 So getting organized finding your stuff now. I'll take questions on this lesson to more or next class as well Because I have a feeling some of you are like Number 12 sure. What was number 12? Oh Is it easier to? Hit a home run off of the fast pitch or off of a slow pitch And then it says using principles of physics and And apparently I chopped off the final few words I go supposed to say using principles of physics right to explain your answer Well, what do you think is it easier to hit a home run after a fast pitch or a slow pitch any baseball players know for a fact? Which one? Yeah Why fast pitch? Sorry Can't remember what they put they probably don't go into the details in baseball. They Mmm, you watch like a science thing. I guess I would answer first of all In with a fast pitch the ball has more kinetic energy And that kinetic energy has got to go somewhere if the bat comes to a stop or nearly to a stop if the bat Where does its kinetic energy go into the ball? So it doesn't absorb much kinetic energy from the ball and also in terms of momentum I think if you write out a nice momentum equation, you'll find that time is shorter when we write input I would probably approach it something like this The change in momentum is also equal to the force times the change in time Okay, and I think the shorter the change in time The bigger the force that would be applied to the ball if I divide by Change in time over to the side smaller it is and I think with a fast pitch. It's a shorter impact speed impact time That's one way to answer it. I don't know. I'll come up with a better one You caught me off guard. Actually, I can't come up with a great little formula right now. It is a fast pitch There's a good thinking question. Any others Jeanette or anybody? Believe it or not today. We're finishing off the unit Really? Oh, yeah. Yeah I didn't report sure. Okay The two kilogram mass below starts at rest I would probably in my mind or even physically Nicole Underline at rest. That's always an important one to me and slides down the frictionless ramp. Good. No friction It then hits and sticks to a collision and They fly off the table find the horizontal distance traveled before hitting the ground Okay, is There a change in height So what I would my first would be to use this kinetic energy initial plus potential energy initial Equals kinetic energy final plus potential energy final because what I'd like to know is how fast is this traveling at the bottom of the hill? Oh Wonder fleet my initial kinetic is zero because it says at rest and for the purposes of math I'm gonna let the ground be two meters high. I'm gonna let this be the ground not this I'm gonna let this be the ground which means I could do that Would you are you able to find how fast it's traveling at the bottom of the hill? You can handle that. Okay. Okay. That'd be my first step. I'm gonna run out of room So I'm gonna kind of just tell you the steps and let you try it my second step once it's right there There's going to be a collision Did I say collision momentum? Okay? Before the collision what's moving mass one mass two or both mass one after the collision what's moving mass one mass two or both Stuck together or separate? How do you know because the word together would okay? Fancy what was the fancy word for a collision where they stuck together? Do you remember? Inelastic there's elastic and inelastic any last it means they stuck together Could you use this then to find out how fast they're traveling when they get right to there the final velocity after the collision? Yes, okay, then step three is going to be what you've really just found is vx That's gonna tell you the horizontal velocity and what they want you to find is the range Which is DX and we said from our projectiles unit DX equals VXT Plus a half AT oh no no horizontally there was no acceleration. Is that okay so far? Do I know vx? Well this to this would get me to there Do I know T nope not yet ah What's the vertical height that it's dropping? Two meters what's its initial vertical velocity? Now give you a hint. What's the vertical height that it's dropping? What's its initial vertical velocity? zero and You know distances to and you know a is negative 9.8. I Think you can find T. You know how long it's going to take it to fall two meters Let's see. I would use D equals a half AT squared VIT is going to cancel because VI is zero vertically and this is vertical vertical vertical and this is vertical vertical vertical and you Can solve for T and then that T It's gonna go right there. That's a tough question I don't know if I'm gonna give you one quite that multi-layered I would feel comfortable with this as the nasty multiple choice to marker I would not feel comfortable with this as here's a nasty seven mark written question Although I like it It's a nice combination of almost everything except friction. I think it's the only thing that doesn't show up in here Is that all right? That's why I signed that one. I thought that was good putting everything together Okay, as I was saying We're actually gonna finish off the unit today. I'll have a take home quiz for you Next class I think I'm thinking right now your test is I can either do it a week from today Tuesday or Thursday of next week just means I'd start the next unit Tuesday of next week Thursday of