 Number one says a 1,300 kilogram car is moving east at 30 meters per second And it collides with a 3,200 kilogram truck moving at 20 meter second direction 60 degrees north of east The vehicles interlock Stick together and move off together Find their velocity after the collision Did I just say the word collision Jacob then the first thing I'm going to do is I'm going to go The sum of all the initial momentum Equals the sum of all the final momentum The sum of all the initial momentum equals the sum of all the final momentum By the way, I sent an email out last night with this year's tutorial Which is only about 25 minutes because people didn't ask many questions But I also included a link to last year's which was about an hour and a half long and probably had a lot more questions So check the emails if you haven't already I see a compass mentioned so I'm going to do my traditional routine Now I'm going to read this question Am I going to be able to do this just mathematically by letting to the right be positive? It's the left be negative or is this one going to involve trig because angles are mentioned Angles are mentioned. Okay Before the collision what's moving The car the truck or both both So I'm going to have this Momentum of the car initial Plus momentum of the truck initial Equals bam there's a collision after the collision what's moving the car the truck or both? Both stuck together or separate stuck together as a picture. It's going to look like this car moving east How big well its momentum is mass times velocity I think 39,000. There's a plus sign Truck moving 60 degrees north of east There's east 60 degrees north of east How big is this arrow mass times velocity? 64,000 that equals the final momentum I'm not sure what that's going to look like Connor how do I add two vectors together tip to tail? Okay, so we're going to get this 39,000 64,000 I Think the resultant is that boy right there. I think this is going to be the momentum of both final and Let's see if this angle is 60 degrees. I think this angle here is 120 degrees Now I can bring out the famous cosine law In the interest of time I'm going to take a little shortcut here Thanks, what quiz version did I give you quiz to version two? Momentum quiz to version two answers. Let's bring it up So I did the cosine law 39,000 squared plus 64,000 squared Blah blah blah blah blah. I got a momentum of 90,072 divide by the mass of both To get a speed of 20 point zero that I need to find an angle the angle is right there sign of theta over 64,000 equals sign of 120 over 90,072 cross multiply shift sign 38 degrees north of east or you could also have 52 degrees east of north And I gave out the four marks I gave you one mark if I saw that one mark if you managed yet the momentum one mark for the velocity speed and one Mark for the direction to give it a velocity Test this photocopied. I think there's one written question like this One written question. That's an explosion And then there's one written question that involves both energy and momentum So there's a straight line collision and a change in height So like the ballistic pendulum or the roller coaster rolling down the hill and hitting or something like that number two Pendulum is hanging from a frictionless massless string that is 15 meters long the pendulum weighs 24 kilograms a point zero one five two point four kilograms a point zero one five kilogram bullet traveling at 300 meters per second hits the pendulum and it sticks what height well first of all is a collision momentum and It's a nice straight one line collision It's going to be the mass of the momentum of the bullet equals the momentum of the both of them afterwards mass of the bullet initial velocity of the bullet equals mass both the final The final velocity is going to be the mass of the bullet times the initial velocity of the bullet divided by the mass of both of them And I get a velocity of 2.36 meters per second Then we move to part two which involves Mitchell energies because there's a change in height The amount of kinetic plus the amount of potential initially has to equal the amount of kinetic plus the amount of potential at the end And wonderfully at the end you're stopped so your kinetic is gone Oh, and at the beginning you're on ground level so your potential initial is zero a Half MV initial squared equals gmgh finally a masses cancel You end up with the height equaling vi squared over 2g And you get a height of point two eight four Bonus suppose the pendulum only reaches a height of point one five How many joules of energy were lost to heat and sound so I said okay? I think I'm solving this using energies. I Said now is going to be kinetic initial plus potential initially was kinetic final potential final plus heat whatever I've lost Hey, that's still zero. Hey, that's still zero heat's going to be kinetic initial minus Potential final a half MV initial squared minus mgh final a half MV initial squared Minus mgh final and I got three point one eight joules of heat must have been Created question Connor Which one mass example three a 100 kilogram shell explodes boom into three fragments Fragment a weighs 40 kilograms and flies off at 32 meters per second At a direction 30 degrees north of