 Mark your own would you like a quiz with which to follow along? Oh you did find it. I knew you would I Like number one. I like number one. I like number one number nine one is a nice question Suppose this mass begins from rest, okay Mass one is 2.8 kilograms mu is the covalent friction is point one two the angle of inclination is 52 degrees Find the time it would take for this mass to slide a distance of six meters down the slope So what this question is asking me to find is? T I Know vi is zero. I know D is six Do I know v final? Nope, I think What I'm really being asked to find is The acceleration because if I find the acceleration then I think I can use d equals vi t plus a half a t squared and I can find t So even though this question is saying find the time I've been I'm gonna be spending most of my time. I think Finding the acceleration. How am I gonna do that? I think I'm gonna label my forces M1g normal force friction I Think I would break M1g into two components parallel and perpendicular M1g perpendicular M1g parallel and we said that this angle and this angle and that being the same which they do So to find the acceleration I'm gonna ask my side. Who's winning? Well, which way is this thing accelerating? Down the hill Who's winning then? Okay, so my equation is gonna be M1g parallel So I'm gonna list all the forces that are parallel to the other one is friction winner or loser What if I was sliding up the hill? Which way would friction be acting? In fact, I would have two winners. I would have winner plus winner Instead of winner minus loser if we were sliding up the hill Which is why sliding up the hill it stops so fast because there's two forces slowing you down, right? Anyway, friction is a loser and there's just one mass so it's gonna be that Friction is what times what? That's a deafening silence makes me a little worried friction is what times what I Don't know the normal force. Oh, but look look look look look I know another force the same size as the normal force in an 8mg. It is M1g perpendicular Let's do a bit of trig parallel is opposite High pot news. I think parallel is sine M1g Sign of was it 52 degrees? Yeah Minus mu and I think perpendicular ends up being M1g Cosine of 52 degrees and that equals M a and this one's kind of nice Cara. Is there a mass in every single term? then in this case Masses cancel I'll take that. I think the acceleration is gonna end up being 9.8 sine 52 Minus what I say the coefficient of friction was point one two nine point eight Coasts 52 and I get an acceleration of something or other Let's see. Oh, I went through this yesterday. You made it Glad you made it. Let's try this again 9.8 sine 52 Minus point one two times 9.8 times the cosine of 52 and I get a lovely acceleration of 6.998. I was tempted to round that to 7 But since this isn't my final answer, I'll actually carry Mitchell 6.998. I'll carry a few extra sig figs Probably won't make a difference, but I'll be paranoid Now I'd like to find t. I know that D equals vi t plus a half a t squared, but vi is zero Which means that? D equals A t squared over 2. There's the one half. I think what this really means is that T equals 2 times D divided by a Square root which is going to be 2 times 6 divided by 6.998 square root 2 times 6 divided by answer Square root of that you guys get an answer of 1.31 seconds people nodding So that's for full marks. If you're wondering how I gave out part marks on this one. I did something like this Did I give you quiz to version 1 or version 2? What's it say on the top? Version 1 that's how I gave out the part marks But if you got the final answer One mark, but a half mark if I saw that half mark for that one mark for the acceleration Half mark for writing that half mark for that half mark for the answer question to Atwood machine Did they give me both masses? Then I'll treat this as one mass. I'll go winner minus loser equals mass of both times a they only give me one mass They'll give me enough information that I can target that one mass and find all the other stuff and use the other stuff To find the missing mass Anyhow when I did that I got an acceleration of 1.75 meters per second squared And I got a tension of 61 newtons Yes, I think atwood machines are kind of from last year, so I didn't do a big song and dance about that one if you would 61 newtons. Yeah No, yes, and I used m1 because tension was winning and it was easier to get tensioned by itself a student of mass m Places a bathroom scale on the skateboard. What does the scale measure does a scale measure mass? Now what is measures normal force so what this question is talk as they talk about a scale I'm always thinking to myself self normal force normal force normal force He then rolls forward on level ground while standing on the scale, which is still on top of the skateboard What will the scale read more than m less than m or m? Yep, I think so Now the student rolls down the skateboard Sorry rolls the skateboard down a ramp which is inclined at an angle I was typing this up on a Mac years ago, and I couldn't find the theta But I could find that funky symbol. It's a fi I think but anyways at some angle while standing on the scale which is still on top of the skateboard What will the scale read more than m less than m or m? Brett I agree