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Conservation of momentum. It's not just a good idea, it's the law. [mumbling]

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All right, well it's important to have a healthy respect for the law. [cop in cop car]

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No kneeling around here and don't seed when you drive, don't litter and don't

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forget to tell your mom you love her. That's not a law, that's just you know being

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nice. Alright but the truth is, there are some laws that you just can't break. Like

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it's impossible, it can't be done. Try as hard as you want, it ain't gonna happen.

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Those are the laws of physics, not the NFL. And if you try to break one of those [two people in lab]

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physics laws, well you won't go to physics jail, or anything. But you might

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not be too happy with the result. Try and break the law of gravity, for example.

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I'll just watch from a safe distance. Well one of these laws of physics, is the

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law of conservation of momentum. This law states, that in a closed system, the total

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amount of momentum always stays the same. Now in the real world we don't run into

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a lot of closed systems. For example when you roll a bowling ball down the lane,

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the bowling balls momentum is transferred to the pins, or it's [bowling ball and bowling pins]

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transferred to the gutter. Yeah it happens. But when the ball hits the pins,

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pins don't just bounce around forever, maintaining their momentum, that gains

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momentum is transferred to the side walls and the lane and whatever the

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technical term is for the back of the lane. All of those surfaces deform

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slightly, as the momentum of the pins, is transferred. So the momentum goes to

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these other things, within the system. But the effect is so small, we can't see it.

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Of course, physics tends to look at ideal systems. And as we know from the fact [cop in cop car with Ferrari speeding by]

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that we still don't have our own Ferrari, well the real world is almost never

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ideal. But there's an equation, that expresses the conservation of momentum

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and it's this one right here. Well this is just fancy math way of saying, that

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the sum of all momenta, for all objects within a closed system, before the

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objects interact, equals the sum of momentum for the objects, after they [equation on note page]

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interact. And fortunately we can write it in a much simpler format. Yah, there

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we go. But really it doesn't matter, because when we start doing the math, for

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actual objects, actually interacting with each other. We replace both sides, of

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these equation,s with the numbers for the objects. So if we just so happened, to

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have someone, oh I don't know, sitting on a skateboard and then throwing a

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medicine ball to someone. Well our equation would look like this. This equation says

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that the initial momentum of the skateboarder, that's the P sub s I, plus [equation]

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the initial momentum of the medicine ball P sub B I, equals the final momentum

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of the skateboarder, plus the final momentum of the ball.

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And since momentum equals mass, times velocity. We can swap those variables

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into the equation, in place of P. So now we have this equation. Which says that,

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the skateboarders mass, times his initial velocity, plus the ball's mass, times its

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initial velocity, equals the skateboarders mass, times his final [formula]

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velocity, plus the ball's mass, times its final velocity. Looking at this you can

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see that if we have more than two objects, the equations can get a little

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long-winded. Which is why we use that shorter

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equation earlier. But let's go ahead and see how we would solve this equation. In

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our scenario, we have teenagers performing physics in public. There's

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nothing criminal in that, although it is a little weird. I've got my eye on you

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citizens. At the start of this experiment, the skateboarder and the ball are not in [two people throwing ball to each other]

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motion. Which means each initial velocity is a big fat zero. Let's put those values

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into our equation. Before we go any further, we can solve the left side of

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this thing right now. Whatever masses we're dealing with, are

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irrelevant. Anything times zero in California, equals zero. So the initial

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momentum of the skateboarder is zero, and the initial momentum of the medicine

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ball zero and zero plus zero equals, seventy three billion 360. Oh wait hold

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on, I spilled my coffee on my calculator earlier, it's on the fritz. [coffee on calculator]

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All right zero, plus zero, is zero. Got it? So we got zilch. That's right, right hand

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side will also have to evaluate to zero. That's only gonna happen if one of the

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momentum on the right hand side is negative. Well remember momentum is a

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vector quantity, so it has a magnitude and a direction.

