 All right, I'm gonna be doing a review of work and energy from physics. I have a test coming up soon Yeah, so I'm just gonna start work Work is force times the distance And so a better Way to explain this or like a more visual way is let's say we have a box and We're pushing it 10 Newtons this way the the mass of the box doesn't matter right now and So we push it 10 Newtons for three meters So the total the total work done on this box is 10 times 3 30 joules All right, but there are also there's also a cat caviar That we call it so let's say let's say we do still go 30 minutes meters but instead the The force being applied is at a 60 degree angle and let's say it's still 10 Newtons right so The the force on applied to the object In order to get the work needs to be in the same direction as The as its displacement so move three meters this way So we need to just get its x component and that's gonna be five Five Newtons. So the total work done on this box is 15 joules Yeah, I forgot work is The unit for work is joules. So it's just written as J All right, let's go over energy So we basically have two types of energies that we're gonna be talking about we have potential energy and kinetic energy We're also gonna be talking about potential energy elastic But we're gonna get into that later. So Let's not talk about that so energy is The capacity to do work, but it's really mostly just used to like Make the math work We don't I never really got a good conceptual understanding of energy, but I know it's really just used to make the math work So potential energy is mass times acceleration. That's our force times distance So We can we can change this to gravitational Energy so to make this clear we do mass times gravity times height. So let's say for example, we have a ball of 10 kilograms on this cliff and Let's say the height of this cliff is 10 meters and Let's also just say that the acceleration Of gravity is 10 meters per second so So there so right now it's not falling but there but it's but it should be but if there wasn't a cliff stopping it It would be going down at a speed of an acceleration of 10 meters per second square. So our gravitate our potential Energy or potential gravitational energy would be 10 times 10 times 10, and then that's 1,000 joules. Oh Another thing to know work is a vector so let's just put a little arrow here to denote that it's a vector and Energy is a scalar So that means they don't really have direction Okay, and kinetic energy Let me get rid of some stuff kinetic energy is Just the energy that the object has as it's moving so it's one half mass Velocity times velocity squared so Let's have this let's have us another ball and let's say it weighs one kilogram and It's going Let's say it was two kilograms because we have to divide by two so let's say it's two kilograms and It's moving at a speed of 10 meters per second so it's kinetic energy is one, you know Two times ten squared over two That'd be 100 times two that that's still be 100 joules of energy Then the reason these are useful is because in a closed in a closed system total energy is preserved so It can be written as this total energy is potential now potential energy plus kinetic energy and It will always be the same so if potential energy changes then kinetic and if it if there's less potential energy That means kinetic energy increases unless it's lost but But we're not we're not going to go over that yet In some equations we have to find out in some problems. We have to find out how much energy has been lost but That's not really important. So Let's start off with a simple problem. Where's my cursor? It's right there. So Let's get rid of this because I need more we are going to do a Say a roller coaster Let's say it is five meters tall Again, we're assuming gravity is ten and The acceleration of gravity is ten just to make it easier. Okay, and let's have a little cart right here and Say it is 10 kilograms So right now at this point its potential energy is Ten times five times ten. That's 500 joules. So it's potential energy is 500 joules So let's say it falls right here At the point where it's 2.5 meters down or it has 2.5 meters to go to get to the ground its potential energy Well, it's half because you have wait. No, it's not half. Yeah, it is. So it would be 200 250 joules this also means the kinetic energy is also 250 joules because Total energy has to be the same so This is we're assuming that at the start we have We have a velocity of zero. So yeah, let's say zero joules at the start Okay, and let's prove that this is true based on how far it went So if gravity is has an acceleration of ten and it went down 2.5 meters What we need to do is just we need to find the velocity at this time Let me do that real quick. All right Sorry about that. So its velocity was ten times the square root of one over two That's its velocity when it's gone 2.5 meters down so Given what we know, let's multiply everything so Let's take This square let's square that And divided by two and that should give us two 2,500 at the end so 10 times This simplifies this inside how it's inside here simplifies to the square root of 50 and the square root The square root of 50 squared is 50. So if we take 50 times 10 We get five hundred and five hundred over two should be two hundred and fifty so This is true At every stage So no matter so no matter which point you still have the same total energy So when it's at the bottom here And it's zero meters it will have Zero joules of potential energy but five hundred Joules of of kinetic energy We're assuming velocity is maintained and it's still Having this velocity go down this way. No, we're just we're just assuming velocity has stayed the same Not stayed the same increased as it's supposed to sorry All right. Oh, what's next? It's gonna talk about. Oh, yeah power There aren't a lot of power problems that I was given but let's just Knock that out really quick. So power So power is measured in watts and it is just work over time So Let's say you have a Some guy and he is pushing a box And let's use the example from earlier. He's pushing it at 10 newtons For three