Convince me Now if you just write that on a quiz, I'll give you marks on a test So here's what I said scale measures normal force and I said the normal force is equal to mg parallel Probably if you drew a little ramp with a good free body diagram that would really help and mg parallel I said in this case is mg coasts and It's always going to be less than mg because cosine is a decimal, which means if you're multiplying by decimal your answer is always going to be smaller If you answered something along those lines if you use the black a be approach if you said well If it was vertical normal forces zero and level if you use the black a be theorem I'll give you full marks there if you're not quite sure how to mark this one lawyer with me afterwards and The last one Assume no friction. I would have no problem including friction by the way. It means you got an extra force one extra force If mu 1 equals 10 and mute. Sorry mass 1 equals 10 and mass 2 equals 4 and the angle of inclination is 56 degrees What did I ask you to find tension? Oh? acceleration and then tension Okay What's the first thing I'm going to do here? Well not dealt the pictures there, but I labeled my free body diagram So I said on mass 1 it's going to be gravity down tension up on mass to gravity straight down tension along the rope and Which is the bigger mass? I? Know this one is when enough this one is bigger It would be a bit trickier because depending on the incline this might not be enough to make it down the hill But if the bigger mass is hanging in mid-air, that's going to be the winner on a hill So I said okay friction is in that direction although did I include friction? Why do I have friction here? Oh? Did I do a part C? Oh for part C gotcha So I added friction later on for part C. That makes sense for now. I said M1g is winning Tension losing tension winning and M2g parallel is losing Winner minus loser plus winner minus loser equals the mass of both of them times a Tensions cancel M1g M2g parallel was M2g sign I Divided by the mass of both of them to get the a by itself and I got 4.7 meters per second square Then to find tension I could have used this mass, but this mass is much cleaner Tension is what no M1g is winning tension is losing M1g is winning tension is losing equals M1a because Joel looking at a single mass But it's pretty easy to get tension by itself. I plus the t over here. I'm minus the M1a over there and Tension Zay was 51 Newtons Part C What would the minimum magnitude of the force of friction have to be in order to keep this entire system stationary if it's Stationary, what's the acceleration? Zero I said okay really what we're saying is This Oh, I just looked at one mass tension, which was 51 minus M2g That has to cancel out friction You could done a bigger equation. I just looked at the one man. I said, oh no actually apparently I went M1g minus M2g Parallel that equals friction because it's winner minus loser Equals zero I plus this over I was in a big rush friction is M1g plus M2g sine theta friction ends up being 65.5. I don't think I did a great job of explaining that but I'm seeing a bunch of you nodding your heads like you got it anyways, so Is that right? Yes So if you can be so kind as to give yourself a score out of whatever this is out of 17 So any questions from last day's homework? Gave you a couple of nasties. We looked at the lawnmower question. There is going to be a lawnmower type question on your test I'll tell you that right now where The picture looks something like this although I May also instead of pushing down. I may have you pulling up with a rope instead In which case your normal force will be a little bit different back. It'll be less not bigger Anyhow any questions from the homework that you wanted me to go over? I assigned one two three and I think that was it. Yeah Yeah Sorry to love to so Here's my mass We have good old Mg down now. It says it's being pulled upwards at an angle like that Brett With 300 newtons of force Definitely there would be friction in this direction. Is that okay, Brett? and because I'm pulling up I'm cancelling out some of gravity. I'm pretty sure the normal force is smaller than gravity. In fact, I know it is Because you're lifting up as you pull up and The normal force is always cancelling out mg. Well, no you're since you're cancelling out some bit It's only cancelling out what's left. Is that okay? I Would also then call this fx and Fy a says find the normal force Well, the normal force this time it looks to me Kayla that Fn that plus fy equals mg the two ups cancel out the down Normal force plus fy equals mg. Is that okay, Brett? Which means normal force is Is going to be mg minus Fy and fy I think it ends up being signed But I are you okay on the the trig part if I let you take that part on your own? Yes, right. Here's your angle opposite. I think it's ended ends up being signed in this case I think this is backward y is signed again because we're not at a wonky angle B Friction is going to be mu times whatever your answer was in part a I shouldn't put an a there You'll think that's acceleration. It's going to be mu times the normal force, which is from there Who's winning? not the 300 The 300 only be winning if you're accelerating upwards and diagonally, but which way are you