 Mr. Dewick, why is this called Lesson 5? It's actually, the two units are combined, energy and momentum are actually two, one big unit. I always break up with the two smaller ones because it's a lot of work for one big unit. But they have something in common, there's a reason why, there's a reason why, there's a reason why we combine these in one unit. Energy is conserved, momentum as you're going to find out in a couple of days is also conserved. We call this the conservation unit. Talk about what momentum is. So it's Lesson 5 because it continues after Lesson 4. One of the most important concepts in physics is the idea of momentum. In fact, Newton first used this concept when he phrased his second law of motion. He never actually said F equals MA. He phrased it differently, he was really interested in momentum. He called the product of mass and velocity the quantity of motion. He said an object can have a certain amount of motion and you measure it by how fast it's going and how heavy it is. For example, and because it's a product, mass times velocity, we actually are going to use the letter P for products. We can't use M for momentum because M is taken by mass. This product has come to be known as, and you can underline this word or highlight it, momentum. Hello. Let's try that again. You can underline this word or highlight it, momentum. It's the amount of motion an object has. Honestly, I think of it as how much damage it'll do when it hits something. Small momentum, tennis ball, ouch. Bigger momentum, baseball, injury. Bigger momentum, car, probably fatal. Bigger momentum than that, catastrophic. What makes momentum so important is the fact that it's a conserved quantity that just like energy where we said how much energy you have before is equal to how much energy you have after, momentum. How much momentum you have before is equal to how much momentum you have after, except it's tougher because momentum is a vector. In fact, this is one of the units that kids find tough because there's going to be lots of trig again. We bring in a lot of trig. Here's the law of conservation and momentum. In an isolated system, a system which has no external forces, so in our magic physics world where we ignore friction and all that stuff, the total momentum of the objects in the system will remain constant. This is the law of conservation and momentum. Any moving object has momentum, so right now the fact that all of you are sitting still in this room, you have no momentum. Momentum is defined as mass times velocity, and now I'm going to get fussy and I'm going to bring in the vector notation again. Symbol for momentum is the letter P for product. Momentum equals mv, and the direction of momentum is the same as the direction of your velocity. What are the units? What do I measure m in? Kilograms, what do I measure v in? Units are kilogram meters per second, and they haven't shortened that. There is a movement afoot right now to rename that unit there in Einstein. It may happen in your lifetime, I don't know. This is one of the longer units that they haven't bothered giving a shorter name, because Newtons was actually kilogram meters second squared, Joules was actually Newton meters. They usually shorten them, but not yet. Momentum is a vector quantity. The direction of the momentum vector is the same as the direction of the velocity vector, which means when you're adding momenta, which is the plural of momentum, when you're adding momentum, you've got to use vector math. We're going to be doing lots and lots of doping and tip to tailing. Newton's second law can be rewritten in terms of momentum, so Newton's second law was f equals ma, which is really m times. The definition of acceleration was change in velocity over change in time. That's where v final minus v initial over time came. And remember we said already last year, Nicole, all times are change ins. We often get sloppy and don't write the change in, but this once I want to bring it back again. And what's change in anything? This is really m v final minus v initial all over change in time. And if I leave the change in time on the bottom and just multiply the m into the bracket, I'll get m v final vector minus m v initial vector. And what is mass times velocity? Momentum. In fact, this is momentum final minus momentum initial. This is how Sir Isaac Newton actually thought of ma. He was really interested in momentum. This is easier to remember, which is why we use it when we introduce forces to you. This is more useful. Newton's second law can be stated in words, in terms of momentum as follows. An unbalanced net force acting on a body changes its motion so that the rate of change in momentum is equal to the unbalanced force. Back to here. This is momentum final minus momentum initial over change in time. And what's final minus initial? I'm reversing a question I ask all the time, change in. That's how