### power lecture

okay hopefully it’s recording now so the most the most common is the size motors and things like that the equation is power equals F dotted with velocity so you find the force so it’s the power of a force right you take the force and you’ve got it do a dot product with velocity you know what dot products are is that it’s the force times the velocity times the cosine of the angle between them that’s the easiest way to do it it’s just like work you know the force has to be lined up with the displacement power that court of the forces backwards and the velocity is opposite that’s a negative power so that’s removing energy power is also equal to the time derivative of work although who cares it’s rarely ever used that way now in general since I teach system dynamics as well in dynamics we’re only worried about power and it’s always force and velocity but in the in the real world you’ll deal with pumps and they don’t have force they have pressure and they have flow rate you’ll deal with circuits and they have voltages and currents and so I’m just giving you a little heads up and you’ll learn this in system dynamics in all systems there is always two dual variables one is an effort and one is a flow so in dynamics the effort is forces torques those are the only two that you’ve seen your flows are velocities and angular velocities okay once a motion and one is a push if you want to think of it that way all systems have that so in electrical circuits you have a pressure which is voltage and you have a flow which is current current is actually something moving writes the electrons moving in circuits they taught you it was positive things moving it’s not it’s the negative things that move okay but it’s actual motion just like a velocities in the case of a fluid pump you have pressures and you have the flow of the fluid okay power is always equal to the product of those two quantities so in circuits its voltage times current and in pumps it’s pressure times flow rate and you have to do unit conversions usually but it’s always that way and you can always add power you know mechanical power and the electrical power it’s all basically the same and then I think for your homework you need a unit conversion so I’m giving you the unit conversions there one horsepower 745 watts and it’s the same things 550 foot-pounds per seconds and then what I’m showing this is not in the homework but I always try to give you a you know more than what you paid for okay so for example here is a trying to show you how you would sighs a motor so on the left-hand side 1 i’m showing is this is a typical torque to speed curve or a DC electric motor and i cut and pasted the the thing so this these lines here are just lines on the paper okay so what it is is it’s a goes like this if you plot torque of a motor versus the speed speeds down here and torque is up here a DC electric motor goes like that it’s a nice straight line so it’s convenient for students to study because it’s easy to do calculations okay so let me ask you some questions if you have a DC motor and you load it up so that it barely moves so its operating right here say how much power do you have very little why you have a lot of torque you have very little velocity so at this point the DC motor doesn’t give you any power or very little what I mean if you let it go screaming like this is running almost as fast as it can possibly run you have no power there either why not no torque okay so at the extreme ends of your of your device and this happens in most devices so for example if you have a pump on one end you can say look I’m going to run the pump and it’s going to i’m going to set it up so that it gives me the maximum amount of pressure that you’ll get very little power out of it okay because typically it won’t flow it’ll give you a lot of pressure but no flow okay on the other extreme you say I’m going to let the thing run and it’s going to pump as fast as it can possibly pump it usually gives you no power because it has no pressure okay no pressure across the pump okay that’s very typical okay so there if there’s no power and they either end there’s got to be power in the middle thank you think that’s why you did motors right half horsepower motor two horsepower motor you want to get some power out of them so where would the maximum power occur how do you know okay in a DC motor it’s true that that’s exactly where it occurs if you had a pump for example your pump