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Well the convention, to have any motion from left to right be a positive, value in any

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motion from right to left be negative. Really doesn't matter though. You can set

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whichever direction you want is positive and the other as negative. Just make sure

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you're being consistent. The important thing to recognize here, is that we have [man throwing woman a ball while on skateboard]

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two masses acting in opposite directions. One will have a negative velocity and

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therefore have a negative momentum as well. So now we can set one velocity to

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be negative in our equation, or just make the overall momentum be negative, like

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this. And once we've done that we can see something interesting. With a bit of

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algebra, we can add the negative momentum, to each side of our equation and find

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that the final momentum for the skateboard, equals the final momentum for

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the medicine ball. See how everything balances out all nice and pretty and [long equation]

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laws of physics can be you know satisfying like that. Okay folks

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experiment over. Let's keep moving, nothing else here to see. In that

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skateboard experiment, we had two objects interacting and it was pretty friendly

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interaction. But alot of times interactions between objects are gonna take the form

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of, collisions. The collision can be a minor fender bender, or a five car pileup.[major car crash]

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And collisions can be elastic, or inelastic. An elastic collision, occurs

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when two objects collide and then bounce off each other going in different

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directions. Think of playing pool. When the cue ball, hits the eight ball, the

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balls don't just stick together, they go in different directions. Unless both

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balls are covered in syrup, which is why waffle Wednesdays and pool tables are

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not a good mix. An inelastic collision on the other hand, occurs when two objects

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collide and then stick together. Say you're riding a bike, when a possum [man riding bike with possum on his back]

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decides to hitch a ride. Well since conservation of momentum is

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the law and you and your bike have now gained mass, in the form of a probably

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dead marsupial. You'll therefore lose velocity. After all that's the only way

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that momentum would stay the same, with an increase in mass. Just be careful that

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this one looks kind of bitey, even if he is

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potentially dead. Alright well because these problems can get confusing fast,

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let's walk through the steps one by one, so we have a roadmap to solve them.

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Step one, identify all the objects that interact with each other. We have two [chalk board step, and biker with possum on back]

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objects that start off stuck together already, like the bike rider and his

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bicycle. We can usually consider those as one object. Step two, if there are objects

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moving in opposite directions, at any point, assign the velocity for one of the

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directions a positive value and the velocity of the opposite direction a

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negative value. Got that? Good. With our biker possum collision, all the velocity

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was in the same direction. But typically we use right as the positive direction.

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If you're feeling wild and rebellious, well go ahead and flip it around. [rebellious people]

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Alright step three, set our balanced momentum equation. It should look

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something like in this one. With mass and initial velocity for each object on the

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left side and mass and final velocity for each object on the right. If we have

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more than two objects interacting with each other, then we add the extra objects

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to both sides of the equation, there we go.

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Step four, if two objects stick together after a collision, we know the final

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velocity will be the same for both objects. That means we can simplify the

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right side of our equation, by adding up the masses of each object and [equation]

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multiplying that sum, by the final velocity. I'll save a little work that

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way. Alright, step 5, plug in whatever values we've been

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provided, or have found experimentally. Since we set up our equations in advance,

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it should be pretty straightforward. Just make sure not to mix up your masses

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and velocities. You don't want to multiply object ones mass and object

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twos velocity. I can't write you a ticket for that, but I can give you a [cop talking]

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stern look. So be careful. Alright step six, remember to make the velocities

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negative for whichever velocity direction, we've designated as our

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negative one. If you skip this step well your right side, won't balance with your

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left side. Which means the equation will crash and burn.

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Step 7, solve for our unknown variable. A lot to say on this one I trust that you

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have the requisite math skills under your belt. Alright, step eight, celebrate

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with a doughnut. Oh sure, cops and donuts are a cliche but [cops in donut shop]

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tell me you don't like, a nice fresh glaze and a circle of fried dough.

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Yeah that's what I thought. Alright one last thing before we look at some problems.

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All the motion we've looked at so far has been along one dimension. I'm not

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sure if you've looked around lately, but life is 3d. So although we're not going

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to deal with it right now, in the future you're likely to run across problems

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that deal with momenta, in two, three, or if supernatural forces are involved, five

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or six dimensions. Who knows? Which means we might have to use trigonometry to

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break the momentum down to XY and z components. We're just telling you now so[people freaking out in classroom]

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you don't freak out, in some of the advanced physics class later. Alright

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well we've got your attention. Let's talk about driving safely in dangerous

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conditions. Say we've got an icy road, three cars are driving, with car a in

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front, driving responsibly. Car B is making sure to keep an appropriate

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amount of space between her car and car A. Meanwhile some jerk, in car C,

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comes barreling in. Going way over the proper speed limit for the weather. Car

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C collides with car B and they stick together going forward, until car B hits [three vehicle car crash]

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car A. Now all three cars are conjoined at the bumper, headed in the same

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direction and we've got a big mess to straighten out.