East Fragment B weighs 25 kilograms and flies off at 48 meters per second In a direction due north Find the velocity of fragment C You'll have to use the sign the cosine law here I'm going to give you an explosion on your test, but it's going to be a nice right angled explosion so you can use so katoa Get the quiz right it So in this case in an explosion I said look my initial momentum was zero so this has to add to zero I'm going to have that momentum Plus that momentum plus whatever this is equals zero and when I say equals zero Sean in vector math What I really mean is draw a triangle that comes back to where it started from This plus this back here I did cosine law and I got a momentum of 21 48 Dividing by the mass and I was able to go 100 minus 40 minus 25 whatever mass left over is 35 I got a speed of 61.4 meters per second The really tricky part here is the angle. I'm not going to give you one quite this yucky but first of all I found theta right there because that's where I'm starting from Theta when I use the sign law ends up being 30 degrees, but that's not a useful angle for me because unfortunately For it to be a useful angle Let's go back to my drawing Theta ends up being 30, but what I really want is this angle here. Oh But wait a minute. I also knew that if that's 30 and this is 120 this also ends up being 30 degrees because I was able to go angles add to a triangle And I was able to say oh, it's a Z. This is also 30 degrees. Hey These two here add to 60 degrees. It wasn't exactly 60. It's almost an isosceles triangle, but quite There's like 60.4 or something like that I'm not going to give you one Caitlyn that yucky for angles. I'll give you one where it's nice silk atone But I'd rather have you find the test easier than the quiz. How many you got the angle there, okay? A couple of you. How many you got the velocity? Okay, like the 61.4. Okay, and number four And all they asked for was the magnitude of the initial velocity. I said, okay Before the collision. What's moving mass one after mass one and mass two draw a picture and it did say The initial velocity what didn't say it was due east so I knew I could draw that this plus this equals that This one was a little bit strange. I could actually because they gave me two angles I was able to say that's 48. That's 48. That's 38. That's 38 I was able to get all three angles in the triangle which meant you could have used cosine law You were fine in using cosine law if you wanted to but because you have a pair You could go straight to sin law, which is just cross multiplying and a bit easier 11.2. I didn't actually go over these I just showed you the answers because I kind of felt like people were doing the hang of getting a hang of this But I will stop now and say any of these ones that you're going. I have no idea what you do it Can you explain the steps better? I'm happy to Well, then add your scores up Out of count them 16 not 12 So I thought I was gonna get 15 out of 12 Out of 16 So the next unit unit 5 Circular motion MAGB quiet, please We're gonna start with a question the question we're gonna ask ourselves is this is it possible for an object to have a constant speed and Yet still be accelerating Yes, or no one convinced me can you have a constant speed and Still be accelerating who says no Connor Can you use calculus? Absolutely Sorry derivative of speed is accelerate derivative of velocity is acceleration. So you guys have by the way Nerdy aside who's in calc? Okay, so what's the derivative of distance? Velocity you learn. Yes. What's the derivative of velocity? Acceleration, what's the derivative of acceleration and you learned that yet rat a jerk Which makes sense the rate of change of acceleration is how hard you yank something. Oh, it's called a jerk What's the derivative of a jerk? so Calculus students Calculus students look up for a second If you have a distance function x You've learned that x prime is velocity quiet, please X double prime is acceleration You guys know what the fourth The fifth and the sixth derivatives of distance are called Physicists have a sense of humor. That's not completely official. That's it may become official, but it's sort of what they're called Answering your question sure Connor. Yeah, but I don't think you need to Can you have a constant speed and yet still be accelerating? I'm gonna tell you the answer is yes and Now I'm gonna say okay if I've told you the answer is yes Can you think of a way that you can be having a constant speed and yet still be accelerating? John then you wouldn't be at a constant speed Brett Brett what? You can because velocity is made up of two things. It's a vector. It has magnitude, but what else does it have? Direction so if the magnitude is not changing What can be changing the direction and acceleration? Nicole was defined as a change in velocity. We never said what that change was in physics 11 It was always a change in magnitude However in physics 12. We're saying. Oh, you know what you could yeah change in Direction, let me give you a great example right now. I Would argue is I'm spinning this around my head It's traveling at a pretty constant speed each time it goes around is taking about the same time. I'm pretty close But I can tell