 Here we go it's mark the quiz those you that did it mr. Dewick's in a grumpy mood now so I Gotta be honest with you Momentum is a unit that kids find difficult from my prior experience and my message is for those you who think you're gonna sluff You don't want to be sluffing at all Number 112 kilogram football player running with a speed of four meters per second tackles another player what impulse What's another word for impulse? Okay, we all need to know that Caitlyn what's another word for impulse change momentum So when they say impulse I'm hanging change momentum must the tackler give the other player in order to bring him a stop to a stop now There's two ways to think about change in momentum There's the actual equation that says that change in momentum is equal to force times change in time Has this question mentioned a force or a time? Nope Connor the other way to think about this is to realize what's changing anything So I think what they want us to do the change in momentum is gonna be the final momentum minus the initial momentum Our angles mentioned at all in this kid. Okay. I think we can assume everything is nice and linear. What's his final momentum? What's his final momentum? That's a number Huh? No, what's his final momentum as a number? Why how do you know zero? Because it's stop right momentum is mass final momentum is zero minus now momentum is mass times velocity So it's going to be mass times B initial is your initial momentum. It's going to be zero minus a hundred and twelve times four negative four hundred and forty eight kilogram Meters per second does the negative have to be there? Yeah, that's the impulse You have to give an impulse to cancel out the runner's initial momentum. You have to take away his momentum Okay terms of marking I would probably go Half mark for that half mark for that half mark for the numbers And a half mark for the answer To What's the magnitude of the impulse needed to change the speed of a 10 kilogram body from 20 to 12 at a time of 5 seconds? Okay, now they're talking about a time and B asks about a force now. I'm going to start out the same way the magnitude of the impulse is Going to be the change in momentum Which is going to be momentum final minus momentum initial Which is going to be mass v final mass 10 v final 12 minus mass Ten the initial 20 What do you get for a the change in momentum magnitude has to be? It's going to be negative now because I only asked for the magnitude if you didn't put the negative I won't be fussy because technically the magnitude is just how big I'll include the negative just to be fussy though 120 minus 200 you get negative 80 And I'll put a decimal for two sig figs Kilogram meters per second the answer to a is negative 80 kilogram meters per second B What force is needed now? I'm going to use the second definition of impulse Nicole the fact that impulse is Also equal to the force times the change in time Right how would I get the f by itself? Turns out the force is Going to be the impulse divided by the time Which is negative 80 divided by five seconds? And I think you'll get a force of negative 16 Newtons if you left the negative off, I won't freak out. What's the negative telling me corner? It's telling me it's in the opposite direction of the motion Is that okay? number three a Cart of mass 3.2 kilograms traveling 1.2 meters per second Clides with a stationary cart of math 1.8 both carts stick together and move off after the collision What's the final speed? Is there a collision? Then the first thing I'm going to do is I'm going to write the sum of all the initial Momentums equals the sum of all the final moment Now what well I ask are there angles involved here or is everything nice and linear? I think a cart rolling on the ground. I think Joe I can use my imagination I think that's all going to be in a nice straight line I'll let to the right be positive to the left be negative if there's a diagram or I'll let the initial be positive in the final Anyways, I think I can I don't need to bring out the sign law and the cosine law like we were doing last class Before the collision what's moving mass 1 mass 2 or both mass 1 After the collision what's moving mass 1 mass 2 or both both stuck together or separate stuck together This is going to be m1 v1 initial equals m1 plus m2 the final The final is going to be m1 v1 initial all over m1 plus m2. It's going to be 3.2 times 1.2 all divided by 3.2 plus 1.8 final velocity is going to be 3.2 times 1.2 divided by 5 I think 3.2 plus 1.8 is 5 you get point seven six eight point seven six eight meters per second Terms of part marks I give you one mark if I saw that one mark if I saw that one mark if I saw that one mark for the answer Is that two sig figs? That I'm fine Doesn't it feel good to be able to ask a question like that on a quiz? Give yourself a score please out of 10 Luckily those many of you that didn't do the quiz it's only going to cost you a 10 spot not a big chunk of marks And if you can put your name on your quiz and pass them in words, please Last day we up the level of difficulty quite a chunk and I realized it was a big chunk Can you all get out lesson six from last day, please? Lesson six from last day two-dimensional momentum Now I do find Kara these questions way more interesting because when things collide they usually do bounce off at angles This is the physics of car crashes. This is the physics of bullet billiards pool Great, and once you're there pause for a second. So that's the bonus video game back to here Kayla here's what we said as soon as we see there's angles and it's usually