 So questions where we use momentum and energy Key idea so we can use work and energy concepts together. In fact, the odds are very good I'm gonna affect more than good a hundred percent I'm gonna give you a question on your test where there is both a change in height somewhere in there Which means you better use energy to find this day and there's a collision Which means you better use momentum to find the final velocity We apply momentum conservation Collisions we use energy to analyze Then it says or the word or shouldn't be there We use momentum to analyze pendulums and curved ramps if there's a change in height in the complex problem Must be carefully broken down into steps. So here's the first one. It's a very famous one in physics nerd terms It's called the ballistic pendulum I don't know if you ever asked yourself How did they actually calculate things like bullet speeds 80 years ago before the advent of radar? You certainly can't do it with a stock watch because your human reaction time doesn't work What they would do instead is they would fire a bullet Into a wood block and if they knew the mass of the bullet Which was pretty easy to weigh that they could do and if they knew the mass of the block Then they would watch from the side and they would see how high the block went up And if you knew how high the block went up, you knew how much potential energy it had at the top Yes, how much kinetic energy would it have at the top? Zero so you could then work your way backwards and say how much kinetic energy did it have here all of it And then you could say oh how much kinetic energy did it have here from the bullet? How much velocity to the bullet in part? Now here, we're gonna be doing it backwards. We know how fast the bullet is traveling Brett We're gonna ask how high is this going? So there's gonna be two parts The first thing we're going to do is we're going to analyze the collision The second thing we're gonna do is we're gonna analyze the swing the change in height conservation of energy. Is that okay mitzu? That okay? Yeah, you with me because I don't think you were here. You're good. You back Yes, okay So we have a collision Bullet hits the block wham Some of all the initial momentum equals the sum of all the final momentum Before the collision what was moving mass one mass two or both mass one message. Sorry, and you know what let's call this mass one, let's call this mass two I Was going to use B for bullet, but then B for ballast would just be confusing B for block would also just be confused I'll use mass one nasty So before the collision we have the momentum of object one initial After the collision what's moving mass one mass two or both? Both stuck together or separate What's the fancy word for stuck together? Is it elastic or inelastic? Think it through elastic rubber band bounce bounce apart Inelastic this is an inelastic collision Okay, I am going to use those terms on quizzes and tests So you need to be able to use the same chain of reasoning that I just or you can memorize them But I usually just think it through that one. So it's going to be the momentum of Both this collision is it in a nice straight line or are there angles looking at the diagram or in the question? What do you think between here and here? You can see it. There's some kind of an angle or something like that So what do you think? That that's not the collision that stuff that's part two in the collision which is right here Nice straight lines, which means no trig will let to the right be positive to the left be negative We can use good old Kayla normal equation solving. We can say mass one v1 initial Equals mass one plus mass two The final because momentum is mass times the Watson What I want to try and find here John is how fast they're moving after the collision because that's going to tell me How much kinetic energy this guy has in? fact We draw the line over here Brett this part because there's a change in height is going to be That's the second part of this question and right here. What's the potential energy? Zero we're going to let the ground be right there and At the very very top of the swing for a split second. What's the kinetic energy? zero in fact, we're going to get this a Half m v initial squared equals m v h final and to call what happens to the m's Here they cancel not but here they cancel As long as there's no friction to dimension friction or heat or anything like great act if they want us to find the height I think the height is going to end up being V I squared over Two g is that right? You would divide the g our vendor. Yeah, and I made the one half of two on the bottom What's vi? Brandon, it's v final after the collision. That's why we have to do this in two parts What's my initial velocity when I start to change my height Matt? Well, it's how fast you're going after they collide it and The mistake most kids make on these is they forget that there's a collision. They want to go Oh, the math of the velocity is a hundred. They want to put a hundred there nope When this bullet hits this block things are going to slow down So is that okay Brett? One block bullet sticks inside the block. They swing up together. Okay Sorry, I should have explained that So here's part one Part two is the collision part three is the swinging. I didn't explain that. That's my fault No, it's not I should have explained it. No, okay, so let's go back to this side Let's find the final What is the final everything's in a nice straight line, so I'm