curves would look something like this they will plot pressure versus flow rate and they usually use Q for flow rate and those things are typically more like curves and they’ll have a series of curves on a pump and then what they’ll do is they’ll show you powers so they’ll draw you maximum power lines like this the reason that you have multiple curves is what they’ll do is they’ll say okay this curve on the inner curve that corresponds to using a pipe size of maybe a half-inch diameter pipe and then the other curve might be for a three quarter inch diamond because they don’t know what pipe you’re going to hook up to the pub right and so what they’ll do is they make these measurements and in a case like that where they’re curved it’s not always in the middle okay so what you do is you pull up you know you buy a pump and the pump will come with I mean if you go to a rate if she’s not radioshack itself up if you go to home depot or something like that you buy a pump they’re not going to give you the spec sheet but if you but if you’re doing an engineering job and you’re going to buy pumps and you’re going to specify pumps for something it will come with a data sheet right and the datasheet will give you a pumping curve and you look at the pumping curve and that will tell you where the maximum power etc is okay so what I did here and we’ll kind of skip it because it looks like you guys are kind of catching on quick over here what ideas I’d arrived where the maximum power occurs so all idea is I said power is equal to torque times speed I took a derivative of it set it equal to zero and comes out to be for DC motor it’s at one half speed so you’re going to get your maximum power when you run your motor at half speed make sense okay all right the other thing that you’ll need for your homework is what efficiency is efficiency is the power that comes out / the power that goes in that’s efficiency okay ready to do some problems all right let’s do some homework problems okay an automobile having a mass of two mega grams travels up a seven degree slope at a constant speed of 100 km/h if mechanical friction and wind resistance are neglected determine the power developed by the engine if the automobile has an efficiency of point six five okay what are we going to do how we’re going to do this why am I going to do a free body diagram right what I’m what I need is I need to know what is the force is pushing this guy up to the incline that’s what I need right and then what I’m going to do is I’m going to say okay if I have the force that’s coming from the engine what I need to do then is multiply it by the velocity and I get the power makes sense so I’m going to get the force from the engine what’s driving it up the incline i’m going to multiply it by the velocity that’s going to get me the power that’s coming from the engine okay and then i’m going to use the efficiency and say if that’s the power i’m getting coming out because that’s what’s driving the car how much power is going into the engine i’m going to use the efficiency that make sense okay so let’s do that let’s do a free body diagram of the car here’s the car what are the forces acting on it normal okay so let me let me draw in a dashed line here this is the that’s the slope seven degrees so this angle right here is seven degrees all right so the normal what else you got yeah says OMG okay good what else you got do what yeah and where does it come from by the way this is just the pier where does it come from I mean it comes from the engine right the engine twists a driveshaft the driveshaft twists your differential differential twists the tires and somehow that pushes you forward where’s it coming from friction underwear or where where’s the friction from the tires now it says no losses right doesn’t say no losses they didn’t say no friction if you had no friction if this thing was ice your tires would spin wouldn’t he right they would spend you’re not losing anything I agree you’re not losing anything but the tires are just spinning right are you going to go up the incline no okay so what you have is you’ve got friction between the

tire and the asphalt the tire in the asphalt right is it slipping no that’s what would give you a loss as if you punched it and you spun the tires that’s what will give you a loss because you don’t you’re burning rubber you’re you’re melting the rubber you see that so just because they say no losses doesn’t mean you have no friction you just have enough friction to wear the tires don’t don’t slide don’t skid make sense okay so what’s happening is the engine is turning over it’s turning the drive shaft drive if it’s rear-wheel drive I have no idea driveshaft well at front wheel does same thing right okay turns the drive shaft the drive shaft turns a differential the differential then rotates your dark puts torque on your tires and the friction between your tire and the road resists that torque and that friction is what propels you up the road okay makes sense okay so you’re going to have a force like this we’ll call it f that’s coming from your engine and ultimately it comes down to the friction that’s on the road right and because you’re not you don’t have any losses I’m not losing any energy you remember the bowling ball example that I gave you right and I showed you that you know if you’re straight like that you know there’s no well what is rolling friction remember it’s the deformations right yeah so like in the case of a bowling ball you’re bending the wood underneath the bowling ball right in the case of a wheel barrel right you’re pushing down the mud that’s why it’s harder to push on mud than it is on the concrete you remember that so this is same thing kind of this happening here okay so you’re not losing any energy from squashing the tire well that’s kind of hard to believe but ok it’s just homework problem any other forces on this no okay travels up the slope at a constant speed so what’s the acceleration so you’re okay can you find the force how you gonna find the force okay very good yeah well what we what I’m going to do is I’m going to some forces in the update incline right and you’ve already done it in your head you’ve got the answer no problem with that okay I’m going to go ahead and sum them up the incline is going to be the positive direction so we’ll say this guy’s plus X and what i have is f minus mg is a sine or cosine I don’t remember is it a lot or a little should be a little right so just kind of a small slope sign of seven is a lot smaller than cosine of seven so it’s probably the sign you can also draw a line or a triangle sign of seven degrees equals what mass times acceleration up the incline how much is zero okay so you can find F F equals mg sine of seven so you got that number what’s the power what’s the power that’s delivered to the car what’s the definition of power very good force times velocity so what’s the velocity oh it’s 100 km/h okay so the power the power equals em gee sine seven times 100 kilometers that’d be 100,000 meters per hour 3600 seconds I think I did the unit conversion right isn’t that meters per second huh where’s the dot product okay which way is the force straight up the incline which ways the velocity straight up the incline what’s the code what’s the angle between those two see zero degrees what’s the cosine of 0 1 so it’s the magnitude of the force magnitude of the velocity times the cosine of the angle between them so which is one good point keep me honest okay so that’s the power that’s the power that is being used by the automobile that’s the power that’s coming out of the engine right what is efficiency efficiency is point six point six point six five is the efficiency that’s equal to what power out / power