accelerating to the right? Which forces the to the right force? Yeah, okay, it's going to be winner minus loser equals ma FX I think it's going to be the 300 times cosine, but I have to do the trig to double-check that Friction you just figured out in part D Mu times a normal force and you figure the normal force out in part Is that enough of a kickstart? I think Yeah, I'll let you crunch the numbers by the way, um What if it was not accelerating what if it refused to move what would your acceleration be? Zero what could you tell me about these two forces them? They're the same size that might give you a different way to find friction Certainly if you didn't know the mass that would give you a different way because you'd know the force that you were tugging at it Wasn't moving you can figure it out that way any others There's only three questions, so any of you have any questions from the great big ultimate forces review now? Remember I would like you to hand in This When you write your test if all possible I'll take it afterwards But it's really dumb to do this after you've written the test if you haven't clued in if you go through this You'll have seen about 95% of the questions on the test and The answer keys are online so you can double-check The answer keys are attached, but the actual answer solution key showing all my steps is online Any of these that you glance that you're going and by the way some of these are nasty which is great The five not too bad a little bit nasty. Oh I like number 10 17 is pretty tough Anyhow any of these you want me to go over Number three went too far. Mr. Duke should have stopped there Okay, I Think I sort of like number three in that I think there's a question on your test I think it's multiple choice. I think where I say to you. Hey, I didn't give you one of the masses. What you're gonna do Okay, here it wants you to find the mystery mass How am I gonna start out here Caitlyn? Same old same old absolutely Mitch you want to sit up and follow along maybe just be thinking Maybe you want to get out the review if you've lost the review I might have a couple extra copies floating around or else. It's online. You print it up Uh Caitlyn I would go like this M1g tension yes, and M2g Normal force tension friction be one extra force if they did Do I know both masses? Then I can't use my winter minus loser equals m1 plus in fact I have to start this one out by looking at an individual mass which mass will look at the one that I know I'm gonna write a force equation just for this guy just for this guy Who's winning? tension Who's losing? No one although if I had friction it wouldn't be that hard care for me to add in friction you times a normal force I don't know the normal force. Oh, but look look look look it's mg in this case and Because I'm just looking at one mass Cara. It's gonna be M1a Do I know mass one? Sorry m2a I'm looking at this mass my bet. Do I know mass two? Yes. Hey. Oh, I can get the tension. I'm pretty easy Tension is going to be four times one point five pack. I can do that in my head tension is gonna be six Newton's Can you see where I'm gonna go now? What Now I'm gonna go look at mass one Who's winning? Who's losing? M1g minus tension equals m1a Do I know m1? No, do I know g? So I'm gonna write this as 9.8 m1 because we're used to having the number and then the variable from math 9. I'm gonna treat m1 like an x Do I know tension yet minus six? Equals do I know m1? No, do I know it yet? 1.5? M1 Caitlin how would I solve that wouldn't I get the m1s to the same side? How? I think I'd minus the 9.8 over because I don't want to have nothing over here So I'm gonna minus the 9.8 m1 and I'll get Negative six equals whatever 1.5 take away 9.8 because those are like terms, right? It's like if like m1 is an x It's really 9.8 x minus 6 equals 1.5 x 1.5 take away 9.8 negative 8.3 m1 Caitlyn final step. How could I get the m1 by itself and Wonderfully the negatives cancel I get a positive mass, which is good because we're not dealing with antimatter here or anything like that, right? Negative 6 divided by negative 8.3 and you end up with a mass of 0.7 222 B So if they don't give me a mass no big whoop Look at the one mass that you do know find everything you can from there Bring whatever you found over to the mass that you don't know and solve for that single solitary mass Is that okay? Yep Any others I Think there's one more like that somewhere else in this by the way We also find it was one or two more where you're finding a mass then we're gonna begin the next unit Which I'm gonna teach as though it's brand new. I covered a bit of it I don't think that's your kamosy covered any of it. So I'm gonna teach it from scratch So we're gonna start this next lesson. I don't think I'll get through this whole lesson. I might we'll see Lots of terminology here lesson one unit three work and energy work first of all work is a physics term and we got a bit of a problem here Joel because It's also an English word when you guys think I'm doing work You think I'm getting tired getting sweaty that that's not what we mean in physics It has a specific physics meaning now. It is a scalar Would I be a good teacher if I confiscated that game for a couple of days as A wonderful lesson about the important of education