next week Okay, so your test is going to be a week from Thursday Is that work someone is actually looking at their agenda which makes more sense to me because they're checking to see Okay, okay I'll do a tutorial Excuse me, I'll do a tutorial next week Monday or Wednesday after school. I don't know which yet. I'll let you guys know Thursday We'll take a boat and see who can make the most of them. So basketball players That's your little warning as well Okay, all we're going to be doing today is just fine-tuning and looking at tough weird questions now I'm mostly going to be looking at challenging difficult questions today You don't need to go is that the test all out? No, some of the stuff will be in a nice straight line on the test But physics 12 is the two-dimensional world. So we are going to look at collisions with angles example one a 10 kilogram curling stone is sliding across the ice when it hits a stationary 18 kilogram bucket of sand After the collision the curling stones velocity is three meters per second due east and The bucket has a velocity of 2.3 meters per second at 43 degrees south of east What was the initial velocity magnitude and direction of the curling stone before the collision? So I like this question. I like this question. You're going to have one like this Can you first of all see that there is a collision that means Andrew momentum? Is this in a nice straight line or by reading the question do you get the feeling this is going to be angles and stuff? I see 43 degrees and in fact that I see east I think over here I'm going to do my standard compass rows to make sure I don't do a dumb mistake along the way Is there a collision Emily? Say yes, because I already asked that question about 30 seconds ago. You back with me now Okay, so I'm going to say this If there's a collision the sum of all the initial momentum has to equal the sum of all the final momentum Now on your test, I will probably give you a picture, but I'm deliberately not here to just ramp it up a level We're going to see if we can puzzle out the adult the picture or ourselves Before the collision What's moving mass one mass two or both? Yeah, so I'm going to go momentum of object one initial There's my collision After the collision, what's moving mass one mass two or both? Both stuck together or separate separate so momentum of object one final plus momentum of object two Final where these in a nice straight line. Can I go straight to doing cross multiplying and algebra and stuff like that? Or were these in angles? Angles then I'm going to dull Okay Let's see what I do know here. Here's my picture Do I know the initial direction of mass one? No, that's what they're asked me to find so I'm going to leave this side blank for a second Do I know the final direction of mass one? Yeah east and I can even tell you how long this arrow is because momentum is conserved What was the final momentum of mass one if you go mass times? velocity How big is this arrow? Well, it's going to be ten Times what's the final velocity? Three okay, this arrow is going to be 30 kilogram meters per second Do I know the direction of mass to the bucket? Yeah, let's be really really careful. It says 43 degrees Connor what of what? Okay Here's east. I'm going to go south of east 43 degrees How big is this arrow? Well, what's the momentum of bucket two of the bucket of mass two if you go mass times velocity? It's going to be eighteen times two point three and Give it to me to the full a number of sig figs not rounding off Matt 41.4 Caitlin, what's this right here underneath my little roving dot? What's that right there? It's meant to be really really obvious. How do I add vectors? Draw them tip to tail even though. I don't know what this looks like I'm going to add these two together tip to tail I'm going to do it up here because I have room and I'm trying hard to keep this all in one page, okay? So it's going to look like this 30 plus little longer 41.4 Where this angle here was 43 Can you see what mass one's initial velocity muscle? Sorry momentum must look like it must be There's my from the tail of the first to the tip of the second vector Here is momentum of object one initial Mitchell, is there a nice right angle in this triangle? Okay. Oh, and I got a real problem I don't have any angle in this triangle. What did you just do on your calculator? Yeah, did you a 180 minus 43? What'd you get? How big is this angle right here? 137 okay now I can do this and it's going to be cosine law well Right so far so good What was the cosine law it was going to be? Momentum of object one initial squared equals it's these two squared minus two times these two coasts 30 squared plus 41.4 squared minus two 30 41.4 Cosine of 137 What's the magnitude of the initial momentum of object one? 30 squared Plus 41.4 squared minus two times 30 times 41.4 Cosine of 137 square root don't forget to square root I Get the initial momentum 66.563 I'll again carry some extra sig figs because this is nowhere near my final answer But my question wasn't asking me for the final momentum You know what was the question asking me to find? Velocity if I know momentum, how can I always find velocity if I know momentum nice and loud you're right But by mass right momentum is mass times velocity and since mass is a scalar I don't need to do any fancy fancy