 I forgot to record this morning. So we are looking ladies and gentlemen at power. Now the problem is power is also a word that's used in English quite a bit. In fact, what happened on Tuesday? We often use the word power interchangeably with electricity. It is not interchangeable with electricity. The word power is used in a variety of ways but in physics power is the rate at which work is done. It's how fast you're doing work or the rate at which energy is transformed. That's what power is and it's a scalar. It has an equation. You'll get this equation on your formula sheet. Power is defined as work over time where work could be force times distance where work could be the area under a force versus distance ground or where work could be change in potential plus change in kinetic work. The units, well it's technically a joule per second because work is joules and time is seconds but we've given them out of special names. Anybody know what measure power in? What? What? What? I'm never going to get tired of that. Sorry, three more days of that boys and girls. Yeah, we call this a watt. It's the bad jokes that are the best joke. Name Dr. Scientist's last name was? What? Okay. A 60 kilogram girl runs up a flight of stairs 3.32 meters high in 2.6 seconds. A, what's her power output in watts? Okay. Power is work over time. Spencer, how much time? I agree. Work is what times, well it's force times distance. It's the area under a force distance graph. It's change in potential plus change in kinetic. I think NAV though we can simplify that a little bit. I think here when we're talking about which force are you resisting when you go upstairs? Gravity. I think this is actually going to be MGH. She's gaining potential energy. Where's that energy coming from her muscles? The food that she ate. This is going to be 60 times 9.8 times 3.32 divided by 2.6. 75.1? 0.1. What? Let's talk about what this means. 751. Sorry. That makes more sense to me. I was going that seems awfully low to me. 751 watts. Never trust Spencer again. Chris, let's talk about what this means. Supposing somebody heavier tried like an overweight person tried to do the stairs. Will they find it easier or tougher? Because it requires more power. Or let's suppose you were running the stairs but Justin you wanted to run it faster. If you ran stairs faster would you be more tired or less tired at the top if you ran them faster? And if this number was smaller what would happen to the overall answer? Bigger or smaller? I don't know if you remember when we talked about work I went on a big rant because I said people think that work is how tired your actually power is tiredness. If you're generating more power you're getting tired faster. Rob, this is why little six and seven year old kids have so much energy on playgrounds. Their mass is so small. Most of you buy now because most of you have hit your growth spurt. Way two, three or four times as much as a six year old. And it means that if you're trying to keep up with your little nieces or nephews or cousins or brothers or sisters you're having to generate three or four times as much power. You're getting three or four times more tired. It's not that they're in better shape. It's that you're having to generate way more power to match the amount of power they require. That's why those seven year olds can go up and down that playground nonstop for four hours. It's easier for them. They're not having to burn as much jewels per second. In fact a 60 watt light bulb, which is your standard light bulb, burns 60 jewels every second. 120 jewels in two seconds. You figure out how much you burn and how much energy in a minute, how much energy in an hour, power. Nice one to one ratio. Now the person who the unit is named after, James Watt, was a British inventor. He didn't invent the steam engine but about 200 plus years ago, he dramatically improved it. He made it safer and way more efficient. And so now if he was trying to sell the steam engine in particular, he was trying to sell it to farmers. He figured that he had a product that could really make their lives easier. The problem is none of them knew what a steam engine could use for and so he made a brilliant advertising move. Instead of measuring it in jewels per second, he created a unit of power. He called it the horsepower. He said this engine is five horsepower. What he was telling the farmers is this will do the work of how many horses. That was a nice easy measurement for them to use and a budget and figure out whether they could afford it or not. Brilliant. In fact so brilliant that the horsepower is still in use even though none of you know how much work a horse can do in one day. I'm sure 150 years ago every farmer knew how much work a horse could do in one day. Oh, five horsepower motor. That'll replace five of my horses. I can get the hay bale that much faster. Excellent. Now, but we still use it. Where do we use horsepower? Yep. One horsepower is about 750 watts. So this girl is generating approximately one horsepower. What's an average car motor? Does anybody own a car and know the horsepower of their motor? If you have a four cylinder especially like a little Japanese car or whatever or an import probably about 120. So if you want to know how many joules per second on your calculator right now go 120 times 750 to go from horsepower to