seconds I'm not for for three meters and it took him three seconds to push the box No, let's say five seconds it took him five seconds to push the box to three meters and apply 10 newtons of 10 newtons of force So That would mean its work is 10 Times three that's it. That's its work. It's work is ten times three and we divide three seconds to get us our power And that would just be 10 watts But if it took him just one second it would be 30 watts so Yeah, it's just your ability to output power over time and if we're If we were to take this to a second if we were to rephrase this power can also just be force times velocity so so if we're pushing a box at 10 newtons and It's going with with 10 newtons of force and it's going at 10 meters per second, that's its velocity then our work would be what then our watts would be 100 Yeah, there aren't a lot of problems that have to that I've had to deal with power What we do have to deal with which is a little trickier is potential energy elastic So that equals One half the spring constant X squared so What is the spring constant? It's a It's basically the amount of Newtons it takes to push in a spring or something elastic to push or stretch Yeah for a certain amount of meters so so the spring constant is Newtons over meters So let's say we have a spring with a spring constant of 200 and 2500 Newton Newtons per meter All right, and let's say we wanted to push it I'd say we wanted to push it one meter. It would take 2500 Newtons to get it one meter to get it to push to one meter. So Let's say we we have that me. I lost my train of thought Okay, I'm back. So yeah, it takes two hundred two thousand five hundred Newtons to push this spring for one meter this way and the same For stretching it. There's another Thing for spring is I forgot what it's called But basically there's a distance X Which is? The distance that the spring is naturally at And this isn't just like it like for any spring This could be like rope not rope like a bungee cord or a rubber band or something but uh, that's why it's just elastic so There's a distance where it's just normal And I forgot what it's called so Yeah, okay, so let's say we push this Let's say we're stretching this spring for Let's say we stretch it for two meters Okay, it took it took five thousand five thousand newtons to get it to stretch that much And let's find out its potential energy Uh the potential energy in this spring is two thousand five hundred over two times two squared So that becomes two squared is four four cancels out two and we get two thousand five hundred times two that gives us five Thousand five thousand jewels. That's the amount of of potential energy. There is All right, now that we have the basics Let's do Basic problem So we should do a spring Problem, so let's say we have a spring. I'm just gonna represent the spring. Yeah, I'm just gonna keep doing that All right, this spring it's normal distance is 10 meters it's uh It's spring constant is 1000 Newton meters I'm just making this off the top of my head and right now It is at eight meters so What is the potential and Let's also make this a little bit more exciting or more complicated. So Let's say we have a box of ten Four kilograms All right, so given what we know And let's say we have a floor that is frictionless. So We want to find out at what speed This box is going to be pushed to So what is the velocity when when the spring is released and it's done? What is the velocity that the box will be? Will be yet. So first we need to find out the potential energy of The of the spring that it's at remember because total energy will remain the same always and its potential energy is one half Well, it's ten minus eight is the x we have to find first and that is two So that's this x right here and again, it's uh, it's spring constant is 1000 So if we take 1000 Times two squared That will give us 500 times four That gives us two thousand So we have two thousand joules of potential energy and Since the and since at the start the box is not moving our total energy is also two thousand joules Okay, when when we release the spring The spring will return back to normal and have a potential energy of zero So the two thousand joules of energy must be transferred to the box as Kinetic energy since the box will be pushed and remember kinetic energy Is just one half mass velocity squared so We can we can say that it's four one half four times V squared equals two thousand joules so Half of four is two half of four is two We want to get a velocity so two thousand over two is one thousand so velocity squared is 1000 and To get velocity on its own we just need to cancel this out by getting a square root and Velocity velocity is the square root of one thousand meters per second So let me get that It's gonna be an irrational That's thirty one point six. So the box will be moving at thirty one point six meters per second All right pretty messy This is pretty messy work, but You get the idea, right? So So, yeah, that's how we I would have done this with a With a grab with gravity and it's actually easier to solve of kinematics problems this way So let's actually do a kinematics problem Just with just with working energy. So if we assume energy is preserved That no energy is lost it's basically the same as saying there is no air resistance So we have a ball and it's eight kilograms. We don't need this potential energy right here All right, we have a ball and it's and it's ten kilograms its velocity Let's see Let's say it starts out with an initial loss initial velocity of five five meters per second and It is going to fall to ten It has ten meters all right, so Right now its potential energy Again, we're assuming gravity is ten meters per second squared. So it's Right now its potential energy is eight times ten Times ten because that's our height mass acceleration height All right, that gives us 800 our potential energy is 800 joules What is our kinetic energy our kinetic energy is one half mass eight Times velocity squared So that's four times 25 and that's 100 joules so our total energy our total energy is 900 joules All right, and we