versus going and standing in line in a store and missing Things I might right now. I'm on the fence in other words. Don't push me, right? It is defined as the product of the force component in the direction of motion and the distance moved Say what work is defined as this? Force times distance. Oh Except both of these have to be in the same Direction in the same Direction the equation then symbol for work is a capital W and the equation is force times distance Fd what are the units for work? Well, what do I measure force in? Newton's what do I measure distance in? It's a Newton meter, but this one is so important. We've given it its own name We call this a jewel symbol capital J named after a scientist whose last name was Example one How much work do you do when you lift a 35 kilogram mass? To a height of 1.5 meters well Work equals force times distance Which force was he resisting? The force is mg and you know what we actually frequently call a vertical distance a Height we often use back. We'll talk about Work done against gravity. We're gonna call it mg h The mass is 35 G is 9.8 Isn't it negative it's a scalar and H is 1.5 meters. How many jewels of work did Joel do? I know it feels strange using the word work and Joel in the same sentence, but well, you know use your imagination What do you get? 500 540 514 point what so not 514 Round off properly 515 Five hundred and fifteen jewels of work. Okay Is that a lot you know what? 515 you wouldn't want to do that 20 times in a row. You'd be tired So that lets you know kind of 500 jewels of energy is a reasonable chunk How much work does a hiker do on a 50 kilogram backpack if he carries it to the top of the 750 meter mountain? Well, here's the nice thing don't write this down But no matter what the mountain side looks like I really don't care because the only force that this hiker is Resisting is gravity, which means all I'm interested in is the vertical displacement I don't care about any of the horizontal junk that went on none of this matters. All I know is work Is force times distance and if you're carrying something up a mountain side the force that you're doing work against is gravity and The distance up a mountain side is H. It's going to be 50 Times 9.8 Times 750 What do you get? 367 thousand five hundred three six seven five zero zero now we better do our sig figs So how about three point six eight times ten to the one two three four? jewels 50 kilograms How many pounds is 50 kilograms? You're not sure multiply it by 2.2. What's 50 times 2.2? What's 50 times 2.2? anyone Sorry 110 so that'd be like piggybacking someone who weighed 110 pounds up a mountain side. Would you be tired? Probably in other words 367,500 jewels that's a fair chunk of work the ball at the end of the example three the ball at the end of the rope is Following a circular path Because of a constant force exerted on the ball by the rope in a direction towards the center of the circle How much work is done on the ball by this force? Look I'm doing this Okay How much work is this string doing on the mass on the end of this? Why is the answer zero? Why is the answer? It is zero by the way. Why is the answer zero? First of all, what did I say work is what times what? But what was the condition about the force and the distance? Same direction now read the question. Which way does it say the force is acting? Towards the center let's pause this suppose I could freeze it right here. The force is acting towards the center But which way is the ball moving? That way are the force and the distance in the same direction then we would say mathematically I'm doing no work I'm doing no work Push it now if I have Trevor do that for a long time will you get tired? Will you get tired? Yes. He's not doing any work though. Wait a minute. He's getting tired has nothing to do Thank you Trevor has nothing to do with work work is what times what? Force times distance Kara was he exerting a force? Yes, was the wall moving a distance? No No work being done Well, why is it getting tired then okay now we're gonna get a little bit specific actually Trevor you were doing work But not on the wall when you were giving Trevor a piggyback you were doing work and not on the wall What was happening was your muscles vertically were compressing and shrinking compressing and shrinking and there's the force and in the Same distance as gravity. Okay, so I should I should be clarifying that in general a Force in the same direction of motion like f1 on the next page Does positive work a? Force in the opposite direction of motion like f2 does negative work You can't have negative work and positive work positive work means you're gaining energy Negative work means you're losing energy. Oh I'm a physics nerd and I threw that in on the side need to figure out how to do this mr. Pen in 1977 turn your paper sideways. Let's see what it says here in Northamshire, England David Perley's race car crashed and his speed dropped from 174 kilometers per hour to zero Kayla in point six six meters He had 29 fractures three dislocations his heart stopped six times But he survived as far as we know this is the human being who has experienced the most G forces and lived to tell about it How many G's did he experience? All right, let's see if we can calculate this guy's