in the power in is always bigger than the power out otherwise we’d be creating energy and we’d be selling that and we’d be making lots of money we wouldn’t need engineers okay right so the power out is always lower than the power in you put more in because it wastes up okay so power out how much is the power out it’s that number right there on the diagram right so I’m going to call it P that’s a power that comes out of the engine because that’s what goes into the car right / the power in so how much power is going into the engine could you find it I think so right so it’s it’s this number p / point 65 that’s the power that goes into the engine okay let’s talk about this is this a hard problem what was hard about this well by the way let’s back up how do you know it’s a power problem well okay yeah but I can give you efficiencies on every single problem on the final exam yeah it says determine the power developed by the engine ah you need power it’s a power problem that’s the only reason to do a power problem okay because you know you can do all the problems well I should be careful you can’t do all the problems using power but you can you do a lot of them using power but it’s really complicated and it’s mind-bending and confusing you don’t want to write the only reason to use power is because somebody wants it and why would anybody want it well I’d like to know how big an engine do i need to drive this car up the hill at 100 kilometers per hour right how big of an engine do i need well how much horsepower do I need right so that’s why I would want to do it you’re going to have a senior you’re going to be successful I know it and you’re going to get to senior design and about half of you are going to build you want to get a motor and put on something to make it do something half of you will and you’re going to come to me and say how do i sighs this motor and I’ll say did not teach you about power that’s how you’ll do it right you figure out what the power is that you need to drive your car up a hill throw in a safety factor because you’ll say well I’ve got friction and you’re going to say I need two horsepower ok that’s the motor you need ok got it all right so how do you know it’s a power not because I gave you an efficiency because I think I’ll do that on everything problem final because it says what’s the power that’s why you use power because you want to know the power that’s the only reason questions you want to another power problem yeah that is the power that is required to drive the car up the hill right that’s the power that car needs to go up the hill and how do I know it’s that way well because they told me there are no losses because if the car had wind resistance and friction and had a loss it would have an efficiency as well I put this in but I wouldn’t get this out why well because you know for example you know if this is what goes into from the engine goes into the car but the car has some losses then the car is not going to give me the output the same that went in it’s got an efficiency what does that mean it won’t go it was fast up the hill that’s what it meetin’s right because the power out would be the this force times the speed and if this is what goes in and let’s say it’s fifty percent efficient you have a fifty percent efficient car because you got friction in the bearings you got you no rubbers squash in whatever it is right we resistance your kids about the hands out the window you know whatever right that’s causing an inefficiency so let’s say it’s fifty percent efficient then I put this power in thinking I’m going to go 100 kilometers an hour rod right but i only get half of it coming out and being used by the car to drive it up the hill right well i get the app yes you’ll get the app where you get the speed no you won’t get the same speed it’ll go slower makes sense right just like back here on the southern right here come on right here you see what will happen is if this is your cut if this is your car engine right here that’s your car engine okay you need it’s got some in efficiencies you need this much force to drive up the hill you have to have that or it won’t go up the hill then what will happen is based on the on the energy or the power you’re going to get a certain speed right so if you have an inefficiency in

