what chapter are we gonna talk about today, gang? what's it? what is it? begins with e. energy. how many people feel energy? how many people wish they had more? we'll be talking about such thing now. but before we talk about energy, i wanna talk about something that is somewhat related. we talked before about the idea of momentum. remember momentum? momentum is inertia in motion. and how do you get something moving if it's not moving? how do you change the momentum of something? you push on it, and you provide what's called an impulse. impulse, right? impulse is not only force. it's not how hard you push only that will tell you how much momentum change you'll get. it's how long you push. and we talked about how long in terms of time, didn't we? we said force multiplied by time would be numerically equal to. you multiply the force that you exert on something, huh?

multiply it by the time that you exert on something, you get a numerical quantity. and that quantity is exactly equal to, not the momentum, but the change in momentum that you produce by pushing, huh? and so we talked about this, you know? and we called this idea here how hard you push multiplied by the duration in which pushing takes place. we had a name for that. see if your neighbor remembers the name, e. don't be an f now, come on. come on. what is it, gang? impulse. yeah, don't be afraid to be a little frivol, all right? and so we said impulse is a change in the quantity, inertia in motion, moving inertia. we call that what? that oomph, what do we call it? begin with m. momentum. okay, don't be shy. and that's what we talked about, right?

and we said for big changes in momentum, you'll have what kind of impulses? begin with b. big. for small changes in momentum, you'll have what kind of impulse. begin with s. small, all right? now, what happens when-- what happens to the change in momentum when bouncing occurs? larger or the same as if bouncing does not occur? begin with a l. larger. and we can show that with this device here. here's a dart. it's like a dart and i have a sharp nail in there. and what i'm gonna do is i'm gonna lift the dart up, and i'm gonna allow it to swing against that wall. it's gonna make a collision. watch this. the block did not tip. i'll try it again. the block did not tip. this time, i'm going to remove the point. and now, i have just rubber here. this time, when i swing it, it's going to... bounce.

and when it bounces, more impact or less? more. wow, hands down, no contest. i don't even have to lift it even as high. i can even lift it this high. watch. hey. so bouncing. more change in momentum when it bounces. when this come down and stop, there's a certain change. but when it hits, stops and then comes back out again, then what? more change or less? more. more change. more change in momentum means what kind of impulse? greater. greater impulse. and you saw that. and it's the impulse that knocked the block over. hey, huh? huh? physics. we're not gonna talk about impulse and momentum today. we're gonna talk about a rebated idea. how hard you push to get something going is one thing, but how long you push is also important. so far, we talked about how long in terms of time, how long in terms of what your watch reads. we can talk about how long in terms of...

distance. distance, that's right. and when we do that, force times distance, it turns out we'll get a change in some other quantity. and that other quantity is not momentum, it is? begins with a e. energy. energy, okay? and this is what we're gonna talk about today. force times distance will produce a change in energy. what is energy? energy is that numerical quantity which appears in many, many forms like mechanical energy. we'll talk about mechanical energy today, really. energy of position, potential energy. energy of motion, motion energy. we don't say motion energy, we use a greek word for motion, begins with a k. check your neighbors, see if your neighbors know it. what kind of-- what's motion energy with k? kinetic, yeah. kinetic energy, okay? and then we can talk about-- later on, we can talk about heat energy, sound energy.

can anyone think of any other kinds of energy? how many said, "no, that's probably it, there's probably no more?" come on, gang, some more. light. light energy. - thermal? - tension? good, radiant energy. radiant, from radium, things like that, huh? - thermal. - good, thermal energy. good, nuclear energy. and turns out energy of being. it turns out everything has this quantity called energy. and that's given by einstein's celebrated equation. later in the course, we'll talk more about this, the idea that energy and mass are two sides, gang, of the same coin. you guys get mass, right? you know what your mass is? [makes sound] squashed up energy. you are all bits of energy all squashed up. and the more massive you are, the more energy you'll have. and sometimes you can convert from the inertia kind to the radiant kind. and that's what happens in the sun and the stars.