watts. Okay. Now that's the maximum theoretical output of your motor. You're never getting that much into turning the tires though because engines are not 100% efficient. Can you hear a car from a long ways away? Sound boys and girls. When you touch an engine with your hand what do you feel? Lots of heat. In fact internal combustion engines terribly inefficient. Much more efficient electric motors. You guys are probably the generation probably sometime in your lifetime CNN or somebody is going to do a story. Today marks the first time that more electric cars were sold in North America than internal combustion engine cars. And then a few years after that today marks the first time that there are more electric cars insured on the road than internal combustion cars. Probably in your lifetime. Unless they come up with an even better more efficient way to move stuff around. Come on Mr. Dick. Next one. Come on Mr. Dick. How long would it take a five horsepower motor to lift a 500 kilograms safe up to a window 30 meters above the ground? It can only do this so fast. There's only so much power to go around. Well the first thing I should do Andrew I think is the power here is five horsepower. We need to convert that. What do we need to convert it to? What? What? Okay I'll never get tired of that joke sorry. So we're going to go times 750 watts is the same as one horsepower. How many watts of power does this particular motor in theory give us? Five times 750, 30, 750? Yeah. Brandon what's this question asked me to find? Call me silly. Power equals work over time. Bye Janet. Justin how would I get the t by itself? Yeah in fact stuff moves diagonally. I think we can say the time is going to be the work required divided by the power and the power is going to be 3,750. How much work do we need to do? Well what force are we going against according to this question if we're lifting a safe up? You know what I think the work is going to be technically giving the safe some potential energy. Mass, G, H. What's the fastest possible that we can get this safe up to the window? And it doesn't matter how hard you press the throttle or how much you floor the engine this is as fast as it can go. Zay what'd you get? Oh never mind. Sorry. Hesham what'd you get? Oh it didn't. Oh you did 39.2? Even if you want to go faster you're stuck. The only way you could go faster is you get a higher horsepower or a higher wattage motor, a more powerful motor. So we said earlier that power Robbie is how tired you get. All right this is why ramps work so well. How do we ever help somebody move their house and move furniture? How do we ever lift furniture into the back of a vehicle? Okay it's much nicer if someone rents a truck that has a ramp. I mean no matter what you're still raising that furniture the same amount of height you're still giving it the same amount of potential energy but a ramp lets you take a longer time which means smaller power required you notice fatigue. Lifting it straight up means we're doing it all along and that's why you get tired lifting things straight up. Ramps are not energy savers they're power savers. They don't get this tired. It's why stairways if they're shallower even though they take longer to walk it's because they take longer to walk. The backfield stairwell is a classic example. It's a nice shallow stairwell you can't do it really really fast but you're really not that tired when you get to the top of it where if they've done that as a normal stairwell where the stairwells are about a foot long you'd be happy to put them up in about time you get to top it most of the time. Yo hustle back please. By the way there's another way to think of power. Power is work over time and Cassidy work is what times what. So that's what I wrote right here. What I'd like all of you to do is actually carefully circle the D and the T like that just to make them stand out. Courtney what's distance measured in? What's time measured in? I think what I've just circled is meters over seconds or meters per second or what's measured in meters per second? Teach them. As it turns out this is also I'm not going to give you that that doesn't show up on the formula sheet Rob it's implied well work over time is force times distance over time is force distance over time just emphasizing that every once in a while you'll get a question and it starts either tells you how much power and it asks you to find a velocity or a force or you'll notice it doesn't give you a distance or a time which defeats much of the force times distance over time I bet you there's a velocity in it somewhere. So a second definition of power force times average velocity and we'll be coming up to one where that becomes important in a bit. I've used the word efficiency a few times today I've said that internal combustion engines gas motors are very inefficient they are so let's look at how we calculate efficiency efficiency means how much bang do you get for your buck or in other words how much useful work is done as a fraction of the total work done how much energy do you get out compared to the amount of energy you put in it's usually expressed as a percentage now I actually didn't know this the first few years I was teaching physics 12 when I was teaching physics 12 I was always taught that the abbreviation for efficiency was EFF or efficiency and then I learned that