you it's accelerating you know why I feel a force on my hand and I know it has mass and forces mass times what? Force is mass times what? Acceleration or there wasn't acceleration. I wouldn't be feeling a force right Fact any time you're traveling in a circle you are accelerating What we're going to look at in circular motion is constant speed Circles not changing speed circles and so we're rarely Brandon going to look at this one because this one you Travel faster when you're going down and slower when you're traveling up We're not going to look at vertical circles very often Unless it's a static circle a fixed circle like a ferrous wheel that we can look at because that one doesn't speed up and slow down because it's It's not a string But absolutely you can be traveling in a constant speed and have a changing direction Therefore you have an acceleration in fact Brett. Did you figure that out or did you read ahead here and look at this? Because it says right here for an object moving at a constant speed in a circle what we call fancy word Uniform circular motion its velocity is changing because its direction is changing and If the velocity is changing the object must be accelerating because acceleration was defined as a change in velocity And we never said what was changing. We just said it's something had to be changing This is the most important fact to keep in mind about circular motion if you are moving in a circle You're accelerating oh And if you have a mass means of the force the question is what direction? Well to find the direction of the acceleration we have to do some vector subtraction We know this vf equals vi plus at yes Which gives a equals vf minus vi all over t now Brett t is a scalar But these two are vectors. This is where the vector direction for acceleration comes from this minus this How do I subtract two vectors together? It's a trick question. How do I subtract two vectors together? I don't what do I do instead Trevor? I? had the opposite Technical comment. We're also soon soon going to show that our acceleration is not constant because the acceleration is also changing direction That's okay We can find the direction by going this minus this because dividing by time won't change its direction So here is my time-lapse photography picture We're moving in a circle and At one point right here. I was traveling this way and then a split second later. I was traveling this way Let's subtract these two vectors So it's going to be the final minus the initial that's going to be the same as the final Plus negative the initial here's the final Now the initial was this way negative the initial Would be like that and we get our direction for acceleration Mitsu if you're moving in a circle, you know what direction you're accelerating towards the center See it in fact if I'd really done this with like a computer software program It would be pointing directly dead center if you're moving in a circle Katie You're accelerating towards the middle and that's very very counterintuitive for us that bugs us because most of us think When we're moving in a circle whether on a merry-go-round at a playground or in a car That's turning a corner or on the scrambler or music express rides at Playland We think we're accelerating outwards or not when you're moving in a circle You're accelerating inwards example three a Ball on a frictionless tabletop is rolled along a circular track track as seen below top view The track is not a complete circle. It's had a chunk cut out of it So the ball rolls this far and then when it gets to here It leaves the track. Which path does the ball follow after leaving the track a or b or c a? Path a due to the fact the ball has circular momentum Which keeps it moving in a circular path for a while after it leaves the track Path B since there is no force from the track so the ball should go in a straight line or Path C since when the track is no longer applying a force of the ball the ball will fly outwards Once again, we're going to vote once again. How high you hold your hand is how sure you are of the answer Who says path eight? One two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen Who says path B? One two three four Who says path C? Convince me that you're right or that someone else is wrong Let's replace the track with a string this If I cut the string so let's freeze frame it imagine we freeze frame it with this right here And I were to cut the string Would these keep going in a circle around my head? No, Katie. Which way would they travel? They'd hit Brandon Square on the head or if I cut the string when it was right here Mitsu they hit you in the head or Emory they Don't want to keep going in a circle. You have to apply a force to move them in a circle So if these wouldn't keep going in a circle when I cut a string Does that help you revise your answer what you think might be the correct answer for this track a or B or C? Knows you that voted a is a very common misconception. First of all Here's the ball right here Top view what are the forces on it get the obvious ones? Gravity would be going into the page There will be a normal force out of the page. Those would cancel each other out. Is there friction? Okay, are there any other forces