the car you’re going to deliver the power from the engine some of that power is going to be wasted in their losses and what you’re left with is force times velocity that will drive you up the hill that’s what’s left over you’ve got to have the F or you won’t go up the hill so the motor will slow down right according to the curb the motor will slow down so until it gets the force that you need and when it gets the force that you need whatever that speed is is the speed you’re going to go up the hill right does that make sense right you throw in a bunch of friction on the car make it less efficient it’s not going to go up the hill as fast right understand is it possible that you need more force than your motor can provide yes try riding your bicycle over transmountain maybe you can do it can I not maybe more for not anymore it’s a combination too much mass and hot enough force right get the idea okay you want to do another problem yes it says it was km/h and I wanted it to be meters per second gosh yes the masses to mega grams or empty so that would be two thousand kilograms so yes my my okay so this this F right here is that the is that the force in or the force out that’s the force I need to drive up that’s not power okay this one okay what is his power can you help him he’s asking what is that power look what I’m taking the car right I’m saying this is the force that the car needs to go this fast up the hill isn’t that the power that the car has to have that’s the power that goes into the car how much of that power is lost by the car no no the engine which is sixty-five percent so you got you let me draw you a kind of a diagram what you have is you got an engine here and you got gasoline going in the gas has got power or energy right and it goes in a certain rate and you know it’s burning at a certain rate so there’s your power its energy per written it / time so there’s your power going in how much comes out I’m going to call it P Prime that’s how much comes out okay it comes out of the engine where does that power go go right it goes to the car goes to the drive train goes to the gearbox it goes to the everything that’s connected up to those tires making it move is there any fishin see in the car you bet you there is but this problem said to ignore that didn’t it it said ignore all the inefficiencies in the car it said to do that didn’t it so if i have p prime going in how much do I have coming out p prime whatever goes in is got to come out or else it gets turned into heat gets turned into other forms of energy I can’t destroy it but it’ll get converted into other kinds of energy okay now what is this this is what I need to go up the hill isn’t it did I lose any in the car okay then this this guy right here is what comes out of the engine you agree what is P prime key isn’t that p that’s the power I have to have to go up the hill that’s the power I got to have to go up the hill and because the car is a hundred percent efficient that’s what I need going into the car coming out of the engine I need that amount coming out of the engine if that’s what I have coming out of the engine and the engine is sixty-five percent what do you got to have going in you got to have more p prime divided by point six five let’s change the problem a little bit let’s say your car is eighty percent efficient okay your car’s eighty percent efficient got it what

what does that mean right eighty percent efficient okay what that means is well it’s not point eight okay it’s 80.8 that your efficiency point eight that means that power out of what what’s the efficiency of the car okay power out of the car / power in of the car is point eight what’s the power that comes out of the car exactly this is the power that comes out of the car that’s the power that comes out of how do I know because they score i watch it it’s going up a seven degree hill at 100 kilometers an hour that’s the power that’s coming out of the car I can see there goes man right or argue with me if it’s not is that the power coming out of the car okay what is being delivered to the car it’ll be the p / point eight that’s what’s going into the car right so what’s going into the engine p / point 8 / point six five that’s what’s going into the engine makes sense if not I don’t know what to tell you you look like you disagree so argue with me or wake up no Neelix he looks like no man you’re lying to me yeah let’s do another problem does this make sense you have to just remember where is it going in where is it coming out what’s it equal to and back yourself back up I don’t think their heart is just confusing don’t you agree they’re just kind of confusing the units are watts power is energy per time so for example it you know we think of horsepower right carb car people take a horse power and that is a special unit it wat is a Newton meter per second is a watt right so wat yeah jewel okay is a Newton times a meter divided by a second newton meter is a jewel I don’t know how specific you want a jewel is a Newton meter so if you have jewels you know code but they’re baked the basic units for power is Force Times a speed so it’s nutan times meter per second it’s pound times foot per second and then it you know horsepower is a conversion off of that etc so it’s forced out of speed is the unit the basic unit for a power okay how about this one oh man come on okay elevator eat and it’s frayed have a total mass of 400 kilograms hoisting is provided by the motor and the 60 kilogram block b and c if the motor has an efficiency of point six determine the power that must be supplied to the motor when the elevator is hoisted it upward at a constant speed of for all right is this a power problem how do you know because it says find the power okay that’s how you recognize it’s a power problem okay I don’t know of anybody that uses on purpose uses power to solve dynamics problems the only time that I know and yeah I don’t know everybody in the world okay but the people i know they’ll use the others because they’re easier to get the solution but if somebody says i want the power okay then this is a power problem okay so how am I going to do this power problem see what’s what’s happening it’s going to go a constant speed they give me the speed they want to know the powers that goes into the motor okay so here’s the diagram here we go what are you going to do why a free body diagram so mass is