acceleration What's the initial 174 kilometers per hour what 174 what I Can't do math with kilometer. How do I go from kilometers per hour to meters per second times by 3.6 or divide by 3.6 which one I heard both which one I mean again, I'm hearing both which one I'll give you an easy way to figure it out What's the speed limit on the freeway? You have your driver's licenses you're getting what's the speed limit on the freeway the easy one No freeway not hot freeway Hundred you've all been on the freeway speed limit there is a hundred. Yes Can you go our vendor at 100 times 3.6, please? Okay, it's okay with me here. Are you traveling so you're saying on the freeway you're traveling 360 meters every second You're traveling three football fields every second on the freeway. I Don't think you times by 3.6. You know what you do that by the way, that's how I figure it out every time I say well a hundred times 3.6. No on the freeway. I don't go for football fields a second not a chance So it's divided by 3.6. What's vi? No, it's a hundred and seventy four divided by three point six. Come on. What's vi? Sorry forty eight point three What's the final? What's D? What equation has those and a in it? I think it's going to be vf squared minus vi squared all over 2d What acceleration did this race car driver experience and survive? Sorry, I can't do this up here because I got my screen flipped sideways Which means my well if I do that it'll just terrify you guys What do you get? Where's your calculator? Sorry Okay, what'd you get? Would you get a little more participation would help boys and girls you get six hundred ninety nine? I? Don't know I can't do mine up here because my calculator sideways. What do you get? It's why I want more if you try this by the way Brett how many numbers are on top to you to put the top in brackets. Yes. What do you get? I? Need a consensus answer here folks. What'd you get Brett? No, no, no, no, what'd you get? Okay? It's way 1,767 anybody else yes anybody else Caitlyn would you get Sorry, how many G's is that divided by 9.8, please? 180 G's in that car accident that's the equivalent of 180 people doing a dog pile on him and he survived Okay So he's the person at least four years ago when I last checked He is the person who has survived the biggest deceleration and lived to tell about it Or at least lived long enough to tell people there may have been people that survived for a brief moment after an accident In something more than this, but they didn't survive long term here in this the nerd part turn the page Or next page over So we said this work can be positive or negative Work in the same direction of motion is positive work work in the opposite direction of motion is negative work Although work can be positive or negative It doesn't have direction. This doesn't mean Direction it means losing or gaining Child is pulling a wagon along the driveway and they're exerting a force F along the handle of the wagon How would you calculate the work done by the child on the wagon? Here's the wagon There's my force F Here angle theta What direction is the wagon moving? Dagonally upwards No, which way is the wagon going to roll? So I need the force that's in the same direction because work Equals force times distance. Yes, but the force in the distance have to be in the same direction in fact What you would want to use is fx and I think you're gonna find it the cosine of theta Equals fx over f in fact Emily if I wanted to get fx by itself What would I do and as a matter of fact? The actual formula for work is f times d cosine theta What if theta is zero degrees? What is the cosine of zero degrees? Can you try that on your calculator right now really quickly? Rihanna, what is it one because that means you're in the same direction anything? Oh, what if theta is a hundred eighty degrees? What's the what if you're pulling backwards? What's the cosine of a hundred eighty degrees? Negative one. That's why we said in this direction is positive work in this direction is negative work. Oh What if you're pulling straight up? What's the cosine of 90 degrees? zero no work and Matt some of that should be familiar to you from our circle from last year But that's one of the many many reasons why the trig values have the values that they do work equals what times what's force times distance ah? Only if the force is constant what if the force is not constant What if the force is changing? Well as it turns out work is also the area Under a force versus distance graph Here's a graph We're graphing force Versus distance and it looks like the force is increasing when we started out It was one Newton, but eventually the force finished up at three newtons And the question asks how much work is done moving this object from two meters to six meters? I guess we're pushing on something Well, there's two meters There's six meters You know how much work was done and moving the object? That much work the area Now I always ask this because maybe there is a math nerd here. What shape is that that we've just colored in first of all Is it a square? No, is it a triangle? No, is it a rectangle? No This is a side that has this is a shape that has two parallel sides and two non parallel sides What do we call that I? Heard someone say it Trapezoid called a trapezoid