triggering I can go now Velocity of one initial is going to be 66.563 divided by M1 which I think was Ten yes, I scrolled down it was ten wouldn't it? Yeah, I knew that in my head six point six Six meters per second, and I'm done or am I have I found the velocity? No, I found the speed I Found the magnitude, but what does it say next to the words velocity in brackets? What does it say in the original question Jacob? Direction more trig All right go back to my diagram. I'll put a little at oh It's going to be That angle right there because that's where my initial vector is starting from oh by the way That's going to be what of what? That's south of east. I'll leave a little space and put that Now I need the angle can I use so katoa here Andrew? No, right angle. It's going to be a sign law. It's going to be the sign of this guy over What's across it's going to be the sign of the mystery angle over 41.4 equals? The sign of the angle that we do know a hundred and thirty seven over Don't I don't oh yeah, I do know momentum one initial 66.566 63 How will I solve this fret? Cross multiply that's going to get sine theta by itself. I'll get a decimal once I finish cross multiplying I'll go second function sign to find the angle fact. I'm going to get this Sign theta equals 41.4 sign of 137 all over 66.563 41.4 times the sign Of 137 all over hey, I have this answer still on my calculator. That's convenient and then I'm going to go second function sign of that and I get almost exactly 25 degrees Okay To me that's fair game on a test probably with a picture Although we handled it okay example to Try example two on your own Both masses are identical that Kind of nice Remember we said the word obliquely. That's a fancy word for at an angle So I'm going to press pause on the video here That little part B. I'm gonna add a little part B right Here B What was the change in kinetic energy Or if I wanted to phrase this differently I could say Emily how much energy was lost to heat because whatever kinetic energy is vanished had to go somewhere Remember I collided those those two chrome spheres together. We actually have enough heat to burn paper in the end We've got to go somewhere Kinetic energy is not conserved Total energy is conserved Which is why I put that note there and I should have put it at the very bottom of the page So but anyways kinetic energy is only conserved in the fancy collision that we called perfectly elastic So what was the change in kinetic energy? Well What's changing anything? Let's find kinetic energy initial kinetic energy initial Before the collision what was moving mass one mass two or both? Because kinetic energy is the energy of motion Jacob before the collision was moving mass one mass two or both Okay, it's gonna be a half m1 v1 squared. That's how much energy there was before this collision 0.5 times five times 0.8 squared How much energy was there before this collision? How much energy was there before this collision Emily? Half mv squared. Yes Did you type it in? That's what I'm kind of working you get the calculator right there Yeah 1.6 Joules of energy after the collision What was moving mass one mass two or both? Well, okay, so they each have kinetic energy so kinetic energy final is going to be a half M1 that v final squared plus a half m2 v final to squared Because they each have different velocities But you'll notice energy is a scalar. I'm not pulling out the heavy-duty trigger That's why we like energy so much more than momentum is it's easier on the math The final amount of kinetic energy is going to be 0.5 Times mass one which was five times. What was the final velocity of mass one? mass a point four squared plus point five mass two was also five and its final velocity was 0.6 Squared how much kinetic energy was there after the collision do you get one point three? Yeah 1.3 Joules so the change in change anything it's final minus initial 1.3 minus 1.6 we lost Three joules of a point three joules of kinetic energy where that energy go heat Some heat was generated by this collision if you ever find that your initial and your final match Then you know it was that magical perfectly elastic that only happens theoretically turn the page So example three is very similar to example two I'm gonna I'm gonna skip example three, but that if you want extra practice There's one for you to try and compare with what your friends got. We're gonna go to example four example four a metal disc explodes boom Into three pieces Which fly off on the same geometric plane got your breath you awake now The first piece has a massive two point four and it flies off north at ten second piece has a mass of two point Sorry to and it flies east at twelve point five What is the speed and direction of the third piece which has a mass of one point four kilograms? Well, I'm seeing compasses and directions so the first thing I'm gonna do Jacob is this Joel was there a collision? No, was there an explosion? So there was a gun. I'm gonna use momentum. I'm gonna start out by saying Some of all the initial equals the sum of all the final before the explosion. What was my momentum? It's a trick question before the explosion. What was the momentum? Brett zero So after the explosion, what does my momentum have to be? Accept did my masses stick together or stay apart? What's moving mass