want to find out its velocity when it's when it hits the bottom so So again our kinetic energy would just be one half eight and Since we want to find out what's at the bottom and we know since at the bottom potential energy will be zero We know that kinetic energy must be 900 so I'm just gonna skip this and do Velocity must be equal to 900 over 4 so Comes out neatly as 15 15 meters per second if we did this with kinematics it would be It would take longer. So let's let's do that with kinematics I prop this is Really more to illustrate a point so I'm not gonna do it then But just trust me that it is It's gonna give you this the same result if you do with kinematics. Whoops And now we're gonna do more More complex problems. I think I only have two problems in mind Why do I still I still preserve this? All right? I only have two problems in mind that we need to do Well, at least I need to do First let's do one that I had on a quiz Let's say this is much more simplified. So let's say we have a a Somebody has some sort of Say a ball And the ball is two kilograms. Let's just put a two here and this person pushes the ball At ten meters and no not a ten meters at a with a force of ten newtons over three Three meters. I'm just using whole numbers Over three meters and Let's say I haven't done a video on on friction But if you're at the point of work and energy, you should know what friction is and the friction of the floor The kinetic friction. I think it's called The coefficient of that is 0.3 Okay, so The question is how far does it go after it's done After after the guy is done pushing it. So There are a few steps to this problem. First, we will need to find It's energy at this point because it will be increasing so we need to find the energy when it's here and Once we do that We can find the amount of pushback it's getting From the friction and we can find our distance Let's say x. Okay, so first we need We need to find the amount of friction that It's friction. So if you know how to get the friction with the friction the force of friction It's very simple. You just get the normal force of of the of the object and The normal force is basically the amount of force the floor is pushing back on the object with This sense the floor is perfectly level. We don't need to deal with any trigonometry. So So it would just be 10 Newton 10 meters per second squared because that's our gravity Times our mass which is two. So our force normal is Just 20 20 Newton's and so our force friction our force of friction that is just our force normal Times our friction coefficient. So it'd be 20 times 0.3 get that and that will equal 6 Newton's So our force of friction equals 6 Newton's And so now once we apply that Once we apply a force of friction of 6 Newton's Let me get rid of something here We know that the net force that's being applied is actually 4 Newton's When now based on this we need to find the acceleration of The object. All right. So now we just need to find the acceleration of our ball And since it's 2 kilograms I hate these boxes. Okay, since it's 2 kilograms Did I call it a box or a ball Okay, since force Since force equals mass times acceleration and our force is 4 Newton's and Our mass is 2 Then our acceleration is 4 over 2 and our that means our acceleration Equals 2 meters per second Squared all right, so we're going at 2 meters per second squared. So now we just need the time The time it takes for For a ball starting from zero and going at 2 meters per second squared to go through three meters and Multiply that by the acceleration to get the final velocity At this point to get the velocity at that point So, oh my god, I Always forget the formula. So I always just alright. So Our velocity is 2 times squared of 3 meters per second That's okay. Cuz what we want what we actually want to find is the work is not the work the kinetic energy and We have a squared in kinetic energy. So the kinetic energy is the mass over 2 Times velocity squared. So it'd be 2 square root of 3 Squared all right to square root of 3 squared. That is 4 times 3 12 I Think that yeah, I think it's 12 All right, so since 2 over 2 is 1 are our kinetic energy at this At this point right here is equal to 12 joules Okay, and since now we have this ball Let me fix stuff up. All right Took a took a little minute. Okay, so now that we know That my mouse is running out of battery But yeah, the ball is going to is being Has a energy of 12 joules and we know that it's that it's friction is pushing back with six newtons and We know that work is Equals to force times distance We want to know when this work will be 12 So, you know that the work is going to be six We want this to be 12 so that kinetic energy is completely canceled out to zero so it's so it's at a rest so Work is a work will have to be 12 Our force is 6 and our distance is unknown. Well our distance is 12 over 6 and so it'll go two meters so x will equal two meters. Yeah Hopefully you followed with me Took I took some breaks just to read my notes because I haven't visited this in a while I'm going to look for another problem. There is a sort of same-ish problem with a with a ski Person I don't know what they're called and we say you got you got some guy he's on skis and We have we have a little slope right here and He starts at a velocity of either zero or something whatever Let's say zero Gravity is 10 again and we think are Let's say our mu for this is point one The ski the ski guy. He weighs 60 kilograms Skeers that's what they're called. They're called skiers. I can't believe it. Okay at this point We have a it's mu is point two I guess And we want to find out how far he goes after he's done here so I'm not going to do this whole problem. So let's just Let's just go over the steps first He would need to find the normal the force normal of this of the ski of the ski guy That would be sign That would be no, would it be sign 30? Yeah No, wouldn't No, yeah, it would be cosine cosine 30. All right, so his normal force would be 10 60 times 10 times cosine 30 This is the gravate The grab gravity's component that way and of course, this is the this is the