we are back and we are ready to start on section 3.2 and finally we are going to start to define the concept of energy and realize right off the bat that we don't have a way to write a nice simple five word declaration define energy is blank blank blank we can't do it with five words so the concept of energy is something that we're familiar with we use the idea of energy all the time but like we saw right at the beginning of the semester when we started talking about our quantities of motion sometimes these things are a little bit more subtle than what our everyday experience makes us think they are so what we're going to do is we're going to come at this idea of energy from a lot of different directions and by the end of the semester we're going to have a good understanding but we still are not going to have a really good comprehensive five word definition so the energy of an object is what what is the energy and you have this intuitive feeling about what energy is but what we are really now wanting to focus on is the idea that energy is the property of an object an object can possess energy and what the object does with that energy well we're going to have a wide array of possibilities but how does an object get energy and if an object has energy how does it get rid of energy so this is where we're connecting to our concept of work and work is the process by which the property the energy of an object can be changed so work is something you do and energy is something the object possesses and that's still pretty vague that is i know i know it is it's kind of vague so what we have to do is start coming at this with examples and start observing energy transfers and energy transformations and recognizing what's happening in these individual situations so that we can link them together with an overarching context so we're going to start off with something that is maybe a little bit less obvious than a guy on a bicycle because if i asked you i am 100 certain that nobody would hesitate you would all recognize that the guy on the bicycle has to do work to propel his bicycle forward and we've probably all been on bicycles so we probably also would recognize that okay it's it you need to do more work if you want to propel that bicycle up a hill and so we've got with that one simple example already we've already got two interlocking ideas because you understand that if you push the pedals you increase your cadence push the pedals faster you're gonna do more work and the bike is gonna go faster but then you probably also realize that if you're going up a hill pushing the pedals faster doesn't get you as fast it doesn't make you go as fast as if you were pushing on a level ground or even downhill so now we've just made two connections here that the motion is your the work you're doing is changing your motion but if you're going up a hill it's also about your position if you're going down a hill it's also about your position okay so that's the first thing that we're going to do is we are going to separate out our concept of energy into two really broad categories potential energy and kinetic energy and we're gonna start with our discussion of potential energy so it is defined as energy that depends on the position of an object and why would energy depend on position well we've got to really think about this for a minute and take a look at that first bullet point several different types gravitational is one that we always start with as an example we always start with gravity because gravity is all around us a real good example so think about if you drop something it falls to the floor okay well let's say you have your textbook and it's a kind of heavy book and if you drop it off the edge of the table and it lands on your toe ouch but what if you were standing and holding the book instead of three feet off the ground what if you were holding it five feet off the ground and you dropped it and it hit your foot ouch right but it would be more ouch why because the position of the book mattered because dropping the book from a higher height meant that it hit your foot with a higher velocity and you understand that concept from chapter two you totally get that idea from chapter two and our discussion of acceleration and the higher the object is and the farther it falls well the faster it's going to be traveling when it reaches wherever it's going to reach so that idea is going to help us here understand but we are going to define the concept of potential energy in terms that are related to work and we're gonna see we're gonna see this in just one second okay but let's talk about position for one more minute here electrical potential and magnetic potential energy are maybe a little abstract for right now because we haven't talked about electrical charges at all but why are we looking at the guy with the bow why are we looking at the guy with his compound bow so how do you shoot a bow whether or not you've actually ever done it i bet you understand the basic principle there's a bow a curved piece and then there's a string and you launch an arrow by knocking it on the string the arrow at the end of the arrow there's a tiny little slit that you can you can you can get that slit so it it stays on the bow string and you draw it back and you just let go and the arrow flies well think about that bow string and pulling it back you're stretching a string and that is the storing of energy because when you let that go this bow string snaps back to its original position and the energy that it was storing is given to the arrow and the arrow flies off so potential energy is positional and you don't have to be moving now an object can be moving and still possess potential energy but it doesn't have to be moving in order to possess potential energy same thing with gravity as with our bow string if we pull it back farther we're going to be storing more energy just like if we have the book higher it's going to be storing more energy so let's stick to