acting on it? Emily if there's no other forces acting on it, how can it change direction? How can it accelerate? It would have to keep going Newton's first in a straight line at a constant speed B The problem is this The problem is most of you your experience with circular motion is going around a corner quickly in a car So why is it that the acceleration is inwards when the push that we experience in the car seems to be outwards? The answer is the push is actually an inertial effect. It's your mass When we are turning in the car the friction with the road turns the car and The friction with the seat turns our lower body, but our head which initially has no forces acting on it Wants to keep going in a nice straight line and You have to then exert a force using your neck on your upper torso and head to get it to move to the center But you don't realize that you think you're getting pushed outwards and you're creating a force reacting to that push outwards you think you're not You want to keep going in a straight line and the car is moving out from underneath you So you've got to push inwards to match the car which is moving inwards. That makes sense Not the way we feel it, but that's what's going on Also, you may remember I've said to you a few times our bodies are backwards accelerometers If you're ever on a ride or in a car whatever way you feel like you're being pushed I guarantee you the acceleration is in the opposite direction. How many been on the elevator before? Okay When it launches you upwards Which way does your stomach feel like it's going? Downwards, but which way are you clearly accelerating? Upwards when it goes downwards, which way do you feel like you're going to fly? Upwards effect you're but you're clearly accelerating downwards our bodies are backwards accelerometers when you're in a car and you come to a stop Which way do you feel like you're getting pushed when you come to a stop? Forwards, but which way are you clearly accelerating when you come to a stop? I gotta be accelerating backwards, right? So when in doubt go with the opposite of which way you feel that comes in handy when we go to playland in a couple of months so From the point of view of the driver inside the car this straight line motion seems to be outwards towards the passenger side door in Fact I think I told a number of you back in the 1950s ask your grandparents about that's your grandfather about this Back when they had bench seats and No seat belts You're going on a date with your lady What you would do is you would take surfers wax and you would wax the passenger seat and then you would sit like this and You would take a very quick right corner and she would come sliding across the seat into your arm and you oh hi honey How are you doing? Now that's not what was happening in actual fact She was continuing going in a nice straight line and you were turning the car underneath her But because your frame of reference was the car you didn't realize that ask your grandparents I've had I've said this told the story a few times now and almost every year I've had someone come back and my grandfather actually admitted to doing that Okay, the reason this is important is Because of bad physics It's because of at least 16 of you Here is the bad physics this discussion is important because many years of experience in a car lead most students to believe that there is an Outwards force in fact people even gave it a name. They talk about Centrifugal force with an F centrifugal force and centrifugal force is not a force at all. It's inertia Which refers to this apparent outwards push. There's even machines called centrifuges which use this force. It's not a force It's inertia. I Hope you'll agree with me Brandon a bird's-eye view confirms that the outwards push is not outwards But actually in a straight line and not a force It's just your mass wanting to keep going if Newton's first law your mass wants to keep going in a straight line at a state speed Furthermore our vector analysis done previously shows us that the acceleration and therefore the force are actually inwards When you're moving in a circle your net force is towards the center You can take that to the bank every time how many you've gone a little playground merry-go-round Okay, which way do you feel like you're about to get pushed when the merry-go-round goes fast? I've just told you your bodies are backwards accelerometers Which way are you actually accelerating them in inwards and in fact It's your mass wanting to keep going in a straight line when you lean out and hold the bar You're actually having to exert the force inwards because you're having to pull with your arms to keep yourself from flying off into space And it's not that there's a force pushing you out. It's you're having to create the force to push you inwards example for If fighter pilots move too fast into a loop they can become unconscious due to a lack of blood flow to the brain Sometimes this is called centrifugal force. They say that the blood has rushed to their feet That is not correct. So here's your Luke. Here's your pilot sitting Okay, there's my stick figure diagram. It's about as good as you're gonna get Brett live with it Which way does his blood want to keep