 That's a little weird. Oh well, I'll go with it for now, and I'll fix it later Here's where we left off. My colors look all weird. Oh well Says you're doing a spacewalk outside the space shuttle with no cable between you and the shuttle and your small Maneuvering rocket pack suddenly quits on you Oh, and you are stranded in space with nothing but a $50,000 camera in your hands What will you do to get back to the shuttle? Sorry Throw the camera which way throw camera away from Space shuttle Brett. I agree with you. Why can you tell me in terms of physics? What's your momentum right now floating in space? Zero what is your momentum then have to be afterwards still? Zero so if I give the camera a negative momentum that way and I know that my momentum has to be zero What will my momentum automatically have to become a positive momentum that way and I should have drawn these exactly the same lengths because to show that they exactly cancel each other out Now because I have a bigger mass than the camera my velocity will be slower But we're in outer space once I have any velocity Newton's first law says I'll keep going forever and ever and ever As long as I aim carefully I'll run into the space shuttle make take 20 minutes I'll get there. That's really how they maneuver in orbit They use some kind of a rocket system and the particles going out of the rocket have a negative momentum Must mean you have a positive momentum in the opposite direction. Oh Like example for a Rocket expels 1.2 times 10 to the third kilograms of gas each second and the gas leaves the rocket with a speed of That will the thrust produced by the rocket be sufficient to lift it if the force of gravity on the rocket is Okay This question has two parts first. Let's look at the momentum aspect of things. I want to find Where am I getting my thrust from? the engine and I think because I see a mass and I see a velocity and I do see a time. I'm gonna go Impulse equals impulse Change in momentum equals change in momentum Where this force here is The thrust of the rocket itself. Let's get the thrust by itself. I Think I'll get Force equals the change in momentum Divided by the change in time. How much time well the amount of time they give me is every single second So I think change in time Kayla is just gonna be one. She's gonna be nice And What's changing anything? This is gonna be final minus Initial now we defined momentum. We said that momentum was equal to mass times velocity So final momentum is MV final You know what I'm going to assume that the gas in the rocket starts out at rest and then gets thrust outwards I'm going to assume that the initial momentum of the gas is zero I think the thrust of the motor is going to be 1.2 times 10 to the third times Five times 10 to the fourth. This is how much Trust the rocket can put out. What do you get? Don't I'll rush for your calculators at once or anything 1.2 times five is 60 Six times 10 to the eight Someone check me No What do you get? Katelyn, what'd you get? She's to the seventh or to the eighth. I thought I think it's to the eighth, isn't it? Am I wrong? I could be wrong. I have no idea what you said. Sorry. Yeah, so count careful Is it really? I don't believe you guys really one Yeah, but it's 1.2 times five which is 60 which one two three four five six. Oh, this should do it because wrong Don't be too scared. I'm wrong occasionally Good gosh. I thought I'd get an extra hero in there my bad Now that's the thrust of the rocket. That's not what this question is asking. It's asking will we get liftoff? I guess I should say liftoff question mark You know I'm gonna do now now I'm gonna analyze the forces free-body diagram Here's the forces acting on my rocket. What are the forces acting on my rocket when it's sitting on the ground here? Get the obvious ones gravity down oh and it tells me the force of gravity and thrust It says that the force of gravity is 5.8 Times 10 to the seventh and we just calculated thrust was six times ten to the seventh Do we have enough thrust to get liftoff? Free do we? Yep, just barely Back to one sig fig. No To two sig figs Barely heck if I was bored I can even calculate the acceleration by going winner minus loser equals ma They didn't give me the mass, but they gave me mg so I can figure out the mass if I really wanted to Momentum is really useful in analyzing collisions Anytime there is a collision I Go to conservation of momentum. I'm gonna go to what we underlined or put a box around back here Example five a 3.2 kilogram cart traveling 1.2 meters per second collides. I'm gonna underline the word collides. That's my trigger With a stationary 1.8 kilogram cart and the two stick together. What's their common velocity after the collision? Trevor was there a collision? I'm gonna start out by saying The sum of all of the initial momentum has to equal the sum of all the final momentum Where the equal sign is the collision itself? Before the collision was the first cart moving did it have momentum? Before the collision was the first cart moving did it have momentum Brett? Before the collision was the second cart moving did it have momentum? So I could go plus momentum to initial, but that's zero after the collision did they stick together or come apart? Read the question We're gonna say then the momentum of Both final because they're stuck together we're gonna treat him as one big glob mass This is gonna become momentum. We said was what tons what? Shawn This is gonna be mass one v1 initial equals mass one plus mass two because they're sticking together V final are they in a nice straight line? Yep, so no trig and that no vector math If it said backwards or forwards Emily I would that one be pop forwards be positive and backwards be negative, but I think The common velocity v final because they're in a nice straight line is gonna be m1 v1 initial divided by m1 Plus m2 it's gonna be 3.2 times 3.2 divided by 3.2 plus 1.8 the final velocity that move off together is You get 0.768 meters per second What we're really saying is when you collide into with something you slow down Didn't work did it? Let's try that again This time let's try pausing the video so I'm not asking my computer They stick