and that's the energy of fusion. and we'll talk about that too. but today, we're only gonna talk about the simplest kind of energy, mechanical energy, and its related idea, work. because this, force times distance, we don't call that impulse, gang. no. force times time is impulse. we call force times distance another word. see if your neighbor doesn't know what it is. who came unprepared, doesn't know? what is it, gang? all together. work. all right, work. we call that work. okay, work equals a change in-- and i'll just put e for energy, all right? if i'm lifting something up, if i lift this block up, i do work on the block when i lift it because i'm exerting a force through some distance. okay? and the higher i lift it, the more work i do. the more work i do, the more what it has--

begins with a e. energy, okay? if i elevate way, way, way up, it's got a lot of energy. and we call that energy energy of position. and that energy of position, you could put the work in today and you could use it tomorrow. so you can store it. it can be there for your potential use. so that being the case, gang, we got a name for energy of position. begin with p, e, what is it? potential energy. potential energy is energy of position. we talked before about a slingshot. when you pull a slingshot back further, okay? boom, the projectile's gonna go faster. and we said it gonna go faster, it got more momentum. today, we're gonna say, "yeah, it's got more momentum." but if it has momentum, it also has something else? begins with a e. try it. all right, ends with y. energy, okay? but now, it's energy of motion. and we call kinetic--we call-- energy of motion what, gang?

kinetic energy. yeah. so i can go like this and pull it with position. more position, more position, more energy, more energy... [makes sound] more what? more kinetic energy, that's right. how about cannons? how about you get a cannon like this? it's that long, okay? and you fire a cannonball. [makes sound] out comes the cannonball, huh? let's suppose you have another cannon, same kind of cannon only larger. now, you fire the same kind of cannonball, the same amount of powder. [makes sound] out it goes. in which case will the cannonball go further? the longer-- how many say the longer one? show of hands. hey. how many say the longer one because there's more impulse on it? show of hands. how many say, "wait a minute, impulse, impulse was the other day. i don't know about today." come on, huh? impulse. what is impulse, gang? it's the force from the time during which it acts.

but couldn't we also say, "hey, it's gonna go further because there's more energy given to it. how many see that? even if the force is the same, 'cause over here, it hit with a certain force. here is certain force. but here, the force acts over this distance. here, the force acts over this distance. which is bigger, this quantity or this quantity? this quantity. so you'll get--you're doing more work in the cannonball so it's gonna leave with more kinetic energy. but we can kinda see if something got a lot of kinetic energy, it got a lot of momentum. if it got a little kinetic energy, it got a little momentum. they're related. they're related. that means it can be confusing sometimes. we're not gonna push that to death, though. just want you to know that when you do work on something, you can change the energy that it has. i can kinda show you that with this bowling ball over here. here's a bowling ball, suspended from the ceiling. and what i'm gonna do is i'm gonna do work

on this bowling ball and increase its potential energy. 'cause what i'm gonna do is i'm gonna pull the bowling ball back. now, it's gonna take a force to do that. this little device here will show the force that i apply. and we can look at this kinda close-up, and we can see that as i pull it more and more the force gets more, greater, greater, greater. notice the force is varying with the angle. it gets very complicated to multiply the force times the distance because the force keeps changing with the distance. so to calculate that, you need a kind of mathematics that we're not into right now, and it's called calculus. but it turns out when i do that and i pull with an increasing, increasing, increasing force higher, higher, higher, higher, higher, i'll get a particular number here. but you know what? i've raised it this high off the ground. if i simply pick it up straight up, it takes more force, but i lose-- i go a smaller distance. and guess what that greater force

times the smaller distance is compared to the variable force times a long distance. take one guess what the energy is at the end, both ways. same, same. take a guess. begins with a s, s. now take a guess. same, same. how many sitting next to someone-- oh, check the neighbor. check the neighbor. what is it, gang? - same, same. - same, same. that's right. that's right. i'll show you another nice thing with this pendulum. this pendulum illustrates one of the most important ideas in physics. what i'm gonna do is i'm gonna hold this against my teeth, and i'm gonna let it go, okay? and you watch and see what happens. fall short. i didn't flinch, man. shall i do it again? i'll close my eyes. oh, now, i really did had my eyes closed, okay?