one mass two mass three or all of them? So it's gonna be zero equals mass one a momentum one momentum two and Momentum three. Are they in a nice straight line or are they at angles? dull Draw a little picture So momentum of the first guy says flies off north so it's gonna look like this and if I go mass times velocity I can do that in my head 24 plus Momentum of the second guy it says it flies off east And if I go mass times velocity, I'm gonna get 25 Plus I don't know what that guy looks like. That's okay. Trevor. I got two momentum Momenta is actually the plural of momentum So I have two of them. How do I add them together? Oh? Let's draw that so it's gonna look like this 24 25 Now careful now Kayla. I am not gonna draw it this way That's incorrect Because the key thing that I know here Nicole is I know my final momentum my final momentum is actually going to be Zero what would zero look like zero would be coming back to where I started from Here is the momentum of the third guy. Oh and Joel what's right here? Ah Nice Which means I can use Pythagoras and Sokotoa Not only that if this was multiple choice Brett how big is this? Read it to me how big is this are those almost the same size? I'd be looking for an angle close to 45 I might even cheat and if there's only one angle in the 40s I just circle that answer and move on if I was pressed for time if this is multiple choice It's gonna be like 44 degrees. I'm betting or 46 degrees. I don't know Right so it's almost an Isosceles triangle. Anyways, let's find momentum of object three Momentum of object three squared is going to be 24 squared Plus 25 squared not cosine law. I'm using Pythagoras Bre what'd you get for the momentum of the third object? 34 Okay, so 34 point what what what that? Anybody else is that right seems right? That's the momentum how do I find the velocity? Okay, so velocity of the third guy is gonna be 34 point six five five four divided by 1.4 What'd you get and now give this one to me to three six big sorry? 24 point eight meters per second at and I think The angle that we're going to be finding here is Always the tail of where we're starting from right there Which Sean is gonna be what of what what's this one gonna be looking at our compass rose? Yep south of It's going this way Isn't it? I think it isn't south of west. I think it's south of west. Don't you don't look at the black arrow You look at where the red area. I know the black here. I was going east. I don't care It's it's I'm going south of west ahead in that direction. Yes. Yes. Yes. Let's add that over here s W. Oh, and this is so katoa. I can actually find the angle using Opposite a jist. Yeah, I can find the angle using tangent. Oh Tangent of the angle equals 24 Over 25 so there's gonna be an explosion on your test. I like it By the way, any of you have your inner nerd and I'm actually going to try and buy tickets Adam Savage and Jamie Heineman are coming to the Queen Elizabeth Theatre at the end of this month for two shows talking about mythbusters and answering questions from the audience So I'm gonna see if I can get tickets for me 43.8. Yes 43.8 degrees How much kinetic energy was there before this explosion? Zero how much after the explosion lots where'd it come from this would have this would be an energy coming from either chemical energy or some type of stored potential energy Example five We'll finish this one then we'll call that a unit. I won't do the nasty scholarship one today like to Kayla can you read to me the first three words of example five? No example five the first three words of example five. We've all turned the page now dear Sorry, what? Mr. Dewick like roller coasters. I Like this question. I like this question. I like this question I also like this because it's again. It's gonna combine energy and Momentum there's gonna be a change in the height somewhere in here And there's gonna be a collision somewhere in here And it's also not too nasty because I think everything's gonna be in a nice straight line So no heavy trick here Says a roller coaster with an initial velocity Vi of 8.6 rolls down a track with a height of 18 meters. It strikes a second identical roller coaster mass 1 equals mass 2 equals 250 kilograms and That second roller coaster has an initial velocity of 2.4. It's already moving The coasters stick together and continue up the next hill. How high can the roller coasters reach? If I were to do it would look something like this Here is mass 1 What's its velocity right now at the top of the hill? Joel, I think you said it. Oh Forever 8.6. Yeah Trevor how fast are we going at the bottom of the hill still 8.6? Really it's gonna go down the hill and not gain any speed whatsoever Let me ask that question again Trevor thinking carefully like a physics nerd How fast will be going at the bottom of the hill still 8.6? Can't possibly so we're gonna have to do some oh, and it's a change in height energy Calculation now we also have mass to mass 2 is sitting right here Trevor how fast is mass 2 going right now? 2.4 and I think what's gonna happen is mass 1 is gonna come along Wham they're gonna collide Which is going to change their speed and they're going to move off up the hill and we want to know How high up the hill can they reach together and? Based on this diagram now you see why I traditionally try and