together and they move off at a common velocity Which is why we were able to say oh the momentum of both final example six a Railway car is coasting along the track at seven meters per second suddenly a load of coal is dumped into the car That's a collision essentially What's its new velocity? The sum of all the momentum initial equals the sum of all the momentum Final before the collision what was moving? What had momentum and that's really what we're asking Matt because once it was mass times velocity I'm really saying is a which one's removing their stationary we can ignore them. What was moving before the collision? I'll call that mass of the railway car initial I'll use a letter R for that Coal was not it was sitting in the case above the railway car They boom drop the coal in and they stick together So afterwards it's going to be the momentum of both final In fact, it's really the same question as we just did. It's going to be the mass of the railway car Velocity of the railway car initial and that's going to be mass of the railway car plus mass of the coal The final Joel does this question mention directions or angles or anything like that? No Joel do you have your actual notes from last day here? Were you here last day and? Would you like a copy to follow along would that help you the final? It's going to be mass of the railway car Velocity of the railway car Initial divided by the mass of the railway car plus the mass of the coal It's going to be 6,000 times 7 divided by 6,000 Plus 2,000 you get 5.25 Yeah, years per second car crashes Example 7 a Car traveling 33 meters per second Clyde's head on with a car traveling 22 meters per second In the opposite direction in the opposite direction If the cars stick together, what's the velocity of the wreckage? Immediately after impact. Is there a collision here Mitchell? Then first thing I'm going to do is I'm going to write the sum of all the momentum Initial has to equal the sum of all the momentum final Before the collision was the first car moving Yeah Mass of the first car sorry momentum of the first car plus was the second car moving before the collision Yeah momentum of the second car After the collision are they separate or did they stick together? So momentum of both Final momentum is what times what? mass of car 1 velocity of car 1 initial plus mass of car 2 velocity of car 2 initial Equals mass 1 plus mass 2 V final is that okay Kara if I want to find V final it looks like the final is going to be the mass of car 1 It's initial velocity Plus mass of car 2 It's initial velocity Divided by the mass of both cars Here we go say what's mass 1 you with me? No, where are you working other stuff? Okay, Mitchell what's math 1 what's math 1 sorry? 1200 What's velocity 1 Mitchell I? Agree What's mass 2 Mitchell careful now what's velocity 2 ah? It's gonna make a huge difference in our answer divided by Gee if this is multiple choice what I also have the positive 22 answer there for you to pick from yeah, sorry. Yeah divided by 1200 Plus 1800 what will these cars move off that by the way if I get a negative answer I know that the first car ends up getting moved backwards Because we let the first car be positive if I get a positive answer. I know the second car ended up getting moved backwards Yes, what'd you get oh? What'd you get Brett? zero zero Exactly zero Really what does that mean? What does that tell us? first of all What was the initial momentum of everything then before the collision? What was my initial momentum? Zero and I guess this is one of those fluke head-on collisions where boom they hit and they came to a stop It wasn't one of them winning and pushing the other car back or the other car winning and pushing the other car back And I've simplified this Jacob. We're having them hit also dead on no angles as well angles two dimensions Then we're gonna have to get into some heavy truth Yeah, zero a couple more. We're done. What impulse Nicole. What's impulse? What impulse must be imparted to a hundred and forty five gram baseball to change its velocity from 40 meters per second South to 50 meters per second north Okay Said impulse. I'll go straight to writing change in momentum I was changing anything Emily and momentum is what times what? Debris bail you out. It's okay. I know this is gonna be mass V final minus mass V initial What's the mass point one four five? Yes What's my final velocity? 50 minus What's my mass point one four five? What's my initial velocity and don't say 40 because it's not Caitlyn Negative 40 or I could have let the final be negative and the initial be positive But I'm telling you I have to let them be opposites what change in momentum if I want to Turn on a pitchers 40 meters per second pitch and send it out of the park at 50 meters per second What impulse do I need to give that baseball would you get Connor? I don't know where you were, but I don't think it was here Then Connor what the drool a little bit there? Jacob would you get 13.5 anyone else 13.05 So 13.1 13.1 what? Units well it's change in momentum. What was momentum Mitchell? It's mass times velocity and I told you they're talking about calling this an Einstein, but they haven't yet So we can't jump the gun For me there's no use. I thought you just said meters per second Okay Right mass times velocity is kilogram meters per second It's it's the longest unit that you'll always be writing this year in that they haven't shortened it to anything yet I'm always I'm waiting for it to happen I Would also accept a negative there if you would let this be positive a negative and this be positive That's fine. The negative would simply be telling you it's in the opposite direction that the ball was traveling at the beginning Be if the collision between the baseball and the bat lasted point one millisecond What force did the bat exert on the baseball? What they want me to find here Force What did I just find here? Connor what did I just find in part a I think I have an equation that has force and impulse in it. It looks like this Yes, Sean. How would I get the F by itself? Okay, let's do that The force is the impulse divided by the time We know the impulse now I'm not gonna write 13.1 was what was