almost certain what is it I want I want power okay power is equal to force dotted with speed now they told me the speed right so what do I missing the force that’s why I’ve drawn a free body diagram because I want to know the force and the only way i know to get forces is draw free body diagram and some horses you know another way okay what force am I looking for the force between the crates and the in the elevator the force and that cable on see you want that or what force really what’s the motor pulling on it’s pulling on the rope isn’t it that you see the Rope between these pulleys this rope let me right here isn’t it pulling on this rope right here so really what I want is I want that tension because that’s what the that’s what the motor is pulling on he’s pulling on that and he’s pulling it in at a certain rate isn’t he okay so what I’m looking for is I’m looking for what’s the tension in the cable and how fast is that rope going in the elevators moving for but how fast is the Rope moving got it so those are the two things I want how hard am i pulling on the rope and how fast is that point moving got it okay how do you going to find the tension in the cave I’m going to draw a free body diagram that’s what I’m going to do ok so what free body diagram do you want what do you want in the system how about I do something like this i’m going to draw a circle around here won’t cut it like this everything inside everything inside the circle is in my free body diagram so good I’ve got two masses inside there so if I have accelerations I’m in deep trouble right because I’m going to have to take the EMA and move it’s going to be a little ugly do you have any accelerations I’ll thank goodness ok this would be an easy problem in all right so let’s some forces ok what forces do I have to draw mg of what of the system can you help me is it mass c or messy huh I could do to free body diagrams if it’s easier for you will do to free bodies right you say ok there’s an elevator and there’s a seed you want to do that ok we’ll do that then all right hey you asked for it man or I can do both i’ll do i’ll do both but here I’m going to do this one ok now is that one easier ok let’s you no great matter has to ok let’s draw that free body diagram what does he look like ok MC times G and attention will call it t 1 because the Rope one and then I’ve got the elevator right you’re gonna let me get away with that didn’t I teach you anything what do you say when I do something stupid like that hey stupid maybe not like that but why is that stupid no why is that stupid that force doesn’t belong in there why not it’s it’s outside outside is the e inside the free body that you wanted me to draw no he’s outside and he’s between what the earth is the earth in there that force does not belong there right you know this don’t let me get away with step okay let me erase it that’s the free body diagram you agree okay don’t let me get away with that okay let’s do the other free body diagram too I think somebody had quite you have questions yeah that’s what I was going to do they not be edited well I think what it does is it eliminates i’m not sure what

advantage you would have but that’s what i did it i didn’t at home i did like that i put a boat together you know if you know what he’s saying is hey it makes sense to me to put them both in there that that’s fine and i’ll show you how to do that otherwise you separate them out you say that’s why deal with the complexity well then separate it out okay let’s do the other free buddy right here we go what mg goes in this one the elevator why not see because it’s outside outside right so always been that way so this is mass of the elevator times G okay now on this guy what else is uh is in there right let me uh let’s see i’m going to i know you all told me not use yellow but this the only but well let me see if I can get a red pin come on yeah there we go red okay so now we use a will use right okay so I’m going to circle this guy right here that’s the system so what other forces do I have in here yeah i have i have t1 i have how many of them one right there ok so a 1 T 1 what else do I have I have one two three we just call them tease is that ok ok how many unknowns here do you know t1 you do how do you know it okay was it given I don’t think it’s given yeah but what you’re thinking is you go to some forces right okay fine so don’t count that equation then because you’ve already used it to get t1 right so either count the equation and count the unknown or you don’t count either one ok how many here TD no T no ok so can we solve them ok t1 is what do it in your head he did it he did it in his head what’s t1 tension is always equal to the weight right tension is not always equal to the weight tension right some forces minus MC g equals mass times acceleration what’s the acceleration in this case in this case zero ok now when it’s zero acceleration that’s when the tension equals the weight ok so you know t1 right you know t2 excuse me t 3 t plus t 1 minus mass of the elevator g equals zero can you solve for T ok so now I’ve got T now all I need is the speed of the rope how am I going to find that rope equation right how many degree afraid I should count in this first how many degree freedom is it okay just because I look at you weird doesn’t mean you’re wrong right it means make sure you’re right you know one degree of free to apply because the elevator can move right okay count one hold the elevator still can anything move without breaking okay one degree of freedom what does that mean means if I give you one dot you can find all dot you want well not a triple dog right but you know right it’s been a whole semester okay are you giving a dot yeah the elevators going up at fourth okay then I need to relate one to another how do you relate them special points is this a special point problem is this a vector Luke problem what is it it’s a rope ok so what rope you want I see two ropes which one you want to use yeah the one that’s got on the motor right that’s the only one I care about okay can you write the length of that rope length of the Rope equals you tell me I’m going to shut up you tell me what it is what’s the length of the rope 3x m.e what Sammy ok so the distance to the elevator will call it x XE it’s a good everybody ok so the distance from the roof to the