pretty obvious either from the picture or from the way They've described stuff We're looking at example four if you want to just kind of jog your memory I started out the same way I still wrote the sum of all the initial momentum equals some of all the final and I even still wrote the same Equation I said what's moving beforehand mass one mass two or both what's moving afterwards mass one mass two or both Did they stick together or are they separate? But then the difference Mitchell was we started delping we started drawing a picture we started doing vector math We said look draw a picture label each arrow not with its velocity Not with its mass with its momentum because it's momentum. That's conserved and then add your vectors tip to tail almost always you're gonna end up with the cosine law unless it's a lovely right angle question then Jadette it's much easier, but almost always you're gonna end up with a cosine law and Then you have to use the sine law to find an angle We're gonna come back to example five, but right now. Let's look at example six Okay, I'd like to think Trevor just glancing at example six. It's pretty obvious angles here Right the diagram pretty much gives it away Is there a collision Trevor? So first thing I'm gonna do is I'm gonna write The sum of all the initial momentum has to equal the sum of all the final momentum Normally, I'd write it down here, but I haven't feeling when I run out of a room. So I'm trying to save space Before the collisions a what's moving mass one mass two or both? Momentum of you know what let's not call it mass one and two. How about mass a and b would that make more sense based on this diagram? Yeah, so mass a initial Momentum of object a initial is what's moving Wham is a collision After the collision what's moving say mass will a mass B or both Stuck together or separate so Momentum a initial sorry initial final mr. Do it and Momentum B Final now. We're going to adult. We're going to draw our little picture. I Think the momentum of a initial Looks like that What magnitude will I put on this arrow? What magnitude will I put on this arrow? for mass times velocity Connor that work I don't care if you don't show if you go straight to your calculator not because I don't want you to but often the arrow is So small it gets cluttered if you write five times point eight equals four So I'm just gonna say that four kilogram meters per second equals after the collision mass a looks like this and I don't know the angle or the magnitude. In fact, this is what I'm trying to find plus Mass B looks like this And it even gives me an angle of 29 degrees right there what magnitude will be on mass B question Kayla Kayla just saying Front row is open best place to learn The call what magnitude am I gonna put on here with more specific really really Three here's the two that I'm adding together. How will I add them together Brienne draw them? Tip to tail and I also know that when I add these two it has to give me a dead horizontal line That'll help me draw the triangle. I think the triangle is gonna look like this for No, not for mr. Do it that one. You don't know. Sorry Momentum of object a final plus three Equals four. I need to find an angle in here. I need to find an angle in here Well, if this angle here is 29 degrees, I'm pretty sure that this angle here is 29 degrees So katala Don't think so Unless this ended up being 90, but I don't know I can't assume Co-sign law, you know how I know side angle side So what's the co-sign law the co-sign law says this? Momentum of object a final squared equals Four squared plus three squared minus two times four times three co-sign of the angle You get four again or no, ah Ah Whoops wrong button. Mr. Duke that's gonna scare everybody Square root this thing. I almost forgot to square root because it's such a nice answer. I think 2.0 kilogram meters per second Trevor here's the problem All I found is a momentum What did the question want me to find the final what the word before that the final what? Velocity if I know momentum, how can I find velocity? I Agree it's gonna be two divided by five The final velocity is gonna be point four zero meters per second at Now I need a direction Well, here's my vector Conor can you see it's starting from down here? I think my angle that I want is this my direction is gonna be What of what? You know what I better put a compass on there. Hey, what is that gonna be what of what? West of north? Let's see here's north. There's west of north That makes sense So which one is this one? I guess north of west Yes, okay, so you know what I'll even be clever leave a space and go north of West East sorry east where'd the west come from there east That's why I draw the compass rose every time because I get those mixed up all the time By the way, my mistake wasn't actually the east-west my mistake was listening to yeah, okay Sorry, I won't do I won't listen to you again How can I find theta so katoa? Yeah, I don't think there's a right angle here sign law So what's the sign law? I got room down here the sign of my mystery angle divided by what's across from it equals? The sign of the angle that I know divided by what's across from it which was 2.0 Not point four zero. I'm not using the velocity. I'm using the momentum because that's how long I'll get the sign of theta equals three sign 29 divided by two three sign 29 divided by two and Then to get the actual theta inverse sign of that and I get 46.6 degrees seven degrees sorry 46.7 degrees 47 degrees really is that okay? Well then Turn the page We did number 11 already Let's try example eight