it exactly on your calculator 13.05 even? 13.05 even divided by and how much time is this it's one millisecond, which I'm pretty sure is point 001 Seconds if I recall How many newtons of force minimum what I need to be able to exert through the bat if I wanted to send this out of the park 13,000 so 1.31 times ten to the one two three fourth Units Kara we looked at a head-on collision in number seven where by a fluke the momentum's exactly canceled each other out usually it doesn't happen What about rending somebody? example nine a 2000 kilogram car is traveling at 15 meters per second and it reruns another car of mass 1,000 kilograms the second car was initially moving at six meters second in the same direction What's their common velocity if they stick together after the impact? Our vendor is there a collision? Yeah, then we're gonna go the sum of all the initial momentum's equal the sum of all the final momentum's Initially Nicole. I think we had car one moving and We had car two moving did they stick together or are they separate afterwards? Okay, if they were separate all I would do is I would write car one final car two final I'd have them separate big deal and I'd solve for whatever I needed to they stuck together momentum of both Momentum is what times what? Anyone momentum is what times what? It's mass times velocity. So this is gonna be 2000 Well, I'm sticking numbers in right away for a change something different seeing if I can Streamline this a little bit times 15 plus 1000 Times times what? Six or negative six which one? Why six? same direction Equals they stuck together. So the total mass is 2000 plus 1000 the final Now Connor I took a couple of shortcuts here I didn't actually write out the formula on a quiz or a test I probably write up the actual M1 V1 initial M2 V2 here We're in our homework or see how good we get because to get the V final by itself What am I gonna do Connor divide by 3,000 both masses? Let's see Get 12 Yeah, even the faster car slows down The slower car speeds up and because the slower car was lighter It speeds up more than the faster car which was heavier slowed down Make sense We're good Turn the page. I thought about doing this as a demonstration, but it's a messy one dropping eggs on the floor Two eggs are dropped from the same height H One hits the floor and breaks The second one lands in a pail of water and survives What's the main reason the second egg survives Well, let's look at this first of all What is both of their initial velocities? Are they both falling the same distance? Yeah Same height So what can you tell me about their final velocity just before impact whether it's ground or water? Okay, yes, I Think this means therefore they each go through the same impulse They both go through the same change of momentum Why does the egg survive that? If they both go through the same momentum, why does that same change of momentum? Why does the egg that lands in the pail survive shouldn't it also crack? Nicole for a candy talk to me my girl Is there an equation that has time and impulse in it? Okay What are you telling me then Nicole know what let's go like this floor water big time little force little time Big force Does that make sense the way I wrote that with just big and small letters that okay, I would never write that on a test I'd actually write out, you know Bigger force smaller times smaller force bigger time, but yeah the water lengthens the time of impact as a matter of fact That's why I bought if we can lengthen the time of collision We lower the force because we're stuck with by the way in any car crash You're all stuck with the same change of momentum in fact Anytime you come to a stop at a red light Haven't you gone from full velocity to zero velocity the exact same change of momentum that you would do in a head-on collision? Except we lengthen the time dramatically Dropping the force dramatically right here's a good Translating graph question. I told you you would start to see some of those So if we look at a graph of force versus time for the egg hitting the floor it'll probably look something like this Which of the following graphs a b or c? Would best represent the force time graph for the egg hitting the water? And it says the egg on the floor graph is shown as a dashed line for comparison purposes I don't did it appear on yours because it doesn't appear on my screen. Do you guys have a dotted lines on okay? So I think it would be something kind of like this Which of those do you think is the best? graph of dropping the egg from the same height in the water Emily see Convince me okay, so I agree I think the obvious wrong answer is that one because if the time of collision is the same amount you couldn't possibly lower the force I Notice both of these have roughly the same time of collision Okay What's this measuring? Of course, what's this measuring? Where does impulse appear on this graph? By the way What you should be trying right now is saying is it the slope try dividing the units or is it the area? Try multiplying the units where does impulse because that's that trick that I showed you in the last lesson of last unit I said when in doubt multiply or divide area Multiply or divide slope where does impulse appear here impulse Which is change in momentum? Isn't that the area because isn't force times time also impulse the impulse is That there so what you're really doing also Emily is kind of eyeballing How big is this area and I think it's about the same size as this area in fact if I draw a line like that down the middle I Can flip this right to there and kind of get that same shape. I think I think this is too much area I need numbers to be more specific Okay Explain your answer we just did Homework so number one now this homework is not due next class. This homework is your homework for Friday number two three four Skip six Number seven is a nice review for last unit So it's not officially homework in that it's the next unit But if you're looking for a good practice graph work question kinetic energy question for your test, that'd be a good one Number eight's a nice little tricky one one for you to think about So skip six basically got a little video to show you