now Believe it or not guys with me back there Okay, please stop because every time I can't that's back there you chatting Believe it or not if it's about physics good, but still there is the formula for the area of a trapezoid there is one Does anybody know it? I'll tell you why you don't know it. You don't need it Every single trapezoid is also automatically a triangle and a rectangle draw that line in and Call the top area area one and the bottom area area two the reason we don't make you memorize the formula for the area But trapezoid is nice. It's one half a plus b times h for what it's worth is well Do you know the area of a rectangle? What's the equation for the area of a rectangle? Really? Length times width we usually say but base times height works Do you know the equation for the area of a triangle? What's the area of a triangle? It has base and height in it Brianna Because a triangle is actually also half of a rectangle. So that's why it's divided by two So since you know both of those in theory We don't memorize a trapezoid Area one is going to be base times height divided by two. It's a triangle. How long is the base of that triangle? Look at your graph sorry For what's the height of the triangle Jacob? Don't say three because it's not one from here to here Jacob in your head with no calculator. Can you go four times one divided by two? Yeah, what? Okay, so the top area has two joules Area two is a rectangle which is length times width or base times height I really don't care how you think about it. What's the length of the rectangle Emily? What's the width of the rectangle Emily? What's the area of the rectangle Emily? So the total work 10.0 joules if that was one person and they were pushing something they lost 10 joules of energy and That object gained 10 joules of energy You got 10 joules tired of Doing this Okay, so there's actually now two expressions for work force times distance if the force is not changing Or it's the area under a force times distance graph Which makes sense to me by the way because didn't you tell me that area was length times width Force times distance if I look at the units it should be the area energy Energy is the ability to do work if you have the ability to exert a force over a distance then you have energy It's amazing. I said the word energy and I saw four yawns You were the final don't worry Kara was the initial There's two in between it's amazing Energy is the ability to do work If you're asking does an object have energy what you're really asking is can it exert a force over a distance? Does this gun have energy my Nerf dart gun? Can it exert a force over a distance on the projectile? Yes It has stored energy we're gonna call that potential energy. There's all sorts of different types of energy the energy of motion we call this ke stands for Kinetic energy, so I'm gonna fire this dart gun at Matt Does this dart have kinetic energy? Yes, when it hit Matt hits Matt it can exert a very small force over a distance But it's moving anything that's moving and has mass has kinetic energy Has kinetic energy Okay, you tried to catch it. I figured you'd be athletic enough to dodge or catch it That's why I didn't pick Well, no Brett would have just flopped and taken the charge, right? Yeah, it's true okay If I had a baseball And I said I've had enough of jewel and I'm gonna throw this right at his jaw As hard as I can Does the baseball have energy when it hits him will it be able to exert a force over a distance? Anything moving has kinetic energy We're gonna be looking an awful lot at kinetic energy this year heat Heat is another form of energy Heat is usually created by friction Can heat do work? How do you think your car engines work? I think steam engines work. Yeah, absolutely heat can do work It can exert a force over a distance Gravitational potential energy this is stored energy due to an objects position It's stored the word for stored in physics is potential. It has potential energy But it hasn't been used yet I Wanted in fact you can give any object at all some gravitational potential energy just by lifting it up Which would you rather have land on your head this or that? So certainly when we come up with an equation for gravitational potential energy, I bet you mass is in it bigger mass more energy more I'll bet you a height is in it because if I raised it higher it would hurt even more Chemical potential energy gunpowder is a great example of chemical stored energy Your food the food that you eat is all chemical stored energy Your body breaks that down stores it in your cells and your cells can transform that into Kinetic energy to move your arms to move your heart It can transform it into heat your blood temperatures all are regulated at a certain level Other forms of energy sound energy Elastic energy, that's the elastic the energy stored in a rubber band Nuclear energy, that's the energy stored inside of a nucleus all sorts of different types of energy If there is a way for an object to exert a force over a distance If it has the ability to do work then that object has some energy example for Sometimes when we do work we make things move it says fill in the proof below to find an expression for motion energy So if an object is moving it has energy it has kinetic energy. What's