Sir Isaac Newton gave his law. A force changes an object's momentum for as long as that force is acting. Big deal. Actually, in many ways, that's a much more useful, more complicated but much more useful version of f equals ma. In particular, this is going to allow us to analyze collisions, car crashes, curling collisions, hockey car crashes, lots of good stuff. I'm going to add the vector on the force as well, because direction, direction, direction. And I'm going to rewrite this, how? I'm going to multiply both sides by change in time. I'm going to move the change in time over to here. This is the formula for this unit that you actually have on your formulas page. Force times change in time equals change in momentum. In fact, we call this the impulse equation. What's impulse? It's a fancy term. Impulse is simply defined as change in momentum. And I'm going to use those two terms interchangeably. Mitsu, I'm often going to say, hey, what's the impulse? And you need to right away realize, oh, that's change in momentum, final minus initial. Or I may say to you, what's the change in momentum? And the question gives you the impulse. You need to realize, oh, they've told me the change in momentum, impulse. It's another word for change in momentum. What's impulse? Change in momentum. What's impulse? Change in momentum. And there's two ways to find impulse. One way is to go, final minus initial. Another way, Kara, is to say, oh, if they gave me the force and how long I can use the left-hand side of this equation, which is quicker. A given change in momentum can be produced by a large force acting for a short time or by a small force acting for a long time. If I were to hit mat with a sledgehammer, that would be a large force for a short time, I could accomplish the same eventual change in momentum by pushing on you with my pinky. It would just take a long, long time to get you up to the same speed. What are the units for momentum and impulse? Well, we already said the units for momentum and impulse were kilogram meters per second, mass times velocity. But from this equation, you can see another way to write the units of impulse or momentum or change in momentum. Not only is it mass times velocity, change in momentum impulse is also on the left-hand side, what times what? Read that to me, Brett, what times what? Momentum can be measured in kilogram meters per second or Newton's seconds. And both are right, Trevor. I write this one if I've gone mass times velocity. I write this one if I've happened to go force times time, but they're interchangeable. Newton's second is equivalent to kilogram meters per second. Momentum can be expressed in either units and so can impulse. The law of conservation of momentum, the law of conservation of momentum, the total momentum of an isolated system of objects will remain constant. And you'll notice I didn't highlight that one because that's the fancy schmancy physics definition. Here's Mr. Dewick's. Well, not quite. You can write that down. We're going to do a better version over here in just a second. What have we traditionally used in physics as letters to represent before and after? I, yes, and not B. Okay. So you know what? Instead of that, a little less writing, except I want to somehow show that there's a total involved that we're going to be adding stuff together. There's a symbol that stands for it, the sum of, and it's this. This means total sum of. The total sum of the initial momentum has to work out to the same as the total sum of the final momentum. This is what we're going to start out writing on almost every momentum question. This is going to be our, hey, what's the first thing I'm going to do, free body diagram? This is going to be our equivalent for momentum. By the way, that's how I hand write it, a capital M on its side. It's actually a Greek letter, capital Sigma. And in type font, it actually looks like this. You can write that if you're one of those people who has to print exactly accurately, but most people, when they get lazy, it just becomes a capital M on its side because you're in a rush. Turn the page. Example four, we have a head-on car crash, boom, a truck runs into a car. If conditions are such that the car and truck end up at rest after the collision, how can we say that momentum hasn't been lost? First of all, momentum, we just defined it. Remember, momentum is what times what? Matt. So after the collision, looking at that diagram, what's our velocity? Zero. So what's our momentum after the collision? Zero. You know what that means? Because Emily, we said the amount of momentum before has to equal the amount of momentum after. And so the question I'm asking is, how the heck can I have zero momentum if the trucks and the car were moving? The answer is momentum is a vector. Momentum is a vector. This direction will be positive. This direction here will be. So let's look at that initial