going? What does Newton's first law say his blood wants to keep going in a nice straight? What nice straight line The plane applies a force in this direction, but his blood wants to keep going in a nice straight line And because it's liquid it can somewhat keep going in a nice straight line so that when he gets to here Even though we say the blood has pooled in his legs What's really happened is the blood has stayed where it wants to his body has moved up away from his blood If I'm really gonna be technical his brain has moved away from his blood and that's why he's blacking out in World War two and I need to double check this I've tried to double check the story my physics prof told me this World War two in the Battle of Britain There was a pilot who crashed and he lost both of his legs below the knee But there was such a shortage of pilots and because he was healthy otherwise and they were desperate They rigged up a plane they put longer pedals on it because he was still able to fly his hands were fine And he would go and he would fly and what he would do is he would get the German pilots to file fuck come right behind him He would dive down and pull up sharply But because he had no legs more of the blood would stay in his break Sorry because he had no legs There was less room for the blood to keep going in a straight line more of it would stay in his brain And so of course pilots all having a huge ego the German pilot would say well He could do it I can follow them because there's no reason why I would black out if he didn't black out And the pilots would follow him into the dive. He would pull up. They would black out and they would crash And in fact it reached the point where the pilots have memorized what his plane looked like and what his number was and they would Radio each other don't follow them into that dive. We don't know what's going on here, but he can do something We can't it's why fighter pilots can't be tall But you know who makes the best fighter pilots females Because females on average are shorter It's why fighter pilots also though wear those G suits if you ever watch a pilot when they're taking huge G's when they're doing a Loop what they're doing is they're tightening every muscle in their abdomen and in their legs because by tightening the muscles You're constricting the blood vessels. They're trying to push or prevent the blood from pooling in their legs Okay, shorter you are the easier it is and the the fighter pilots have suits that are designed when the G forces increase They actually have inflatable cuffs like a tourniquet that inflates and cuts off the blood flow to your lower body Forcing the blood to stay up here. There's a reason if you ever see fighter pilots either on TV or an interview None of them are in bad shape You can't be fat and out of shape because if you're fat and out of shape There's too much room for the blood to go down here and you'll black out. So how can we calculate circular acceleration? To be honest, the proof is a bit long. I'm just gonna give it to you. What letter do we use for acceleration? To show that it's centripetal or circular acceleration. I put a little subscripted C Well, and it's not a vector equation. It's a scalar equation. I know the direction. You know what the direction is towards center and It's equal to Your circular velocity squared divided by the radius V squared over R, but I want to distinguish that V to say oh, it's It's the speed connor that I'm traveling in this circle. However fast I'm going Kara the next logical question is okay, mr. Do it. I'm pretty sure I know what R is radius How do I find circular velocity? Well Velocity is distance over time If we're going at a constant velocity and we did say we're going at a constant velocity because we said our acceleration Is due to the inwards motion, but we're not changing the velocity What's the distance around a circle math 12 who did radians yesterday may remember? What's the equation for the distance around a circle the circumference? Okay? Circular velocity is too high R And we have a symbol if you go once around the time that it takes you to go once around is Capital T. It's called the period Does somebody have a formula sheet handy in front of them Brett you do is this on the formula sheet Can you look for me under circular motion and gravitation? No, no, no Is Vc is velocity on the formula sheet? No, this you need to know But I just showed you how you can derive it This is on the formula sheet V squared over R and yes, I know there's another expression that we're gonna look at in a second Where the speed here is the circular speed. Hey, um, what if I plug this Into there I get this That's V squared over R still I'm not gonna bore you with the algebra. Well, some of this we can get what's two squared What's two squared? What's pi squared just plain old pi squared? What's R squared? Well, how many Rs are on top? To how many Rs are on the bottom? One you're gonna have one R left behind and a T on the bottom This is your second equation for circular acceleration. There are two equations Kara V squared over R or two pi squared R over T squared When do we use mr. Doek? I use this one if I know how fast we're traveling I use this one if I know how