you know what, gang? what's this illustrating? how many say, "oh, it's probably not illustrating anything. it's just a bowling ball going back and..." come on you guys. this illustrates energy conservation. the idea that you don't create or you don't destroy energy. you just slish slosh it from one form to another. when i lifted this up, it had energy of what? beginning with p. position, right? and when i let go, it turns into energy of motion, kinetic, right? and so the position, motion, position, motion, position, but here's the idea. when i started, i did work and lifted it to a certain amount, it got a certain amount of energy, call it a thousand units. when i let it go--whoops. well, it did a little work on the wall, okay? but the idea is it will never come up higher. if it came up higher, it would have more than a thousand units. and we have a little dictum in physics: no can be or we've never seen such a thing.

never has anyone record it and verify the idea that something could put up more energy than what's put into it. we call that idea the conservation of energy. the pendulum at this level is lifted and has a certain potential energy at this point, a potential energy, with respect to say, this level. that's how much potential energy. maybe it's a thousand units. let's call it a thousand. those units, by the way, would be called joules, newton meter. we're not gonna get too much into that, too deeply into that. but say a thousand units of energy here, now it goes in the-- no more potential energy. it's all what kind of energy, gang? kinetic. kinetic. some people know the value of the kinetic energy there, and some people don't. see if you're sitting next to someone who do.

how many say it's a thousand? how many don't really know? how many, "i don't know. i ain't paying attention, man. i don't know what it is." show of hands. okay. it's a thousand, yeah. a thousand joules. and when it goes to the other side, what will it be? a thousand or not quite? not quite. it turns out not quite. boom, energy's been destroyed. yes or no? yes. no. and it begins with the n. no. account for the energy then. it turns out when you swing it never quite comes back to where it was. you know why? yes. it's transferring the energy somewhere else. guess where? how's the temperature feel today, gang? relatively cool.

how many say, "that's strange. it seems to be warming up." [laughter] okay. a little exaggeration, but it is. that thing's banging into the air. and when it bangs in the air, boom. what happened to air molecule? move a little faster. and we'll learn later on that kinetic energy of air molecules--honey, we're talking about temperature. and so what will happen is the energy will go from that to the energy of the molecules in the room, it dissipates in the form of heat. see? but you always have it there. it always adds up. and that's kinda nice. all the physics experiments you do, you always find out the energy score remains the same. and sometimes when it doesn't seem to, you discover things that maybe you didn't know about before. it's marvelous-- a marvelous principle of physics. conservation of energy. let--calculate the energy of any system, maybe it's a galaxy about to explode. calculate the total energy. let that galaxy do no matter what it wants do, spin around, i don't care what. [makes noise] some big event. then you draw a dotted a line around it, calculate the energy in the air again.

what do you got? guess what? same darn number. it might be different forms now, maybe more light than before, but the energy just transforms from one form to another. and that's kinda neat. let's suppose we have the case of a person up at the top of a flagpole. and up at the top of that flagpole, and then gonna dive into a little bucket of water. they used to do this in circuses, okay? now, here's a dude up here. he's gonna jump. and let's suppose up at the top there, he has 10,000 units of energy. that's his potential energy, isn't it? he's at rest. so being at rest, what would his kinetic energy be? zero. zero. we'll just say zero. and here-- [makes noise] right into the bucket. when he gets down to the bottom of the bucket, the potential energy is what? zero. zero. 'cause we took this with respect to the ground.

so down here it's got a potential energy of zero. i know you're sitting next to someone knows what the kinetic energy of splat is. i know you do. the--just double check to be sure. what's the value of the kinetic energy here? how much kinetic energy? 10,000. how many people don't say 10,000? --you guys. it's gonna be 10,000. 10,000 units. hey, when the dude gets halfway down, the potential energy is only half. 5,000. 5,000. there are people who can calculate what the kinetic energy must be. see if you're sitting next to one. what's it gonna be, gang? 5,000. 5,000. let's suppose when he gets three quarters the way down, his potential energy over here is now--what? one quarter of this, one quarter of that. looks like 2,500. will the kinetic energy be more or less?