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What's the conservation of momentum equation, for this scenario and we need

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to break it down to masses and velocities. Okay, so we know the shorthand

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equation, the sum of momentum before interaction, equals the sum of momenta

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after the interaction. But we could also write it like this, with P sub a P sub B

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and P sub C. But we need to break it down to masses and velocities. So let's work on the

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left side first. Makes sense, since it's the, you know, before side. We'll go step [equation formula]

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by step. We know our three objects are cars A, B

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and C. So we'll start with M sub a times, V sub AI and we'll add, M sub B, times V

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sub B I and last but not least we got the one that started it all, M sub C

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times V sub C I, aka jerk. All right, how about the right side. We definitely need

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to add up the masses of each car, but since they're all sliding along this icy

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low friction road together. We'll only have one velocity to deal with. [cars conjoined in crash]

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So the right side of the equation will be, M sub A, plus M sub B, plus M sub C and

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all of that will be multiplied by V sub F. Alright now we don't have any values

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here, we're just setting up the equation. Do we have any negative momentum to deal with? Well

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no, this wasn't a head-on collision. All the cars we're moving in the same

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direction, so we don't need to worry about anything negative there. Here's how

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we want our equation to be, before we plug in any values, right there. Okay,

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let's think about another scenario. And say we've got two ice skating kangaroos. [kangaroos ice skating]

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Which may sound crazy to you, but I've seen some things in this line of work

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man. Yeah, I've seen some things. Anywho, well they're working on their ice

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dancing routine and at one part of the routine they come together on the ice,

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standing motionless, facing each other. It's really a beautiful, marsupial moment.

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Then they push off, going in opposite directions. You can hear the music

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crescendoing, kangaroo one has a mass of 102 kilograms,

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slides away with the velocity of 2.1 meters a second. Kangaroo two who we're

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gonna call kanga two. Because well it just sounds cooler, has a mass of 109 [2 kangaroos ice skating]

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kilograms. What's kanga two's velocity as he gracefully

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slides away? Well let's walk through this thing step by step. First we identify our

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objects. Easy enough, we've got kanga 1 and kanga two step 2. If we have

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motion in opposite directions, we set one is positive, the other is negative. In

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this case kanga one's velocity has already said is positive 2.1

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meters a second. So kanga 2 will be negative velocity and momentum. Next we

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set up our before-and-after equation. Sum of moment of each kangaroo, before they

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push off each other, equals the sum of momenta, after they push off each other. [kangaroo formula]

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All right, step four says, if two objects stick together after their interaction,

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we add up their masses and multiply that by the final velocity. But in this case

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we have two animals that start off together, then move apart. So we can

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add up their masses and multiply that, by the initial velocity. Okay, so now we've

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got our equation set up. Step five says, we can start putting in the numbers. All [equation written out]

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right on the left side, we've got one hundred two kilograms, plus hundred nine

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kilograms and an initial velocity of nada.

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On the right we've got a mass of 102 kilograms, times velocity of 2.1 meters a

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second, plus a mass of 109 kilograms, times velocity were solving for. What

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is that number? All right, right away we can see the left side is going to equal

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zero and we can do that math on kanga one, to find a momentum of two hundred

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fourteen point two kilogram meters per second. Then we can subtract kanga two's

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momentum, the mass, times the unknown velocity there, from both sides of the [equation worked out]

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equation. Leaving us with negative 109 kilograms, times V sub 2f, equaling two

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hundred fourteen point two kilogram meters per second. And now people all we

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have to do is, divide each side by negative 109 kilograms, to solve for the

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missing velocity. And Kenga two's velocity equals about negative 2.0 kilogram

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meters a second. Which makes sense kanga two has a smidge more mass, than kanga one

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so his velocity should be a smidge less. Truth is you can break most laws. I might [cop in cop car]

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not see you speed on the highway and if you're super careful, jaywalking isn't

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gonna be a big deal most of the time. And your mom might say you get away with

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murder, but that's just a figure of speech. Please don't take her literally.

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But yeah you're not breaking the law of conservation of momentum. Don't even

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bother trying. All right if the Isaac Newton and Rene Descartes

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say it's law, well you better take their word for it. [court room with people in it]

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