there is actually a letter it's the Greek letter eta which looks like a lowercase n with one longer leg you can use that in my notes in my answer keys I think most of the time I just wrote EFF for efficiency but if you want to you know nerd out go ahead and use the eta symbol it's usually used to represent efficiency efficiency is defined as how much work you get out divided by how much work you put in times a hundred percent to make it a percentage w out divided by w in oh I know what I can do w out divided by w in Tyson looks at us says wad over win hot no or power out divided by power in energy out divided by energy in or well I'll write those three for now Brendan I don't actually remember any of those what I do is if they ever ask me for the efficiency of something I remember the universe that I live in in our universe we can never be 100 efficient we're always losing some energy if you're doing an efficiency question and you're telling me that your answer is more than 100 efficient if you're right you're winning the Nobel Prize in fact if you invented something nav that was more than 100 efficient we would name a unit after you the jassel it would be there and you know when we talk about scientists we would talk about Newton and Einstein and jassel fact you know what if you did actually invent a machine that gave us more energy than we put in we would actually talk about jassel and then Newton and then Einstein because you would have invented a perpetual motion machine you would have solved the energy crisis and if we solve the energy crisis with a bit of ingenuity we can translate that to any other crisis you want to grow unlimited food if you get unlimited energy I'm pretty sure we could find a way to grow lots and lots of unlimited food trust me but sadly nav that's not the universe that we live in now if you do invent a machine that's more 100 efficient when you win your Nobel Prize please mention my name I'd like to thank my physics teacher for telling me that this couldn't be done hey do it in your face I'll even live with that okay that'd be good by the way the reason I'm saying that is because you'll notice in the equation I gave you Alex I used out over in out over in outward there is one question I know which one is coming down in the future where just the way it's worded the word out appears in front of the thing that's the in and the word in appears in front of the thing that's the out and you're going to be so tempted to tell me that this machine is 180 efficient and I'll write next to that no Nobel Prize for you so you know what I remember I really remember this smaller number over bigger number because that's my universe a typical household light bulb transformed energy at a rate of 60 watts however most of the electrical energy unfortunately is transformed into heat instead of light in fact in the 60 watt bulb about 57 watts go to heat and only about three watts go to light an incandescent bulb is only about five percent efficient now that has led to some bad science I've been putting this on the internet record right now I believe in January our government is telling us they're going to phase out incandescent bulbs I think that's coming in January all you're going to be able to buy in stores are those screw-in fluorescent ones because somebody who has a bad physics background working for the government said oh if I can make the bulbs more efficient that'll save us energy here's the problem are most light bulbs outside or inside think about inside so when you turn a light bulb on inside is it giving off heat yes but that heat is being captured by your house in fact your household heating bill goes down by exactly the same amount of heat that that bulb gives off there's no energy loss or energy savings it's more energy going to the bulb but less energy and most of the electric heat is more less energy going to your heating bill swapping the bulbs isn't going to help at all now it will help for outdoor bulbs do we have very many incandescent outdoor bulbs first of all road bulbs what are those are those incandescent no those are all fluorescent ones right we have very few incandescent outdoor bulbs those ones I do agree when you flick those ones on you're losing a lot of energy into heating up the planet but that's not very many of them now someone who understands a little bit of science that still has a bad physics background might counter my argument and now they might say mr. do it what about in the summer in the summer when you turn a light on that's heating up your house and I know in the summer you don't want to heat up your house now you're spending energy to cool your house surely you're not saving or breaking even then we live in the northern hemisphere in the summer are our nights longer or shorter way shorter do we use bulbs anywhere near as much in the summer compared to what we do in the winter I'm not so sure for a northern hemisphere country but this is going to help us at all in fact I'm pretty sure we're going to end up losing a lot of money because the fluorescent bulbs are more expensive to make and they cost more energy to make and they all contain mercury which means they're a pain to dispose of LEDs but I bet you those are five years away because right now they're 50 bucks a bulb Jessica I'm a scientist there is no way I'm spending 50 bucks on a bulb in fact