not drawing my vector pictures here much nicer breeze So how would I get be final by itself? Straight divide. Hey, I like that The final is going to be m1 v1 initial divided by m1 plus m2 The final velocity after the collision is going to be mass of the first object 20 grams so point zero two Velocity tell me it was a nice number hundred divided by 4.02 the mass of the block and the mass of the bullet After the collision how fast will the block and the bullet move off together? You get point four nine seven five one two three Blah blah blah blah blah Yep, I'll go point four nine seven five because it's not my final answer. I'll carry a few extra sick things In fact, I'll use that exact answer on my calculator meters per second and this is Now your initial velocity Once they start to move off together, so does that make sense they hit Sticks together and it starts to swing up Okay So if I want to find how high this goes It's going to be point four nine seven five Squared all over two times John negative nine point eight or nine point eight convince me What are we finding? What are we using? What are we doing? What was our initial approach? What do we call this? We called this a law. No, this is not momentum. No, no, no, this was thunder and lightning What was this law called folks? Conservation of conservation of what? Conservation of what? Energy worker scalar. Sorry energy scalar or vector So John negative or not No, not absolutely by the way if you did you get a negative height, which wouldn't make sense Okay, so could also just figure it out by doing the math Plano nine point eight. How high will this go? Mr. Do it use your answer answer squared divided by bracket two times nine point eight and I get it going about not very high point zero one three meters About that high about that high so Back to this now. Here's what they would have done in the old days to calculate the speed of the bullet That's what I said. This is how they did this Instead of me telling you vi squared and finding H. Can you see from here if you knew H? Could you find vi? Yes, and if you knew vi you would put that right in here for v final and You could solve for the initial velocity of the bullet by dividing by the mass of the bullet It was a nice way It was a nice way to be able to calculate the speed of a bullet without using a stopwatch And it was reasonably accurate You would probably repeat the experiment a few times to you know sources of error average out your error. Hopefully It's very nice. So there's an example of a combination momentum and energy question I sort of like that question and what I mean is there's two questions here that I sort of like one of which you almost certainly see Depending on which version of the test again, so I'll say I like this question. I like this question, but Depends which version you get and this is nice because it's like bullets and ballistics. Oh boy example two Example two if mass one equals mass two equals mass three equals four kilograms so every mass is four kilograms and Mass one has an initial velocity of three point two meters per second find the final speed of mass three If the height is point eight two Okay, oh and all collisions are hit and stick. What's the fancy word for hit and stick? Let's write that just to remind us what's this going to do to that is there a collision Yeah momentum Then they move off and what do you see right here? Is there a change in height? energy Then they hit M3 did I say hit M3 collision momentum this question is going to have three parts There's going to be an initial momentum a conservation of energy Sean in the middle and Even though it's curvy. I don't care because conservation of energy John is a scaler and Then a collision and what I like is I notice Jeanette the collisions are all in nice straight lines No Tip-to-tail stuff from last day Okay So I'm going to divide this up into three parts The first collision since it I said collision. I'm going to write this Before the collision what's moving mass one mass two or both? How do I know mass two is not moving? Oh, they put the word rest underneath there. Okay fair enough And you know what since mass one and mass two and mass three are all the same mass I'm not going to call them mass one mass two and mass three Why don't I just call every one of them M because maybe some stuff will cancel along the way? Okay, I'm going to have Mv1 the initial sorry Equals and I skipped this step. I didn't actually write out the equation I'm going to see because this is nice and linear if we can take a little shortcut here After the collision, what's moving mass one mass two or both? Both stuck together or separate M plus M The final by the way, what would a shorter way to have written M plus M be I could have written to him I'm gonna on my next line Let's find out how fast these two guys Move off together the final velocity after the collision is going to be M vi divided by two M Conveniently, you know what happens to the m's here. How many m's on top one? How many m's on the bottom one? No, well, sorry Two m's. I'm using math 12 with the exponents. The m's are going to cancel a two is going to be left behind In fact, I'm going to get this What was the initial velocity scroll down? What does it say in your diagram or in your instructor in your 32? they move off at 16 meters per second. I'll put a big one right here on my diagram, so I know this is what we're talking the collision I Think the second part we're going to talk about is this