hey everyone mr abramovich here we are gonna be talking about work and energy today which will get us ready to start our new unit in homework packet four which as you can see is all about work and energy so what we're gonna do today is figure out what's work what units do you measure it in what's energy what units do you measure energy in notice that they are both measured in joules which is not a coincidence we are going to be looking at the work done by a specific force in figuring out whether it's positive negative or zero and then we're going to use the sign of work done to decide if energy is being added to a system or being removed from it so what is work well work is the amount of energy transferred by a force when it moves an object through a displacement what i mean by that is it's not just like i'm going to work in the morning or i have a lot of work to do but in the context of physics work specifically refers to energy transfers putting energy into something removing energy from somewhere getting it to go somewhere else and then what is energy do you ask energy is the ability of an object to produce a change in itself or its environment so um if an object um is moving and it smacks into something it can change its environment by smacking into something else if an object like a rubber band is stretched out it has something called potential energy it has the ability to snap back and come into a different shape so by doing work to something you can either increase an object's abil ability to change itself or something else or decrease its ability to change itself or something else uh the specific kind of energy we're going to be talking about is mechanical energy which is energy due to position or motion this would not include things like electrical energy light energy thermal energy nuclear energy we're we're really just talking about how objects move here and how they change their position go to different places so we'll get into some different examples of mechanical energy shortly as i mentioned earlier both work and energy are measured in joules uh you might remember joules from chemistry but i know you also use things like calories the reason we use joules is because it's based off of other units that we commonly use in physics like newtons and meters so it makes sense that both work and energy have this unit because work is the quantification of how much energy is exchanged between objects or how much energy is transferred from one form to another so if you're doing work to something you're basically dumping joules into an object or taking joules out of that object changing the number of joules of energy an object has one last thing to note is that work is a scalar quantity it does not have a direction but it does have a sign you might ask how can something have a sign if it doesn't have a direction but in this case the sign means something different in this case the sign doesn't mean which way which direction is work being done in it means are you adding energy into something are you taking the energy away let me show you what i mean think of a pitcher throwing a baseball the pitcher is doing positive work here which means the energy is being added to the object or system so picture throwing a baseball adding energy to the baseball making it go faster than it was before you threw it that's positive work it doesn't matter if the pitcher is facing left to right the direction that the ball moves in relative to the outside environment doesn't make a difference the only thing that matters is is the pitcher increasing the ball's energy or decreasing it a catcher on the other hand would be taking the ball's energy away and absorbing it into his glove this is negative work you're removing energy from the objective system so when you catch the baseball it's no longer moving energy was removed from the ball so how do you figure out if you're doing positive or negative work you look at how the directions of the force and the displacement of the objects traveling in compare so if the force in the displacement in the same direction like for example the pitcher the force is to the left the ball is moving to the left that's positive work negative work occurs when the force and displacement are in opposite direction so going back to the catcher catcher is taking energy away from the ball and that's because while the ball was moving to the right the force was to the left so by putting a force in the opposite direction that the object's moving and displacing you could do negative work to the object and take its energy and put it somewhere else so let's look at some examples of whether positive or negative work are being done if you look at the basketball player shooting the ball you can see that the force is up into the left the displacement of the ball is up into the left since the force and the displacement match directions we're talking positive work and you can kind of check that by seeing if it makes sense is the ball gaining energy that it didn't have before if it is it's positive work so that makes sense that the ball is going to be going to a higher height with more speed than it had before he shot it how about this goalie saving the ball well the ball was moving to the right but the goalie forces the ball to the left to stop it from going past the goal line so since the force and the displacement are in opposite directions that indicates negative work and once again let's do a sense sensibility check we figured out that it's negative work well if she saves the ball the ball is going less fast than it was before so negative work does make sense how about the skater riding here the force that the skateboarder applies downward on the deck what kind of work is that force doing well his normal force down on the deck is is downward but the skateboard's moving to the right so what happens if there isn't any part of that force that is acting with or against the displacement you actually end up with zero work done let's do a sensibility check there's zero work done there shouldn't be any energy transferred into the skateboard and you can basically see from this that the skateboard isn't gonna go any faster or slower because of the person's force pushing down on it so it makes sense that there's zero work done in the last case we have our friend here pushing on the door that says pull the door is not going anywhere so what happens when you have a zero displacement you can't even compare the direction of the force in this place because there is no displacement so that would be zero work done as well so to summarize it if you're doing positive work there's got to be some part of the force that acts in the direction of the displacement and obviously i'm realizing now as i'm shooting this video that should say displacement and not distance and that subtle difference you'll you'll get it more later when we do some problems but um if you're doing positive work the force and the displacement have to match directions if you're doing negative work the force and the displacement are going to be in opposite directions you can have zero work done if the force acts in a direction that does not go with or against the displacement or if either the force or the displacement are equal to zero you might wonder what happens if the force is acting at an angle compared to the displacement where it's not totally perpendicular but there might be a component of that force that acts along the direction of the displacement are you doing work and the answer is yes this is how it happens you do more work if you apply more force and if that force is applied over a greater displacement think about following through when you kick a soccer ball or swing a baseball bat the more you follow through the more distance you are forcing the ball the more work you're doing so you can quantify this with an equation by putting force and displacement into the equation but notice that this equation has an angle theta in it and over to the left you see the force symbol with the two little lines as a subscript that is basically saying that the part the component of the force that acts parallel to the direction of displacement is the force that you use in this equation so if f is your force but only part of that force component acts in the direction of displacement then you only use that component what that angle refers to is if you take the overall force and use the angle between the force and the displacement that you're including