you know what I'm going to be doing this weekend I'm going to go into London drugs and buying about 60 light bulbs I'm going to clean up the stock and I want to see if I can last for about a year because the incandescent ones I'm not a big fan of okay hey when you guys vote get it changed or I agree with Jessica once the price comes down LEDs are the future because they require almost no energy and they don't get very warm I agree that would save energy I believe but replacing incandescent with fluorescence if they're indoors you break it even right now you're heating up your house with them in fact I was going to say girls but maybe boys we are in the new millennium girls and some boys you may have owned a toy that baked with a light bulb some of you know easy make up yet see but again you were breaking even you were getting work out of that extra heat sorry there's my end of rant example three a 250 kilogram mass is lifted at a constant speed of two meters per second for a distance of 12.5 meters hey find the work done okay um we're lifting work equals force times distance did they give me a distance yeah okay I think we can use which force when we're lifting something in fact Ashley I'm going to argue that this is really just the change in potential energy mgh how much work was done 250 times 9.8 times 12.5 what'd you get give me the whole answer because I'm going to use this for part b and c then I'll do my six sig figs 30625 and since they also want this answer I'll go 3.06 times 10 to the fourth karson units jewels with authority work jewels spencer what's part b want me to find power is work over time which is force times distance over time oh wait a minute we figured out how much work didn't we how much divided by how much time they didn't tell me betcha that means chris I can probably figure it out let's see what else they told me now I know the distance that we lifted it for was 12.5 meters yes I know that my initial velocity is two oh wait a minute in fact spencer what did I just underline what's that tell us I think that tells us this d equals vi t but no plus a half at squared because a is zero yes simran how would I get the you said we want to find time yeah how do I get the t by itself simran 12.5 over 2 you know what I think I can divide by 2 in my head I'm pretty sure 12.5 divided by 2 is going to be 6.25 a two times table even I can do tyson I think I'm going to put that 6.25 here how many watts of power is this motor putting out units what what by the way hope that's also a stupid dumb way for you to remember the unit right I mean you know whatever works right random what's c want us to find find what okay now here's what we said efficiency is how much you get out divided by how much you get in what I really said it's always going to be the smaller number divided by the bigger number what number did they give us in c 10 kilo kilo is uh what 10 000 watts okay you know what the efficiency which is that lovely greek letter right there is going to be we got 4900 watts of power out but the motor claims to put out 10 000 watts of energy of power I think you get 0.49 or 49 percent efficient or the other 51 percent of the power of the energy go sound heat mostly those two basic one is the hotter a motor runs the less efficient it is later on this year you'll find that one of the reasons we like electric motors is the faster they run the colder they run in other words electric motors are at their most efficient when you're flooring them our car motors that they're most efficient when you're flooring them new yo what's the most efficient like type of motor I don't know that's a great question I will ponder or google it but I will ponder because even even among electric motors there's various designs and they're still tweaking those all the time as well the latest one they're talking instead of having one electric motor because you also lose energy sending the current through the wires to the tires or through the gear system to the tires somebody had the bright idea of saying why don't I put four small motors one on each tire oh yeah and boy you probably need a much smaller gear mechanism you just need a computer to control it all but that we can do for cheap so look for those down the pipe saw that about three years ago when in a prototype example four a mass of a hundred kilograms is pushed along the floor at a constant speed hey rob what am I going to underline darn right of two meters per second if the coefficient of kinetic friction is point two five what's the power output well power work over time work is what times what work is what times what I think work is force times distance over time does this question mention a distance no does this question mention a time nope what does this question give us two things what well three things a mass what else ah you know what I hear Jessica I think I am going to do that work sorry power is also force times velocity what velocity Jessica how big two what force ah here is my mass what are the forces acting on it the obvious ones mg down absolutely what else normal force what else well something must be pushing it forwards I'll call that the applied force what else now what can you tell me about the length of my friction arrow how long should it be exactly rob why constant speed means we're in bounce so over here what I should really write