section going up the hill Mitchell is there change in height energy or any of these? Zero is your initial kinetic zero? No, what about your initial potential? Oh, yeah on the ground What about your final kinetic? Are you stopped at the top of the hill? I don't think so What about your fun? Oh, did I say top of the hill then your final potential can't be zero because I said top of the hill didn't I? a half m Now it's actually going to be a half two m The initial squared equals two m g h plus or hang on mr. Do it do kinetic energy first a half two m the final squared plus two m g h because it's both masses and we said if you have one mass But you notice is there a two m in everything? Turns out the two m's are going to cancel I really could have gotten away with being sloppy and just putting an m there and saying yeah I know I can't masses are going to cancel because they don't mention friction or heat And what I want to find is how fast we're traveling at the top of the hill now You may remember what I liked to do because I wasn't a big fan of the haves is I like to put a 2 there a 2 there and a 2 there Which would cancel there which would cancel there and just stick around there. I would get this The initial squared equals The final squared plus 2 g h and It's this v final that's going to become the v initial in part 2 And we want to find v final Brandon. How would I get v final by itself? The 2 g h and then what? That would give me v final squared square root v final is Going to be v initial squared minus 2 g h Square root John am I going to put a negative 9.8 or a 9.8 in for g why? scale it Okay, so I'm going to get the square root of 16 squared minus 2 times 9.8 times What's h? Oh, it tells me in the question point it to yep. What are we trying to find here? We're trying to find v final right and Yeah, it does matter Big time What was the height point to is that what I said? Okay? So once both of these Hey, let's call them roller coasters for that bumper cars Stuff together train cars Make it up this hill. How fast will they be traveling? Do you get 15.45? Sorry 0.49? Yeah, not a very big hill. They don't lose much kinetic energy. They don't lose much speed 15.49 then they collide That's going to be The third part of this equation There is a collision the sum of all the initial momentum equals the sum of All the final momentum before the collision What's moving? I think these two guys stuck together Yes 2m The initial and you'll notice I'm back to vector notation because this is not a scalar They collide After the collision what's moving? I think all of them stuck together or separate What would the mass of all of them be? 3m v final and this v final Brett is not this v final This v final is actually going to Become v initial right there. Hey once again the m's do cancel, which is kind of nice They didn't need to tell me that it was a four although I if you'd left the fours in you would get the same answer You're just doing more typing on your calculator, and I'm lazy How would I get v final by itself? Is this in a nice straight line Nicole or are there angles in this last collision? Looks the ground looks level good great great. So how would I get v final by itself Nicole? Divide by three absolutely V final is going to be two times v initial divided by three It's going to be two times fifteen point four nine Divided by three now this question here is not fair game three things. No two things. Yes That's a great question would be Given you this ask you to find v final. I think that would be totally fair game two times this answer divided by three and I get ten point three meters per second Direction oh wait a minute Shawn. What did they ask for the final what? No, what did they ask for the final what? Read the question speed. Oh, I don't need to worry about to the right or Easter. Yeah good Okay, turn the page This is the second question that I like This is mr. Deweyck attempting to do art This is why mr. Deweyck usually uses computer graphics okay a Roller coaster or maybe you can think a mining car on a track With an initial velocity of 8.6 meters per second rolls down a track with a height of 18 meters It strikes a second identical roller coaster That has an initial velocity of 24 meters per second the coasters stick together and continue up the next hill How high can the roller coasters reach? well How much kinetic energy will they have at the top? Zero so if I figure out how much kinetic energy they have here. That's all gonna be potential energy, and I can find the height How much kinetic energy? Depends on how fast they're all going What does that depend on depends on how fast this guy is going at the bottom of the hill Did you hear me say bottom of the hill change in height energy? We're going to again have three sections. I said to you three sections wasn't fair game. Maybe I did The first section is down the hill The second section is the collision the third section is top of the hill, so let's do the first section From here to here is there a collision? So momentum or energy. Oh cuz also change in height Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final or any of these zero Final potential We'll call that ground level a half m v initial squared plus m g h initial equals a half m v final squared Yeah, the m's cancel Yeah, mr. Duke's gonna multiply everything by two Yeah, the two and the half and the two and the half cancel Brett do I have v final by itself already? So I don't need to worry about which way I'm gonna subtract or anything like that except I got to get rid of the squared how Turns out v final at the bottom of the hill is going to be the square root of v initial squared plus two G h v final is going to be the square root of what did I say v initial was 8.6 Plus two times nine point eight times the high 18 How fast are we going at the bottom of the hill here point six squared plus two times nine point eight times? 