gravity for a few minutes here and really try to understand how we're going to define because when we define this concept of potential energy for gravity we're going to define it the same way for other sources the expression or the equation might look a little bit different because gravitational force isn't the same as electrostatic force but we're going to define it the same way so let's do it for gravity and we get an equation for potential energy so i'm using pe to be the symbol for potential energy and where does this come from it is literally the definition of work and the definition of work is force times distance we spent a good amount of time on that in the first section and what you should remember about force and distance is that idea of parallel that the force and the displacement are going to be parallel and so the force of gravity is a vertical force and mg that force on the object m mass of the object due to the pull of the earth g okay the weight of the object and that is directly down toward the ground so that force is always acting straight down toward the ground because that's the only way gravity works and then h again i'm going to use that the letter h as an indicator so that it gives us that visual image that we're talking about height which gives us that vertical image in our head that we remember that horizontal distance doesn't matter so gravity won't do any work on an object to move it in the horizontal direction gravity will only do work on an object that moves in the vertical direction and that is literally the definition of work right there force times distance okay so why are we taking the definition of work and applying it to the force due to gravity the reason there's a really good reason for this the reason for this is because on the previous slide i had that little list of all the different kinds of potential energy that we were going to look at not all at once but all of those forms of potential energy are the result of work done by a force and the behavior of the force is something really interesting the behavior of the force is something that we call a conservative force so in physics conservation means that whatever you started out with that's what you end up with there's no gains there's no losses that's what a conservation means but when i say that a force is a conservative force now i'm going to express this idea a little bit differently it's the same idea but i'm gonna express it using this idea the concept of work so let's just think about we had on our first slide the guy lifted the box right and it was just a very simple problem well it was a simple problem because we ignored something that was happening we only looked at the man and the force that the man applied to the box we ignored the fact that the box itself has mass which means the box itself has weight which means that the force of gravity was acting on that box the whole time the man was lifting the box gravity doesn't get switched off so now let's do the same thing but now ignore the man and only think about the gravity so if the box moves in the up direction now we're ignoring whose hands are on the box lifting it because right now we don't care the box moves in the up direction the force of gravity is in the down direction and we know what that means from section one that if the force and the displacement point in opposite directions negative work gets done so let's say the box we raise it up i think it was 1.5 meters the number doesn't really matter we raise it up 1.5 meters gravity did negative work on the box and now we just picked it up we changed our mind and we realized we didn't really want to move this box so we take the box and set it right back down on the floor so the displacement initially was up and now we're going to come back down and if we look at it as a displacement problem what was our total displacement zero how much total work got done how much work did gravity do on that box on the way up displacement and force that's going to give you a negative number on the way down displacement and force that's going to give you a positive number it's the same amount of force and the same amount of displacement each time same box same mass same weight same distance up same distance down so what that means is gravity the total amount of work done by gravity in that example is zero the total amount is zero and that's a unique behavior so the force of friction as a counter example doesn't act that way so now the box is back on the floor and what happens if you slide the box this is like our baseball player example out of the previous section we saw with our baseball player that if you slide forward you slide forward the direction of the force of friction is going to oppose that and negative work will be done what happens if you slide the box forward negative work gets done what if you then like we did with the box we lifted it and we put it back down but what if we slid it forward and then the next step what if we slid it right back would that add up to zero the way it did with gravity it isn't that one isn't going to add up to zero when you slide forward friction is backwards negative work gets done but now you slide backwards your friction is forwards more negative work gets done so this is the really important idea the work done by friction stayed negative we could push the box forward backward left right and the work done by friction would always stay negative but with gravity the work done by gravity could be either positive or negative and that's why we're taking gravity out and saying this is a special case so let's call this potential energy now it's still exactly the same concept of work but there is one thing about gravity and gravitational potential energy that we're gonna have to look at closely pick it apart a little bit and focus on so i'm going to stop this video here and we'll come back and take a look at our gravitational potential energy a little bit more in a little bit more detail