guy's mass So that would be its force normal And then we would also need to find the force. It's going at this way. And so it would just be 60 times 10 sign 30 All right Then we would need to of course get its friction. So it's just force normal Times point one times. It's mu force friction Okay To get its net we would just need to subtract This from that so I don't know what it would be. So let's just say, yeah, we just get our force applied net All right, and then based on that we get an acceleration and find its Acceleration at this point the guy's acceleration at this point now now the tricky part here is That it's is that we would need to just take its component Let me read this one more time see how I did it. All right, correct me if I'm wrong, but I'm pretty sure When you when you're at this point, we just need to take So, you know how the guy the guy's velocity is going to be pointing this way, right? We just want to take its x component Because all of it all of its white of the velocity This guy's velocity is y component will be absorbed by the floor. So we just want the x component of the guy's velocity All right using that we can get the x component of Kinetic energy, but it's a scalar So yeah, if you made it to this point in the video help me figure out what I'm getting what I'm getting wrong here But if you already know this stuff, you're probably not gonna watch this video anyways Yeah, so so we would just take this scalar We just take this vector to find the kinetic energy at this point. So again, it would be Let's call it Vx Vx squared times 30 that would be our kinetic energy And we also want to get it this way. So that would be 10 times 60 times point 2 Newtons that would be the way it would point That would be its force that is pointing that way I can't speak today Okay, so then we would just get this amount of joules So we would just need to do ke Equals and we would need to know what amount of work. So we get this force Right here it's f half at the bottom times Distance and that would be the distance it travels. So we just do kinetic energy Divided by that and that would be our distance All right, that was the only sort of unique one. I hate doing stuff with angles because I just take so I Get my signs and cosines mixed up and it takes a while. There is another one about a cart This one seems interesting. It's a little bit more complicated All right, I'm simplifying all this all of these problems. They have more come weirder Things so let's say we have a shopping cart and Can or a brick let's just say the shopping cart has a brick on top the brick is one kilogram and The car is 19 kilograms All right, and it's going to be rolling Down a slope of 30 degrees There's a little there's a little um Little thing right here, you know, what are those called? You know how it's how in some places they have I Want to look this up Whatever, I don't know. I don't know what they're called. But basically they're to stop cars From crack from going into places where people are walking Tell me in the comments what they're called. Please. I want to know now okay, so we're assuming no friction because I'm tired of dealing with friction and And There's a car parked right here Okay, and when when the can This car is going down and when the can hits the car it makes a dent of Let's say Three centimeters The question is with what? For Oh What is the force or the newtons that the car applies to the can? All right, so what are the steps of this problem? Obviously, we need to find the velocity at this point and we would need to take its x component So the one meter wouldn't really matter it just would stop accelerating here and would keep going with its same velocity All right, so the combined mass Of course is 20 kilograms and We just need to take the component of gravity that pushes this way and That would be sign 30, right? Yeah, that'd be sign 30 and we know that's point five and of gravity is 10 So we would have it accelerating at five meters Per second squared over 10 meters We know and since you know that we know its potential energy So its mass is 20 times 5 Times 10. This is its potential energy at the top right here That would be 50 times 20 1000 All right, it's potential energy up here is 1000 Okay, and it keeps going and it has and it maintains that velocity Till it hits here and we just need to take the x component of Of that velocity so since we know since we know potential energy is zero That would mean it's kinetic energy is 1000 so we take 20 over 2 Velocity squared 1000 I'm getting really lucky with my numbers here because I keep picking nice numbers. All right, we divide these two be squared equals 100 velocity equals 10 Meters per second at the bottom right here All right, and so we have 10 meters and this car is get push It's pushing at 10 meters per second right here. So we just want its x component and it's x and so For the x component of the velocity, we just need to take a 10 cosine 30 So so let me Do that real quick All right, that's 8.7 meters per second So it's going at a velocity of 8.7 meters per second and since this is getting cluttered I'm gonna unclutter it All right, it's going at 8.7 meters per second the 1 kilogram brick That we had our shopping cart. It's moving that way At 8.7 meters per second So there's no air resistance. There's nothing it maintains that speed and so we know it's kinetic energy now is One over two since our mass is one times 8.7 squared So I don't give us a kinetic energy of 37.4 joules I'm not doing significant figures because I forgot the rules Okay, so 37 not point four point eight All right, so it's going out so it has a kinetic energy of 37.8 And it takes three centimeters of the of the car Just to stop it so A three centimeters that's how many that's point zero three meters And so that means our Newton's times our distance must equal 37.8 and 37.8 Over 0.03 that is 260 newtons So that is what the car pushes back the brick with that is the amount of force the car pushes the Brick with so I Think that's it. I hope Whoever is watching Learned from this from this video. Yeah, that's about it. Thanks for watching