18 square root You get twenty point six five eight Notting okay Twenty point six Five eight. Is this my final answer? No, I'll carry a few extra sig figs then all right What happens right here? Bam a collision did you hear me say collision well then The sum of all the initial momentum has to equal the sum of all the final momentum Before the collision what's moving mass one mass two or both? Both stuck together or separate Before the collision separate Momentum of the first guy initial plus momentum of the second guy initial Wham there's the collision after the collision what's moving mass one mass two or both? stuck together or separate Stuck together looking at my terribly drawn diagram momentum both final That section of track does it look fairly level to you? Well, it was supposed to but I can't draw to save my life it is so we're not pulling out the trig We're not going all vector e tip to tail Momentum of this is going to be mass one v one initial plus mass two v two initial equals mass one plus mass two V final Brett how would I get v final by itself? Okay, I can because it's straight line So if I hear you correctly sir, you're gonna say v final is gonna be the first mass times It's initial velocity plus the second mass times. It's initial velocity, which makes sense That's how much momentum I have before lesion divided by mass one plus mass two Let's see if I can fit this in on one line mass one was oh it says they're identical. So 250 velocity one initial 3.658 plus 250 times 2.4 Screen froze fair with me for a moment. Yeah, I'm trying the wireless thing again. I bought a new one I'm gonna try it over the holidays to found one on sale for cheap from a different company See if it's a bit more consistent, and we should be back in about three two one Should be a beep from over here Hey, it is screen goes black screen is back Okay, we're back. Yep 2.4 divided by 250 plus 250 although I guess I could have written 500 because that math I can do in my head After the collision how fast do they move off together for a split second? Let's see Bracket 250 times my last answer plus 250 times 2.4 divided by 500 you get 11.53. No Yeah, 11.53. Okay That's after the collision they start rolling off together, but what do they hit right away a hill? Did you hear me say hill that sounds like a change in height, you know how we're gonna solve the third part To find out how high these guys go energy so part three Kinetic energy initial plus potential energy initial equals kinetic energy final plus Potential energy final already of these zero. Sorry Potential energy initial I think we're starting out on the ground absolutely Kinetic energy initial zero. No, no, no, we have we have speed anything else zero Ah at the very top for a split second. How fast will you be going? Oh, this is actually a nice easy equation Then a lot less than the other ones. We're going to get a half m v initial squared equals m g h Final now the m we're talking about is 500 it's 250 plus 250 But do you notice Brianne here? I could be a sloppy because what's going to happen to the masses? And How would I get h final the final height by itself? I? Think the final height is going to be v initial squared divided by 2g which I think is the same equation We had a few minutes ago in a different question It's going to be 11.53 squared divided by 2 9.8 final height 6.78 meters No, is that wrong? Right Okay Sadly on roller coasters. They don't have slow-moving cars that you crash into except me a great ride however If you're ever on bumper cars again, that's great momentum collisions with almost equal masses The cars have a big enough mass that the difference in the mass between the passengers probably doesn't make that big a difference And you can decide well head on momentum's cancel That's why you both come to a stop or there are angled collisions which you can push somebody sideways I'm a you've all been on bumper cars before yes Turn the page Football are there dare I say some collisions in football? So great momentum Okay Example three a hundred kilogram fullback is running with a football at two meters per second He's met head on and he sticks to a tackler which tackler is more likely to stop the fullback a 200 kilogram lineman moving at one meter per second or a 50 kilogram cornerback moving at four meters per second or both the same and convince me Joel what oh Trevor what Trevor says the same Trevor I agree with you amazingly convince me convince me they both have the same momentum First of all how much momentum does the fullback have and yes, I made up nice numbers so we can do the math on it How much momentum does the fullback have? 200 if we bring him to a stop how much momentum must he finish with them? Zero so we got to get rid of 200 kilogram meters per second We have to apply an impulse of negative 200 kilogram meters per second How much momentum Trevor does this guy have mass times velocity how much momentum does this guy have mass times? Okay, so the same Each delivers the same Impulse they'll both bring this guy in a head-on collision to a stop and you