type or use diagrams that I do on a computer I think Jacob. This is a three-part question. I think we have change in height collision What do I use for collision? Look up Momentum and then change in height There's gonna be our three pronged approach. So I'm gonna call this situation a situation b Situations see just so we can be organized in our notes. You don't have to do it this way on your test You can just start but this way we know what the heck we did and in situation a we said It's gonna be energy kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final A is from here to here Kayla ready these zero Kayla Kayla look in the wrong place. Sorry Kayla ready zero Kara's was yeah, let's see is our initial velocity zero Okay, is our initial height zero? So both of those are not zero is our final speed at the bottom of the hill zero is our final height at the bottom of the Hill zero You know yay a half m v initial squared plus m g h initial equals a half m v Final squared. Oh, yeah, my mass is cancelled too. I'm trying to find the final Emily How would I get be final by itself times by two and then? Square roots I'm gonna go like this times by two right now yay those cancelled But it's gonna be a two right there. I think I'm gonna get this be final equals big square root of The initial squared plus two g h initial I can put that biggest square root 8.6 squared plus two times 9.8 times I think the initial height was 18 What's my final speed Trevor at the bottom of the hill? It's definitely gonna be bigger. Yes Plus two times nine point eight times 18 square root Y'all get twenty point six five eight one seven zero three Blah blah blah blah. I'll go twenty point six five eight that brings us to situation be Matt Bam the collision Did I say collision before the collision? What was moving mass one mass two or both? Mass one mass two or both And both this time. Okay, so I'm gonna write Momentum of object one initial Plus momentum of object two initial and they're not stuck together. So I have to list them separately After the collision what's moving mass one mass two or both? Both stuck together or separate any elastic? Caitlin is this collision in a nice straight line or are there yucky angles and junk in here? Ah So, you know what I'm gonna go not dull. I can go straight to MV MV MV and solve. It's gonna be mass one V one initial plus mass two V two initial equals mass one plus mass two V final and what I'm interested in is Asking how fast they move off together after the collision. I want the final is a how would I get B final by itself? Divide by what mass one mass to yep? By the way, since mass one and mass two are the same you could just write mm and probably some stuff cancels along the way whatever You're gonna get this mass one V one initial plus mass two V two initial all over mass one plus mass two mass one two hundred and fifty V one not eight point six twenty point six five eight mass two two hundred and fifty V two initial was two point four all over mass one plus mass two which is five hundred Good you on mr. Rediman Good you back now though Because I don't have to blow something up again to get your attention. I can what'd you get Brett? Eleven point five two nine one does anybody else agree with that? Yeah, no. Yeah, eleven Point five two nine one Which makes sense the faster one's gonna slow down the slower one's gonna speed up That's in the ballpark. I was hoping for an answer between two point four and twenty point six five eight that brings us to part C change in height energies are any of these zero Cara any of these is my initial speed at the bottom of the hill zero No, how high am I at the bottom of the hill? Oh That's nice Is my final speed at the top of the hill? Zero I think if we're asking how high can we go? I think at the top for a split second how fast we'll be going I agree, but my final height will be zero. This one actually simplifies quite nicely. I like this I'm gonna get this a half m v initial squared equals m g h Final now this mass is the mass of both of them. Oh wait a minute Doesn't matter because these two masses cancel as well Mitchell, I'm trying to find the final height. How would I get the final height by itself? Final height is going to be v initial squared divided by two g The two comes from the one half of the front. I'll put it to the bottom because that looks tidy your joke So if you still have the eleven point two nine one support five two nine one square it and divide by In brackets two times nine point eight or maybe by this time, you know that nine point eight times two is nineteen point six Because we've been doing it fairly on which get six point seven eight Anyway else six point seven eight Yeah Now the only risk here is don't round off along the way carry extra sig figs along the way because you're doing so many so much Squaring if you rounded this answer to twenty point seven I'm willing to bet you'd be way off by the time you got here. So it's seven eight. So he said Direction did they ask for velocity or did they ask for speed in the question? I don't height Scaler I like that question. I don't know because I somehow for some reason thought it was a speed There's my first mistake of the year Plenty more where that comes from Meet scholarship question, but I'm gonna pass What's your homework the entire unit review?