more. you know it's gonna be more. [makes noise] picking up, huh? and what would the kinetic energy be at the one quarter of--huh? 75. such that what? do you see the rule here? here, here, here, here, anywhere gonna have the same energy. and when he finally comes down here, the kinetic energy goes to zero. boom. calculate the heat of the bucket and the heat of his remains and what do you got? bet you'll get 10,000 units of heat energy. and that dissipates, dissipates, dissipates. but it's always there. energy score stays the same. i'll show you something kinda neat. here, i've got a piece of metal. i'm gonna weigh it.

the hunk of metal weighs a little bit more than 10 newtons. just about 10 1/2 newtons, see that? okay, 10 1/2 newtons. now what i'm gonna do is i'm gonna hold it with two scales, and you guys tell me what's the reading gonna be in each scale. and this is full of stuff. one scale there, one scale here. okay, i have one more hand. it should be half, gang. is it half? let me take this one off and add an angle. it gets wild. information overload today. so we'll only talk about straight up and down, okay? my klutziness is showing. here we go.

half? yes. so i can hold it up with half as much force when this supplies the other side, huh? is that right? okay, now i'm gonna do work on this and lift it, okay? let's suppose, first of all, i do work and i lift it like this. i wanna lift it. let's suppose i wanna lift that up to the 20 centimeter mark right to here. okay, watch this. how high did i move my hand? i moved the bottom of this up 20 centimeters. how far did my hand move? more, less or the same? the same. did you see it's the same? no. if you take that reading, just about 10 1/2, and multiply by the 20 centimeters, you'll get a number. okay? that's the number. that's the amount of work i'm doing when i lift it up, okay?

and it's gonna take that amount of work to lift it up 20 centimeters. let me put that on the board. the work i'm gonna do is force times distance is going to be-- let's round it off to 10, okay? 10 newtons, and the distance i raised it were--was 20 centimeters or 2/10 of a meter. 2/10 of a meter. and that's gonna be equal to two newton meter and we call it a joule. 2 joules of work to lift it up 20 centimeters. i'm gonna lift it up 20 centimeters again. but i don't like having to pull so hard. i don't wanna pull with 10 newtons. i'm getting tired. i like to pull with about five newtons. how could i do that? i could tie this onto here. we have to wonder if the ancients who constructed the pyramids

knew about so simple an idea as we're talking about today. because now i can lift it, as you've seen, with half the force. half the force. now i'm gonna lift this up 20 centimeters and you watch how far my hand moves. where's the 20 centimeter mark? right here. how far did my hand move? more, the same or less? more. in fact, how much more? twice. can you see twice as much? i moved my hand through 4/10 of a meter. but the force i exerted was only five newtons, but i had to exert it through twice as much, and what's the result, gang? two joules. this is like a machine. some people think that a machine can change the amount of energy. those people are wrong. a machine can't put out any more energy,

any more work than put into it. what a machine can do is change the force that's required to do that work. so whether it's a pulley system, or whether it's a lever, the work you put in is the work you get out. and you could hold the lever at different positions and you could get different forces to do the same work. but watch out, gang. no machine can put out more energy than is put into it, okay? what can it change? see if your neighbor knows. we can kinda see the answer to that when we look at the equation for work. work is what? force times distance. since the work input, work output is the same, what you can do is you can slish slash back and forth between whether you're increasing force or increasing distance. consider a huge truck, the flat tire,

and that truck gotta be lifted so the tire can be taken off. can you imagine the ancients back when the pyramids were being built, seeing a little girl using a pumper jack to lift the mack truck, a little kid? and they'd come by and they'd say-- they'd see the kid go-- [makes sounds] --and they'd see the truck come up in the air. so they're "gosh, kid, how did you lift that truck?" and she's "well, i had to just do some work on the jack. "and the work on the jack, it worked on the truck. "and the work on the truck, same as the work on the jack, "no big deal. this is 20th-century stuff." he says, "but i'm not 20th century yet. could you explain that to me?" and the little girl would say this, "well, look at this. "when i push down, "i have to push only a little force "compared to the force of the truck. but when i push down, look how far i gotta go." she said, "multiply my push times the distance i push. you get a number, right?" you know what all the people say? "yeah, you got a number."