elevator will call it XE now what’s the length of the rope three of those plus or minus some constants right ok 3x e take a derivative plus a bunch of constants you’re right plus a bunch of constants take a derivative what do you get don’t tell me 0 equals is l constant it is the Rope the Rope is being pulled in right so I don’t know it’s held on equals 3 what’s this guy what’s Vee loss of the elevator do I know it what is it it’s for so l dot is 12 so what does that mean well actually I should do this like this right l dot is XE is a negative this should I should write it like this x e dot take the derivative 3x e dot what’s XE dot it’s the magnitude is for is it plus or minus is XE getting bigger or smaller smaller what’s going up right so this guy right here is a minus for isn’t it okay so this is a negative 12 right the l dot is negative 12 is l getting bigger as hell getting smaller and smaller you knew that right ok what’s the power power of the motor power coming out of the motor it’s the force times what philosophy and what’s the speed that I’m going to use what’s it pulling on the rope how fast is the Rope moving here’s a little red dot on the rope okay let’s draw a little red dot there’s a little red dot right there what’s the force on that dot T right isn’t it t how fast is that red dot going for or 12 he’s going 12 ok what’s the power at that red dot T times 12 right that’s T times 12 so what’s the power coming out of the motor t x 12 so the power out is 12 t what’s the power going into the motor I have efficiency of what point six okay so point six efficiency equals what is it in or in / out out over in out 12 t that’s what comes out of the motor what goes into the motor pn can you find pn now is the hard problem or just kind of confusing it’s confusing it’s not like the numbers are hard but what you have to do is say well look you know what’s the motor pulling on the motor is pulling on the road all right I want what’s the tension what am i what force am i applying and how fast is it moving not the elevator right not the elevator I want to know what’s the what’s the power from them from the motor so what’s the motor pulley and how fast how would I do with you of the entire thing yeah I think if you do you end up with an extra unknown with a tension on this guy this is what I was going to do this would be a mass of the elevator G and mass of the sea G and then I would have a tension one and three tensions up right my mistake that won’t give me I need to Dupree potties when I did it at home I did it in my head and it didn’t work obviously when I write it down so clearly I was wrong everybody makes mistakes especially we but if I did that I would suddenly just like it is now say whoops too many

unknowns T in p1 and then I said well okay I’ll drawn on the free body diagram and I would have been embarrassed like I mm okay no we’re finding the velocity of what telling what we’re why the rope attention yeah because you know if I’m looking for the power of the motor I said well what’s the motor doing he’s pulling on the rope and how fast is he pulling the rope I don’t care about the elevator yeah another way to do it would be to come in and say okay I tell you what I want the power that’s going into the elevator well what’s pulling on the elevator one two three right and then this guy but then you’ll notice that the energy it’s kind of confusing but you go one two three tensions and what’s the velocity four so I have three key times they’ll be the same power but I think that’s more confusing yeah well why did I get a negative 4 what’s XE XE is measured from where to where and isn’t that a positive number right there ok now when I take a derivative which I did here I was getting sloppy I was trying to do in a hurry want to take a derivative right here it’s x e dot right ok so then I ask myself is xe getting bigger or smaller elevator is going up so X he’s getting smaller right that’s why i put in a minus 4 and what do i get negative 12 well was the negative me well l dot is a negative 12 is l getting bigger or smaller smaller so it kind of works out but you don’t need the positive negative you just because the guy is pulling on this way right he’s pulling up and he’s coming up isn’t he so he’s doing positive power and you can see I was sloppy I was just going to say 12 and I thought I bet you they’re going to catch me on that one so I went back and slowed down and said it’s really a negative 12 right because the Rope is getting smaller but what’s happening i’ve got this dot I’m the motor I’ve got this this red dot on the rope and I’m pulling it up and it’s coming up so I’m doing positive power does that make sense right I’m doing positive power so do whatever you need to for the pluses and minuses but you’re putting in power okay know if you want to slow something down you’re going to take power out of it right so you got this Mack truck and I want to stop it so I’m going to push on it right hope it doesn’t run meal and we’ll push on it and it’s coming at me and I’m taking power out of it friction wind resistance take the power out that’s a negative power engine braking takes power out of the car right I guess it eats it up in friction I’m quite sure where it goes I know what it is I’m not the head and thought about where it goes i guess it goes into the downshift and you ease the clutch out so you burn it up your clutch ok any other questions about power okay that’s all I was going to cover all I was going to do now is just review so if you’ve got a question you got something that’s bugging you for the final let’s just let’s talk about it you

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