play football for a couple years Yeah Conor you play football for a couple years or no less. Okay, so Connor Which tackler will cause more hurt? This is the more interesting question to me a 200 kilogram Limon moving at one meter per second or a 50 kilogram cornerback moving at four meters per second which one will cause more hurt Hurt is not in terms of momentum hurt is in terms of how much kinetic energy Because the kinetic energy has got to go somewhere too Where's the energy going to go into work work was what times what? Force times distance more kinetic energy means more compression of the force over a distance more rib crushing essentially so What's the kinetic energy of? this guy If you go a half m v squared, what's the kinetic energy of the lineman? On your calculator really quickly, or you might be able to do it in your head Trevor. What'd you get? Point five times 200 times one squared. I guess you'd Trevor stop stop. What's one squared? times 200 half of that Okay, this lineman has 100 joules of energy and assuming he comes to a stop afterwards That means he's got to send that energy somewhere. Where's it going to go into? hurting the player Deforming the players rib cage Force times distance What's the kinetic energy of this cornerback? Well, that's also going to be a half m v squared so Trevor this one I do want what's four squared times 50 times a half sorry 400 he's got way more kinetic energy to burn and Those of you who watch football who makes the most spectacular hits Why free safeties and not cornerbacks because free safeties actually have a little bit more considerably more mass than a cornerback and almost as much speed they're the best balance between extra mass and Maximum v squared the cornerbacks although they have a little bit more v squared. They're almost always pretty light often very short like five eight Five nine we're often the free safeties about six two six three and probably about 30 pounds heavier and just about as fast That's why those are the most spectacular collisions so kinetic energy equals hurt so for those of you who are football fans now you know and I think I mentioned this last time but I'll say it again the Real freaks are the people with a lot of mass who can also get a lot of velocity in the 80s There was a linebacker named Lawrence Taylor. He was an athletic freak He was 260 pounds and he could outrun the running backs No one had ever seen anything like it one of the only defensive players to win most valuable player He changed defenses forever. Nobody had ever seen anything like that in the 90s There was a running back for Kansas City named Christian acoya called the Nigerian nightmare He played for about four years five years but his knees couldn't handle it because he had so much mass but he was six foot five two hundred and sixty pounds and Could run like a little he ran a four three Nobody'd ever seen anything like that. Those are the really unusual athletic specimens where they combine the best of both worlds example four says nasty scholarship question a 15 gram bullet traveling parallel to an inclined ramp Strikes a 2.74 kilogram block of wood and becomes embedded in it The impact drives the block a distance of 26 centimeters of up the ramp The ramp is inclined at 28 degrees and the collision friction is for what's this is an example of a scholarship question We're not going to solve this all we're going to do is dull and talk about it okay So we have a ramp like this with a block of wood And it says the bullet is traveling parallel to the ramp. So the bullet There's the bullet it hits and it sticks and it drives the ramp. Sorry it drives the block and the bullet sticking together up The ramp a distance of Point two six meters. It says 26 centimeters. So here's what do they want you to find? Speed and thankfully not velocity because you have to angle it speed Okay What's the speed of everything here? At the very very top zero Do you know how far it traveled? Point two six Would you be able to go winner minus loser and find the net acceleration using friction and MG parallel and all that and if you knew the acceleration which you could find its acceleration after the collision and you know It's distance and you know be final you could find the initial How fast it was moving up the hill and Once you knew via initial you could say there is a collision I can work my way backwards and find how fast the bullet had to be traveled. It's a tough question. We could do it This is not fair game. So let's make a little note Not even as a nasty multiple choice. This would be overkill But this is what the scholarship exams used to be like that makes sense my explanation that we could we could be a lot of work So Sample five I'm gonna pass on as well because it's Christmas. It's also a nasty scholarship question We're gonna talk about it. Now you guys are zoning out. Okay, fine What's your homework? number one now Take a look at number one What's be asking? Sorry How much work what be is saying is first of all are they in a nice straight line with each other? Work equals the change in potential plus the change in kinetic There is no change in potential Find out how much kinetic energy there was before the collision Find out how much kinetic energy there is after the collision and The difference is how much work was done in deforming these in heat in sound. Okay, so try number one I haven't done one like this with you Curiously being figure it out To is good for is good nasty vibe is good