long it took to go around once Yes, thank you Kara fix that T squared. Good gosh For pi squared R over T squared. These are the two equations that are on your formula sheet I've got a bit of a problem What letter is that right there Matt? What letter is that right there if I wanted to turn acceleration into a force What do I have to multiply an a by to turn an acceleration into a force? Mass, you know what the most common mistake is because these equations are so complicated kids have F equals 4 pi squared R over No, that's F equals a what have they forgotten they've forgotten to put an M in front of it So that's one thing we'll talk about and I'll yell at you That's one of the common mistakes kids think this is a force notes acceleration to change it into a force better Put an M in front of it By the way a concept closely related to period is the frequency We define the frequency is the number of cycles per second The unit cycle per second is also known as one Hertz For what it's worth Period is how many seconds to go around once? Frequency is to go around once and how many seconds they're reciprocals of each other Period is one over the frequency Frequency is one over the period example six an Object is moving at four meters per second in uniform circular motion Can you all right now underline the phrase uniform circular motion? It accelerates at two meters per second squared for three seconds find a the final speed d the distance travel a a V final is four point zero meters per second No, mr. Deweyck. That's v initial notes v final But mr. Deweyck, there's an acceleration. What direction is the acceleration if we're moving in a circle toward the center What did we say uniform circular motion meant stay on this page? We defined uniform circular motion as So there was an acceleration, but Brianna that was to throw you well No, it wasn't to throw you off that it was to tell you that you're moving in a circle and you're accelerating towards the center But your speed is not changing Your speed is not changing You'll notice I left the vector off the direction is changing in fact You know what your direction your speed is always it's always perpendicular to the radius Your speed right now is that way your speed right there is that way your speed right there is that way your speed right there Is that way it's always traveling oh? I can use a math 11 word tangent to the radius remember your tangent lines and all that from math 11 B asks for the distance traveled D equals Vt Mr. Deweyck, what about plus a half at squared? The a is towards the center. It's not in the same direction of the speeds. I cannot use them in the same expression The distance traveled is going to be four times three It's going to have traveled Exactly 12 meters in a circle. I'm looking at this here, and I think I meant to put it in This box here it says since ac equals v squared over r and vc equals 2 pi r over t We can substitute vc into a and we get ac equals 4 pi squared r over t squared where t is the period that's the time to go once around and r is The radius it's okay to write it twice Technical comment in uniform circular motion of this range situation The object is moving at a constant speed, but it's also accelerated Because direction is changing The acceleration direction is changing all the time right now the acceleration is kind of down and left right now The acceleration is up and left. It's always towards the center But because you're moving around the circle the direction towards the center is changing all the time This means unfortunately we can't use these anymore We have to use circular acceleration and circular velocity speed What's your homework? You're going to find in this unit. You're going to be using the data sheet an awful lot Finally so on your formula sheet the back page has all sorts of data You want to look at it has the mass of the earth the radius of the earth the radius of the sun's orbit the radius of the sun the Radius of the moon's orbit the radius of me all the stuff that we need to do that Oh, it has the period of the earth. Oh What is the period for the earth to go around once? How long to take the earth to revolve around itself once you know all know this 24 hours you can convert that to seconds. What's the period to go around the sun? Well, it's 365 days, but it's not quite exact I think they actually give you the period in seconds on your sheet and that includes the Quarter of the day leap year thingy that doesn't work out. Okay Find the for number one on the earth on the equator the frequency the speed You're traveling on the equator and the inwards acceleration required for that to occur Same for the moon Same for the Sun number four says examine how the spin cycle on a washing machine works to partially dry clothes and Part of this question got chopped off. Mr. Dewey It was supposed to ask which way does the water move if you actually look at the spin cycle The water does not move this way if you look at it very closely. The water is always moving 90 degrees to the radius because that's what direction your speed is Sorry, I guess I'm gonna have to nuke number four because I didn't somehow copy it properly Five is good Seven is good Eight nine. We're gonna pause there