're driving Oops You think after this all this time I'd be used to the camera Whether that Although the same problem every should get the same number so if you've got something check it with somebody if you're going to speak in German with anybody Allen Not yet You know nobody recognizes Bill this is Bill He's the guy watch for the half that's reason you don't recognize him today I've ever seen your hair I know less about you're gonna know about mine Everybody agree Okay, we got some agreement what's it look like Len, what'd you get 23.8 meters per second? Simple as that I think that they try to get out of measuring the skid mark length and the tapes and recording the coefficient of friction and the like then they'd be able to figure out just how fast Samantha had been going Oh do this do this for me. Let's check something else see if it's true or not Do this for me find out the kinetic energy. We don't need that Kinetic energy of the system before and The kinetic energy of the system after calculate those two things as well Units wrap up so we make sure we got everything here Ask you Give me what I asked for The the kinetic energy after collision how are we going to find that? One half one half what's the two together because after collision. That's what they are so I'll put m Vt for total that's m1 plus m2 times what? v prime square Make sure it doesn't look like v to the 12th Because that's wrong Make it look like v prime square So that's pretty easy How do we do the kinetic energy before collision when they're separate? Calculate the kinetic energy separately adding two kinetic energies before energy And all this different parts in the system just add together remember what you're doing that with with spring potential Gravitational potential then we just add them together when we got more than one So this is ke one before that's ke two before One half m1 v1 squared v2 squared remember in this case the one and the two don't mean before and after The prime means after Because we have two different cars going here ones and twos our system of particles. We just add stuff together At least energy and momentum we sure do get some numbers on those I need I need two more things make energy before and after So get those two numbers check with somebody when you agree Relax the chances of just to prove that you're right if you agree. You don't agree Sort it out take it outside It's a little section. It's uh, you know something with forces first one Something what? Yeah, now now now that we now that we know what m delta v is on one side that's got to be able to f delta t however We know the product f delta t now, but we don't know what f is because we don't know what delta t is vice versa So we know what that product is f delta t We don't know What good parts are of it individually, but we're gonna need that f delta t in a little bit in fact You're gonna need it All right, we got lots of agreement on these numbers Tyler now you check my food you check away check with somebody else Geez you could weigh all day for Bill You guys agree? Martin Andrew Patrick who you check Text text down What do you get say yeah, what do you get that's Andrew? It's right here Man what is giving you trouble the times are this where All right, let's see what we got first thing Let's double check here one of the units on m V momentum Well, yeah, obviously, let's see we got kilograms meters Per second. Obviously that's mass times velocity. Oh by the way in reports when you write these reports for me Don't do this square bracket thing around the units. I'm doing that at the board as I analyze the units But remember every time I ever put a graph or something like that I have here I just put s there maybe in parentheses or put the units right on the thing Don't use these square brackets and usually in in writing that means something else entirely It's usually used for when you have references in your reports So I saw that a couple times in the reports What else does this equal? Because that's not the only thing it equals If you remember over here when we first had it we had minus f delta t equal Delta p that was of the first one right the one with the minus was the first car Check back to your notes. We had that we had to write up here in the corner here only I had minus f delta t equals m one times The prime minus v one, but that's delta v one And then one delta v one is p one. Is that right? Okay, so the units for momentum, which we just got Must be the same as these units. What are these units? Seconds so these are the same and you can double check that take out Newton's put in a kilogram meters per second Square, then they're the same so those are the units You could come up with other combinations, but that's plenty right there So what's the kinetic energy of the system before collision? 620 kilojoules something 566 something like that right was energy conserved No, most certainly not in fact good chunk of energy looks like About a sixth of it was lost where to go because when when we were doing the work energy equation and There were internal forces how much works done by internal forces How much works done by internal forces? And journal forces are equal opposite. They cancel they're not pertinent to this situation. So there's no work being done Remember now picture your mind the work energy equation there it is It's beautiful glory if you haven't gotten your tattoo of it yet. You put it right here because it fit there In case you need it Work energy equation. There's no forces no external forces. So there's no work Why is an energy conserved there? There is no work if The left hand side of the work energy equation is zero isn't the right hand side of the work energy equation zero So why is there a change in energy? When there's no work being done and there shouldn't be a change in energy This is just kinetic energy There's other things going on there's places where that energy is going. Where is that