the equation? Well first of all work equals force times distance and Force equals what times what from this past unit f equals f equals ma. So I'm going to write this as m a D mad yeah, and then I'm going to get really clever here I'm going to put a One-half in front and a two right there if I multiply by one half and I multiply by two Do those guys really cancel each other out? If I multiply by a half and I multiply by two don't they cancel each other out So I haven't changed the equation, but I got a good reason for doing this. You see two ad Vf squared equals vi squared Plus two a d. What's two ad? What's two ad the same as if I get the two ad by itself? I can replace the two i ad with the vf squared minus vi squared and If your initial velocity is zero you get a half mv squared See it That's the equation for kinetic energy kinetic energy is equal to a half mv Squared you don't realize it yet, but that equation there has a huge impact on athletics because of the squared Because of the squared so hockey Who's my hockey players here? Okay Hockey stick if I want to give more kinetic energy to the puck I Can make the stick twice as heavy that will let me give it twice as much energy Or I can swing ties as fast now if I swing twice as fast that to actually get squared I'll have four times as much energy Have sticks gotten heavier or lighter over the past few years Why lighter? Because it's all about velocity the more velocity you can the faster you can swing your stick The V is squared that gives you way more bang for your buck Otherwise, why wouldn't you just make a stick out of aluminum like a baseball bat in college? Well, you want it lighter to get more speed Tennis rackets tennis rackets have gotten lighter over the years, but the serves have gotten harder. Why? Again, if you double the mass you'll have twice as much energy But if you double the velocity because the two gets squared you look four times as much kinetic energy They'll go four times faster and go four times faster car accidents if You're in a car accident at 20 kilometers per hour Versus a car accident at 40 kilometers per hour twice as fast. You'll do four times more damage If you're in a car accident at 20 kilometers per hour Versus 80 kilometers per hour What's 80 divided by 24 times faster 16 times more damage? You're probably not gonna live half mv square No vector symbols because kinetic energy is a scalar By the way, just to give you some frame of reference about energy and jewels One jelly doughnut contains about 10 to the 6th jewels of stored chemical energy and One mosquito push-up Is about 10 to the negative 13 jelly doughnuts. It's about one herd just for the nerd. Yes. That's a mosquito push-up Yes, I looked it up turn the page Let's assume. It's a mosquito doing a push-up. Would that not be what a mosquito push-up is? No Next page so a golfer wishes to improve his driving distance. What would have more effect doubling the mass or doubling the speed? Doubling the speed. Oh have golf clubs gotten lighter over the past 20 years. Yes Are people hitting it harder? Yes Who's my golfers here anybody go okay, so Sean and they're always talking about club head speed That's what they're talking. How do you hit hard? It's all about club head speed Nothing to do with strength nothing to do with how heavy the driver is Club head speed the more club head speed you can generate the harder the further the ball is going to go. Oh Since kinetic energy equals a half MV squared Doubling the mass gives you double the kinetic energy Doubling the velocity gives you four times the kinetic energy four times the kinetic energy Baseball players so I have baseball players in here Okay, they always talk about bat speed That's what sends the ball out of the park how strong you are how heavy the bat is It's all about how fast you can get the bat moving and if you can get the bat moving faster Any increase you gain by the square of the increase which means way more bang for your buck Sometimes when we do work we lift an object and we give it height energy Also called gravitational potential energy Fill in the proof below to find an expression for height energy Also called gravitational potential energy or PE for short work equals what times what? What did we say at the beginning of this lesson work equals what time what Katie? Okay, so let's fill that in force times distance If you're lifting something which force are you having to resist? MG and we call a vertical distance a height gravitational potential energy is mgh Both of those are on your formula sheet in fact I'm pretty sure those are the only three formulas in this hole. No never mind There's one more formula. We'll look at power in this unit, but on your formula sheet The four formulas in this unit Work equals force times distance kinetic energy equals a half MV squared Potential energy equals mgh and the one for power which we'll get to next day Usually in this unit we're going to focus on mechanical energy Mechanical energy has two main types Kinetic and potential We almost always say an object is moving or it isn't and it has some height or it doesn't we're going to pause here What's your homework? You're writing a test next class Sometime during your one of your blocks. I'll do a tutorial today after school and Study