momentum. Momentum of the truck initial plus momentum of the car initial. Is that okay for abbreviations? And I'm going to be fussy because I want to reinforce the notation, Kara. I'm going to put the vector bar and the vector bar to remind myself, don't. You dare just add these like you did in energy. Direction, direction, direction, direction. We're going to have to now be careful with negatives and positives. We said that, let's write up here momentum is mass times velocity. So what's the mass of the truck times? What's the velocity of the truck plus? What's the mass of the car? What's the mass of the car plus what's the velocity of the car? Notice I did not say speed. I said velocity, so don't tell me 24. Emily, you're right. I think this ends up being no calculator necessary. I think this ends up being 24,000. Take away 24,000. Now I knew that my final momentum had to be zero because everything came to a stop, which I said Emily, because of the conservation of momentum law, means my initial momentum had to be zero. What was my mission momentum when I actually calculated? What is 24,000, take away 24,000? That's why this is true. So what was the question? It said if conditions are such that the car and truck end up at rest, which means the final momentum is zero, mass times velocity, mass times zero is zero. How can we say that momentum hasn't been lost? Because my initial momentum was zero and I just proved it. It was. And that's what's happening in any head-on collision. That's why if you have a smaller mass, you have to be going faster if you want to cancel out the other person's velocity. Football players. Where's my football players here? I have a couple of them. No one here played football? You played, yes? Running backs. Running backs. Small mass, usually. Big velocity, yes? So how can we stop them? Tell me your typical defensive linemen. Do they have a very big velocity? Can they get going very fast? So what do we do instead? Bigger mass. This collision here replaced the big numbers with masses of big offensive or defensive linemen. Small, fast moving running back. In fact, if I want to stop a running back easier and I'm playing NFL, I can get fatter as long as I can continue to move OK. If I can put on 20 extra pounds, that actually helps me be a better player. Helps me stop the guy easier. Helps me cancel out his momentum easier. The worst ones are the freaks. The occasional, if you watch NFL football, the occasional 6 foot 5, 240 pound running back. A guy who has a big mass and a big speed, those are the ones they don't enjoy. But usually those guys can only play three or four careers before their joints give out because your bodies weren't meant to handle that. I don't know if any of you are football fans. Anybody watch NFL? Any of you guys remember, this is dating me now. Any of you guys remember a player from about 15 years ago named Christian Acoya? His nickname was the Nigerian Nightmare. He only played at a high level for about four years and then he blew his knee because he was about 6 foot 4 and about 260 pounds and he would have run a 4,340. No one had ever seen anything like it. Ridiculously fast and big. He was a scat back running back who could also run through guys easily because he was that big. Terribly tough to stop. He ran for like 1800 yards a season for about four years, but your body wasn't ever meant to take that momentum. It's why offensive and defensive linemen are heavy. It's actually an asset, not because they're fat and lazy, it's because it makes them better at their position. The law of conservation and momentum can be written in several ways. Kayla, you can write it in English. Total momentum initial equals total momentum final. We're never going to do that. That's too much writing. If you have two objects, you could say the momentum of the first object initial plus the momentum of the second object initial equals the momentum of the first object final plus the momentum of the second object final. I will always start with this one here. The amount of momentum before equals the amount of momentum after. That's going to be my, hey, now the question is no longer blank approach. Or because momentum is mass times velocity, Jacob, you could say mass 1, velocity 1, mass 2, velocity 2 initial equals mass 1, velocity 1 final, mass 2, velocity 2 final, if you're looking at two masses. When do we use this? When there's a collision or an explosion. Example one, a rifle bullet of mass 0.06 leaves the muzzle with a velocity of 6 times 10 to the second meters per second. If the 3 kilogram rifle is held very loosely with what velocity will the rifle recoil? Is there a collision or an explosion? When you fire a rifle, that's a controlled explosion. So I'm going to ask again, is there a collision or an explosion? Yes. I'm going to write the sum of all the initial momentums equals the sum of all the final momentums. What two objects are