energy going? It's Being stored up and bending that metal if these cars were made out of bouncy springs, which would be awful fun Then they hit and they bounce off each other. We get that spring energy back We get the kinetic back to the kinetic energy energy would then The kinetic energy we could get restored from the spring energy But we're a lot of this kinetic energy is going into the deformation of the metal Then breaking of the glass the heat and the noise that's generated and it's all lost Energy is conserved. It's just a lot of the kinetic energy is taken out put somewhere else and It's unrecoverable. We haven't looked at unrecoverable energy before We could always get that spring energy back We could always get that potential energy and the gravitational potential energy back this energy We can't get back this energy is lost All right, what else can we do with this? Well, we can do the very same calculation. I guess with with the two coming towards each other Well, let's go ahead and do that Let's let's say same speeds same masses But this time I knew Samantha was on the highway. I figured the best thing to do is turn around Go back the other way figure in You know the way she drives. There's no way. She's going to be on the highway She'll be up in the sidewalk or something. I'll be safe going back the other way So I'm going the other way that speed now. It's a head-on collision Now what's the prime and now what's the kinetic energies? before and after You can do that real quick. You know all the units You know You run through the question you should be able to do that real quick same thing Only this time I'm going the other direction before the crash Now I want to know what happens After the crash we'll assume we still collide and stick together I want to know which direction are we going after the crash And what the kinetic energies were the same situation changes anything Some stuff changes. Just do it. Just think there This is not exactly the same problem everything changes for now. What's the kinetic energy after Should be almost done. We're used to this calculation. It should be quick. I already know the units work out. Okay This is a pretty easy one when we're doing momentum before and after as long as we've got the same units They're automatically going to work out So we wouldn't want one in kilometers per hour and one in meters per second. That'd be disastrous Got something Phil check with anybody yet. Check with Alan. Alan's done If I fill you know if it's set in between then you could work with Len and Alan And those days when Mike's kind of sleepy you wouldn't get all scared You wouldn't check with him It's going to get a bad grade on On works and plays well with others very he's going to get a minus And not even get a check mark. Certainly we'll get a plus What Yeah, nobody ever makes the same mistake twice Anybody agree yet so we can get going Right because it's right here in black and white Do you have Like when you subtract Just do it So Do we have it's sort of like a two people at least to agree let's go Anybody agree yet, okay We've got some agreement v prime equals 5.1 meters per second. We'll call it just to be Quick here 5.1 meters per second in fact Who had more momentum Before the crash without calculating momentum of each Who had more momentum just look at that result. Tell me who had more momentum before the crash Remember the momentum doesn't change in these collisions Here I have a positive velocity meaning what did anybody get a negative here? I have a positive velocity. This is the two cards together So now we have Plus 5.1 No tiny arrow Or our momentum is to the right going into the collision I had momentum to the left If we finished with the same momentum we started with we had to have started with a total momentum that was to the right So who had more absolute Momentum magnitude of momentum car one did because If that's all the momentum to the right and we still ended up with momentum to the right Then she had to have a lot more momentum going into the crash if we had the exact same amount of momentum As each other what would our velocity be after the crash? Zero if we had the same mass same velocity we hit and stop instantly Or if we had a combination of m times v that was equal we'd hit And stop Since we end up with rightward momentum We know then that her momentum was greater than my momentum Absolute value the police could look at that too Just look and see which way the cars went after the collision And instantly know which one had the greater momentum Just based only on the direction the crash Uh, the the coupled cars went after collision. They instantly know who had the greater momentum How about the kinetic energies? What we start with Same as before but wait. No, no, no one car was going the other way Doesn't matter you square the velocity. So direction doesn't matter in kinetic energy. What was it 566? Oh, yeah, no there it is right there 6 20 just the total moment kinetic energy after collision Hardly any now We lost a whole lot more Energy where'd all that extra energy go? Same place it went the last time only an awful lot more of it. Which collision would you rather be in? Bimped from behind Or head on same speeds wouldn't you rather be bent from behind? How many people ever you hear get killed because they get bumped from behind? lot of people Get killed and head on collisions because there's so much more energy that goes into the collision itself. There's that much more deformation That much more damage those cars and head on collisions. You've seen them sometimes There's not much car left That took a lot of energy To do that kind of damage That there's there's the energy right there An awful lot of energy All right, uh, oh, that's good. We'll we'll uh, we'll take up with more of our system Systems of particles then on uh on monday Very useful tool Imagine if you had a bit for our announcers they ought all be the same here