say, "no, multiply the force on the other side by how high it go and you get a number, right?" and guess how big the numbers are compared to each other, gang? same. same same. what if she went like this-- click, click, and the truck went click, click? honey, that's magic. that's my physics. hear me, okay? but isn't that neat, that it always turns out to be-- the force down times the distance equals the force times the distance. we kinda show that like this. the force she might push would be like that and the force she lifts might be like that. but the distance she pushes is like that and the distance it rises is like that. and these would be the same. not quite the same, some of the energy goes into working and heating up the jack a little bit. so this number is always a little bit smaller. and how much smaller, you know, the idea of efficiency? won't talk about that today. but with ideal efficiency, this can never be bigger than this. so you're walking down the street,

you see some dude pulling on a pulley system-- [makes sounds] --and you see him single-handedly lifting a piano and the piano's going up in the air. a piano that a human being could never lift. one of those grand, grand piano type jobs, okay? and here we go-- [makes sounds] --and that piano goes up in the air. how can be such a thing? well, first of all, if the pulley system means that the piano is being held by 10 ropes, then the rope tension will be the same in all 10, barring friction, then the-- his free hand, he's pulling one of those tensions the same as those, so he's got 1/10 the weight of the piano on every rope, the one he's pulling. so the piano weighs a thousand, he pulls a 10th of a thousand, what's that? a hundred. he can pull a hundred, up it goes. but furthermore, you multiply how many meters of rope go through his hands by the force he pulls, you get a number, yeah? yeah. now, multiply the weight of the piano--humongous, huh-- times the amount of meters it goes up,

smaller number, yeah? multiply those two together, what's the biggest that number can be? same same. yay, same same. ain't that neat? it works, it works, energy. i remember years ago, i use to hear people talk about the so-called conspiracy of the oil companies, that there are cars, automobiles with little gadgets, usually involving magnets, attached to the carburetors of the cars, would allow cars to go fantastic distances, but the oil companies have bought up the patents and they're withholding it from the public, so the public will have to guzzle down more oil, make more money for the companies. see the idea? that maybe--i was told one time, for example, that with these devices, one could put a couple of liters of gasoline in your car and drive from boston, massachusetts, to san francisco in a couple of liters. but the oil companies won't let you do it, so you have to burn a couple of barrels

or something like that. well, how about that, gang? is there any-- are there any rules that govern this sort of thing? answer begin with a y. yes. try it. ends with a p. try it. yup, there is. and that's the energy conservation and let's talk about that right here, okay? we're gonna push the car across country. it's gonna take energy to do that. it's gonna take energy to do work on the car. and that work is the force times the distance that we're pushing the car. now, what's the force that keeps a car going even in a straight road? what's the car? what's the force? it's the force against friction. and for a very streamline car, that force can be something like a thousand newtons, a thousand newtons at highway speed. so let's see what happens. what's the energy over here? that's the energy given to us by the gasoline, and that's a certain amount. it turns out gasoline has an energy content

of about 40 millions joules per liter. 40 million. now, this is what the energy thing means. if you have 40 million units of energy to spend, that's the energy content in your gasoline. what we're saying is these two numbers multiplied together can't be bigger than that 'cause that's what you got to spend in your gas tank. i don't care what kind of gadgets you got. that's it. now, how are you gonna do it? you're gonna push your car through some distance. let's see how far you can push it. how far can you push it? well, if you're pushing it uphill, it's gonna take more force, so this must be smaller. pushing it downhill, maybe gravity will do it for you, you don't even need anything, okay? but along a level road, you gotta push against the air drag. isn't that true? the fast you go on an air drag-- and let's take an average unit of a thousand newtons,