underneath the f is f applied times v but I can't find f applied oh but look look look look look I know another force the same size as f applied what rob and for some reason that aren't all wonky and we didn't let's try that again so if I hear you power is going to be friction times v rob friction is what times what I don't know the normal force oh but look look look look look look and another force same size is a normal force what this is going to end up being mu mg v how much power does it take to push a hundred kilograms at a constant speed of two meters per second with friction of point two five coefficient point two five times a hundred times nine point eight times two uh okay this in my head maybe uh hundred times nine point eight is ninety half of uh do you get four hundred and nine yeah four four hundred ninety four thousand nine hundred four hundred ninety four hundred ninety every second using four hundred ninety joules which is why it's four hundred ninety watts of power is that a lot I was riding my exercise bike the other day and I noticed it had a setting for power in watts so I clicked on it after riding for about half an hour I put out about a hundred watts four hundred ninety that's actually a fair bit of power that's more than biking at a reasonably slow speed speed for a half hour example five a girl pushes a three times 10 to the second newton box oh carissa they didn't give me the mass they gave me the weight of the box because it's in newtons along the floor for a distance of four meters the coefficient of kinetic friction is point three three she then lifts the box up 1.2 meters what's the minimum amount of work that she has done what's the minimum amount of work that she has done well change in potential plus change I didn't go force times distance because we're changing direction I don't think I want to go with that I'm going with a scalar approach here over here the change in potential carissa what's changing anything what's your initial potential energy it's implied by this question where we starting out how high on the ground because it says slide across the floor and then lift it up so I think my initial is zero my final is going to be mgh final is that okay carissa now initially I'd written my change in kinetic energy here but I ran to a roadblock because I said did they give me a v no where is this object getting its kinetic energy from I think it's going to be the force person is pushing with times the distance is that okay alex which force of certain first of all which distance what's the horizontal distance this question says this mass was pushed alex okay easy enough to find which force is well here's my mass what of course is acting on this mask at the obvious ones mg down what else no yes we do what else absolutely normal force well Jessica absolutely and what's the last one friction now I don't know how hard she's pushing but Rob the fact that it asked me for the minimum amount of work suggests how long should I draw my friction arrow not long if it was longer it ain't moving exactly the same what I guess she's exactly matching friction she could be doing more this is the minimum amount of work she's doing to get this up keep this object moving so I'm going to argue Brendan that this is really friction force times the distance friction is what times what I don't know the normal force oh but look look look look look at on the force same size is normal force what it's going to be new mg times d fact I think this equation over here is going to be m gh final there's how much potential energy I gained plus mu m g d there's how much kinetic energy I gained where did the energy come from me or the girl that's why this is how much work the girl had to do do I know the mass no in fact what did they give me here not the mass what did they give me here the weight which as an equation is what what oh so instead of finding the mass what can I replace this mg with Andrew cut you mid stretch my bad instead of finding the mass by taking this number and dividing by 9.8 you know what this here is just mg mg times h plus mu 300 all right 3000 thank you what was that okay coming from you how could it not anyways here we go Brandon what's mu redeem yourself what's mu redeem yourself Brandon redeem yourself again what's mg what can I replace mg with that's the nice thing in this question I didn't bother finding the mass I was going to divide by 9.8 but Courtney I glanced at my equation and I noticed m was never by itself it was always next to a g if they gave me mg why don't I replace them both at the same time and what's uh distance here Courtney what's the minimum amount of work that this girl is going to do am I recording picking this up Alex what'd you get oh I'm not done yet what's the minimum amount of work this girl did Justin what'd you get 4240 anyone else doesn't seem like that number doesn't ring a bell with me 756 75756 it's a little more than one horsepower and this is work jewels okay I like number six but I'm going to skip it because you guys are tired it's a bit overkill and I'm going to say the same thing say the same thing about number seven and I'm going to say the same thing about number eight your homework number one number two number three not number five sorry look nerd look cool so one two three nine you can now do every question on the year that review as well