mentioned in this question? How fast is the bullet traveling before we pull the trigger? How fast is the rifle traveling before we pull the trigger? So here's my question. What's my initial momentum at the beginning? You know what that means my final momentum is? It's going to be 0 except we're going to use the 0 on the left hand side and we're going to actually say this is going to be the momentum of the bullet final plus the momentum of the rifle final. D for bullet, R for rifle, is that okay? And we've defined momentum, what did we say momentum was? What times what? Okay, so this is going to be 0 equals the mass of the bullet times the velocity of the bullet final plus the mass of the rifle velocity of the rifle final. What's this question want me to find? Wants me to get this by itself. I think I would minus both of these over to the zero side and then divide by the mass of the rifle. Now stop, put a vector there, put a vector there. The only reason we're not doing trig is because a rifle and the bullet travel in a nice straight line, no angles. So I can use grade eight and grade nine algebra. Velocity of the rifle final is going to be negative mass of the bullet, velocity of the bullet final divided by mass of the rifle. Is that okay Connor? Let's plug in numbers. The final velocity of the rifle is going to be negative, what was the mass of the bullet, 0.06. What was the velocity of the bullet, 0.600 divided by, what was the, hello, hello. Let me hit a little pause here. So let's keep going, velocity was 0.600 and mass of the rifle was what, 3. So with what velocity will this rifle recoil, Mitch what'd you get? You're lucky you're wearing a tie, sorry what? Negative 12, yes, no. What's the negative telling us Mitchell? Opposite direction of the bullet, so now it does imply a direction, okay? Example two, football. What's the momentum of 112 kilogram football player running at 4.8 meters per second? This isn't asking for a change and this is just saying what's the momentum, okay? We've defined momentum, how do we define momentum today? Momentum is what? Mass times velocity. So mass is 112, velocity is 4.8. How much momentum does a football player, this particular football player who's running, how much momentum, how much quantity of motion, as Newton called it, does he possess? Sorry Brett, 538 units, kilogram meters per second. Is that a lot? Well we'll talk about that. We'll start to quantify some of this eventually so we can see what's a lot of momentum and what's a little bit of momentum. B, what impulse, impulse is another word for what? Change in momentum, okay? What change in momentum must a tackler impart to the football player and A to stop him? We don't need to do any calculations here. You know what the answer is? Why negative? Because it better be in the opposite direction, yeah? If you tackle him from behind and push him forwards, you're increasing his momentum. That's why in football games, when there's a short yardage pile up, you may see a player pushing the running back from behind, even though it's technically illegal, they all do it, right? And this is where that final impulse equation can be very, very handy because now we can quantify this into forces. If the tackle is completed in 1.2 seconds, which is probably high, a tackle doesn't take that long, but whatever, we're making up numbers here. What average force must the tackler have exerted on the other player? So now we're going to use our impulse equation. Our impulse equation said that impulse equals impulse. Change in momentum equals change in momentum. This one is on your formula sheet. Brandon, what's this question asked me to find? C, what's it asking me to find, kiddo? Oh, how do I get the force by itself? The average force is going to be the change in momentum divided by time. And you'll notice once again, we're getting sloppy Nicole, and we're dropping the delta in front of the time because time, by definition, is always a change in. But we put it in this equation to remind us it's a change in and a change in. Is that okay, Katie? What's the change in momentum? B divided by? How long did the collision last? 1.2. What average force did this tackler impart? Jacob? I missed that, sorry. 448 what? Negative 448 what? It's a force. It's a force. Yeah, we know it, right? Memorizing our units. By the way, if the time of collision got shorter, if this number got smaller, what would happen to this number here? That's why we like the big hits in football because they're short. Short big hit automatically means it better be a bigger force, otherwise it can't possibly cancel out his momentum. I mean, you could graze the guy for a short hit, but if it's not a big force, it's not going to stop his momentum. So this is the physics of tackling, this is the physics of body checks and hockey, physics of curling, physics of car crashes. In fact, I think on that note, we're going to...