Do you guys want to try number eight on your own? Yeah, no, I can do it with you or if you want to give it a try first and then I go over it It's up to you. How about I'll do it up here try it on your own But I won't turn my screen off so you can if you get stuck Look up see if you can figure this out object B. I don't think has an initial velocity I think it's initial velocity is zero and This is my hideous quick drawing if you're one All the previous ones were stolen from old Provincials or somebody else of me it up This was me. Mr. Do it going really quickly with graphics Right, I don't know The answer is she got the same answer as me. Which gives me confidence It's gonna be two of these on your Who needs more time a few more. Okay. All right. How many you got that? Oh Great Now if you're getting the hang of this that means two of these on the test times seven 14 marks that you could get it's a hundred percent on 14 marks assuming you don't get sloppy mistake But even if you do this by the way Connor is why you show work It's if you make him a straight I can still follow what you did and see you know, you move the decimal point over wonder Your two became a three on the next line, you know thing the dumb things our brains do Brains Turn back, please if you would To example five Example five this one here about it a Metal disc explodes boom into three pieces Which fly off on the same geometric plane what that's saying is let's assume they all stay flat because 3d you need calculus to do this The first piece has a mass of 2.4 kilograms and it flies off north nor oh better draw compass Flies off north at 10 meters per second. The second piece has a mass of 2 kilograms and it flies east at 12.5 meters per second. What's the speed and direction of the third piece which has a mass of 1.4? kilograms Here's bomb forensics now really the FBI or the RCP if they're actually looking at a bomb Of course, there's more than three pieces, but the principal is going to be the same They're gonna start out with a basic assumption Is there a collision no is there an explosion? Yeah, then they're gonna start out by saying Before the explosion What was the momentum of the metal disc? It's a trick question that could be really obvious Brat zero, so you know what the final momentum has to be zero Now we're gonna put zero for the first before But after the explosion what's moving mass one mass two mass three for all of them stuck together or separate Momentum of object one momentum of object two Momentum of object three What does momentum of object one look like well it says north and It's 2.4 kilograms 10 meters a second. I think it's 24 pointing to the north Plus what is the momentum of object two look like well it says east Connor which direction is east on our page to the left or to the right? Excellent Connor Connor what number am I gonna put on here? What's the magnitude of this line? Did you do that in your head? I hope you did did you? Thank you. I saw someone reach for their calc at your two times table come on plus Do I know anything about the third one? Okay Well, I'll add the first two vectors together Let's do that we can do that and they're nice. They're at a right angle. It means this is gonna be so katala, which I like 24 25 Now some of you might say hey, mr. Do it gets out. It's not this it's not this What was my initial momentum our vendor my overall momentum what was it? Zero you know my final momentum has to be then What will that look like in a triangle back to where you started from there's momentum of object three That's the magnitude. Oh and the call the direction is going to be That and this is what they do in bomb forensics now Just imagine this procedure, but instead of adding three vectors. They're probably adding several thousand But they can get a pretty good idea mass How far it's traveled you can figure out roughly what its velocity must have been to get that far It's more complicated, but the principle starts out here So I'm gonna give you a lovely two-dimensional explosion on your test Because it's explosions. How can I not like that? How can I find mass three? Do I need to go all cosine law on you? So how can I find momentum three? Do I need to go all cosine law on you? Like these Pythagoras for Pete's sakes. Oh, this is great. You get 34.655 Yeah Momentum of object three equals thirty four point six five five Okay, oh How can I find the velocity of object three because this is the momentum of object three? If I know the momentum, how can I find the velocity? This is by my mass very good mass three mass three mass three one point four twenty four point eight Yes, I would accept part 25 right to six eggs Theta. Oh, is there a right angle? Yeah, because they went north and east. I know that's a right angle So I can actually not sign law. I can say hey, which trig function And running out of room. I've got some more. I got a little bit of room here tan theta equals opposite over Adjacent shift tan of twenty four over twenty five Forty three point eight degrees What of what Connor? What of what? Yes Yes, yes That's what's happening in any explosion in any explosion your initial momentum is zero assuming the thing wasn't moving yep south of Isn't it going this way down this way? I'm not looking at which way the black vector is going I'm saying to get the red one. I'd have to go south I'd have to head east and head south of that to get that angle and end up down there wouldn't I? two-dimensional momentum What's your homework? Well, I didn't attach an assignment to this from the ultimate review you can now do numbers one 14 22 and 34