then by multiplying the force and the displacement by the cosine of that angle you'll be getting what's called a dot product where it only takes the part of the force that's parallel to the displacement um also if you look off to the side you'll see it that the units make sense if force is measured in newtons and displacements measured in meters we know by definition of what a joule is a newton times a meter gives you joules so that's why we use joules here to quantify work and energy let me show you what the variables in this equation represent more in an example i'm not going to go through this example right now you're going to watch another video where we do a problem but you can see that if mrs fields is pulling a crate of cookies with 120 newtons at a 39 degree angle above the horizontal not all that 120 newtons is going to contribute to the work done pulling the crate sideways it would only be a component of that force that acts parallel to the displacement so by taking that overall force vector of 120 newtons and multiplying it by the cosine of the angle 39 degrees you'll get the part of the force that is parallel to the distance and then you could take the product of the force and the displacement and get the work done so we'll do this example another time so i mentioned earlier that our work equation applies for mechanical energy it doesn't work for things like thermal energy or electrical energy there are different work equations that'll get you um that'll allow you to quantify those types of energy but our work equation is going to apply to any kind of energy due to position of motion so for example kinetic energy the energy due to motion different kinds of potential energy um such as gravitational potential energy this comes from the work done displacing something through a gravitational field so if you think of lifting up a heavy object it takes it takes work to do that you have to apply a force over displacement to pick it up against the direction of the gravitational field you're then going to increase the stored energy in that object because when you release it the object has the ability to move that it didn't have before another kind of potential energy is elastic potential energy which we will get into in packet five this comes from extended or compressing elastic materials so think about rubber bands you stretch out a rubber band you have to apply a force over a displacement to stretch it out when you release it it now has the ability to snap back that it wouldn't have had before when it wasn't stretched out so you can store energy and objects by doing mechanical work and giving them more potential energy than they had previously uh what we're going to do next is we'll get a little bit into the formulas that we use for these kinds of energy like i said we're not going to solve any problems in this video but just familiarize you with some of the variables that matter so kinetic energy this one's pretty easy if you think of a ball falling to the ground and making a loud sound during impact what's going to give this ball more energy to transfer to the ground well a more massive ball would definitely give it more energy like a bowling ball falling a couple meters hitting the ground is gonna definitely hit it with more energy than a tennis ball would also the faster it's going matters too more speed the bigger the boom when it hits the ground so kinetic energy is based on mass and speed and i'm saying speed i'm being careful not to use velocity because remember working energy are scalars so it doesn't matter if the ball is moving left or right we're only looking at the magnitude of how fast it's going to figure out how much energy it has so put it into an equation you have mass and speed in there one half mv squared you get kinetic energy we could do a units check here um if you plug in kilograms for mass and meters per second for speed the meters per second squared or sorry the meters per second gets squared so you get meters squared over seconds squared and then if you regroup the kilograms of meter squared in the second squared you can get newtons times meters and that comes out to be a joule so once again the same units that we're using for work we can use for energy to show how work will increase or decrease the energy in a system or object so on that same note there's this equation that we'll use later on this week in this month where you can see the network done on a system is equal to its change in kinetic energy think about what this means conceptually think about the baseball players the person pitching the ball did positive work to the ball which means the ball will end up with more kinetic energy than it started with so positive net work means a positive change in kinetic energy meanwhile the catcher did negative network to the ball it's gonna be a negative change in kinetic energy the ball ends up much slower than it started ends up with zero kinetic energy so that was a negative change we'll do more examples with this coming soon uh we're gonna be working with gravitational potential energy in this unit as you can tell gravitational has to do with gravity potential is any kind of energy that's stored within a system so that's where the name comes from potential energy is stored energy from gravity by the way that variable u u is a generic variable for different kinds of potential energy so whether it's elastic potential energy electrical potential energy you always have a capital u there but the little subscript tells you what kind of potential energy it is so that's what the g stands for um up on the right top right corner you'll see that there are a few different ways that potential energy is sometimes notated you'll see on the various worksheets in your packet they'll use all three versions g p e p e sub g or u sub g so just get used to seeing any of those and knowing that it's gravitational potential energy think of the equation for gravitational potential energy once again the variables should make sense the stronger the gravitational field the more energy you'll have stored in something when you work against that field the higher up it is the more energy it has for when it falls and that energy gets converted into kinetic and the more massive it is the more energy it's going to have when it falls through that height and hits the ground so the variables should make sense in this equation um once again we could do a units check if you plug in kilograms for mass meters per second squared for little g and m in meters in for height you'll get kilograms meters squared per second squared which simplifies down to a newton times a meter which gives you a joule so once again work and energy same units couple things to remember about gravitational potential energy you're always going to define your gravitational potential energy based on an arbitrary reference height uh basically think of it like a an origin of height so for example um if i call my floor zero zero meters of height if i fall out of my chair and hit the floor it's not that much of a change in potential energy so there's not gonna be that big of an impact because there's not that much energy involved but if i fall through a hole in the floor and hit the basement like 15 meters below if the basement's my zero height that's a much bigger amount of gravitational potential energy relative to the basement floor so you could obviously see how it would hurt me a lot more if i fell through a hole in the floor and hit the basement floor because that would be a much bigger height we were dealing with so you should always solve your problems based on a convenient zero height and it'll always work out the last thing is going to make more sense in the context of problem solving so we'll go back to this idea later but gravitational potential energy is not dependent on the path taken only dependent on the final position so if i climb straight up a ladder going vertically or walk up a um diagonal staircase to get to the same height i would end up with the same amount of gravitational potential energy at the end of both of those motions it doesn't matter where how i get there just what my final position is um but like i said we'll circle back to this another time so that's all we got for today once again we basically just defined work and a few different kinds of energy and showed how they're related to each other so in the next video we'll dig into some examples but hope this helped and we'll talk to you later