Ch 09: Work & EnergyWorksheetSee all chapters
All Chapters
Ch 01: Intro to Physics; Units
Ch 02: 1D Motion / Kinematics
Ch 03: Vectors
Ch 04: 2D Kinematics
Ch 05: Projectile Motion
Ch 06: Intro to Forces (Dynamics)
Ch 07: Friction, Inclines, Systems
Ch 08: Centripetal Forces & Gravitation
Ch 09: Work & Energy
Ch 10: Conservation of Energy
Ch 11: Momentum & Impulse
Ch 12: Rotational Kinematics
Ch 13: Rotational Inertia & Energy
Ch 14: Torque & Rotational Dynamics
Ch 15: Rotational Equilibrium
Ch 16: Angular Momentum
Ch 17: Periodic Motion
Ch 19: Waves & Sound
Ch 20: Fluid Mechanics
Ch 21: Heat and Temperature
Ch 22: Kinetic Theory of Ideal Gasses
Ch 23: The First Law of Thermodynamics
Ch 24: The Second Law of Thermodynamics
Ch 25: Electric Force & Field; Gauss' Law
Ch 26: Electric Potential
Ch 27: Capacitors & Dielectrics
Ch 28: Resistors & DC Circuits
Ch 29: Magnetic Fields and Forces
Ch 30: Sources of Magnetic Field
Ch 31: Induction and Inductance
Ch 32: Alternating Current
Ch 33: Electromagnetic Waves
Ch 34: Geometric Optics
Ch 35: Wave Optics
Ch 37: Special Relativity
Ch 38: Particle-Wave Duality
Ch 39: Atomic Structure
Ch 40: Nuclear Physics
Ch 41: Quantum Mechanics
Intro to Energy
Intro to Calculating Work
Work By Gravity & Inclined Planes
Work By Variable Forces (Springs)
Net Work & Kinetic Energy
More Work-Energy Problems

Concept #1: Intro to Energy & Types of Energy


Hey guys we're now going to talk about work and energy which are two concepts that are very closely related, I'm really excited about this chapter because energy is a really big part of physics and you're going to see it come back in several other chapters so it's really important that you get good at the stuff let's check it out. Alright so energy is a physical quantity without a precise definition if you read through a textbook it most likely says something about the difficulty in explaining exactly what energy is and we don't know exactly what it is and we don't know exactly why things work the way they do but we know how it works, OK? We don't know exactly what it is but we know how it works there's a bunch of definition and they're all kind of weak I don't like any of them but it doesn't matter the key thing to know about energy or one of the key things to know about energy is that it exists in many forms, there are multiple types of energies, OK? And energy also cannot be destroyed it must always be transformed between types or converted one type of energy to the other, Ok? So, here's a quick chart of the main types of energies that you're going to see in this class. So, we're going to in this course we're going to focus almost exclusively on mechanical energy, right? The first part of physics is almost exclusively mechanical energy so much so that we're going to split up all the types of energies into simply mechanical and non-mechanical, non-mechanical is technically not a category of energy I'm just saying all the energies that are not mechanical we're just going to bunch them up here because it doesn't matter so you have atomic energy, chemical energy and all kinds of different things, OK? Mechanical energy has 2 subgroups one is potential and the other one is kinetic, OK? Potential energy is split into two groups; gravitational and the elastic energy which can also be thought of as a spring energy and then we also have kinetic energy so when you write the equations for these real quick I'm skipping these two because we're going to get back to it but gravitational potential energy is MGH, mass gravity 9.8 and then the height and the elastic potential energy is given by 1/2KX squared, OK? K is the spring coefficient or the force constant and those are the same thing and X is your spring deformation you might already have seen this and kinetic energy equation the equation for kinetic energy is 1/2MV squared. On the non-mechanical type, I'm going to the only one I'm going to mention that we need to sort of care about is thermal energy and everything else just goes here, all other types of energies go here and the reason why I'm singling out thermal energy is because one of the things you see is that static friction when two things are rubbing on each other that rubbing causes heat, right? It causes heat so we're going to say that's kinetic friction rather, kinetic friction is going to convert kinetic energy into thermal energy cause of friction kinetic transforms kinetic energy when you rub you are slowing down so you're losing kinetic energy and you're getting thermal energy which can also be thought of as heat, OK? We'll talk more about that later let's keep going so I mentioned we don't know much about exactly what energy is but we know how it works and we know that it's conserved and that's the most important part about energy that's why it's such a big deal it's because it's this physical quantity that is always conserved, right? So, we're going to use this idea to make old problems easier as well as to solve new ones let me give you a quick example over here in this white space.

Here here's an example of a problem that we could have solved earlier, right? If you have a block and it slides down and I want to know what is the final velocity down here? you could have solved this earlier you would write F=MA you'd find what the acceleration of the block is and then you would pick one of your 3 equations of motion to solve for the final velocity so it's a two-step process it's not that bad you've done this before but now with energy we're going to solve this in one shot, right? Another thing is you going to be able to solve new types of problems that you couldn't solve before so something similar to this but that you couldn't solve was a curved path something like this so the block is here but the path this curving so the angle is always changing and therefore the acceleration isn't constant and we can't really solve problems of variable acceleration early on, OK? So, this is an old problem that is going to be easier and this is a new problem that we couldn't solve at all, in fact whenever you have a curved path you're always going to solve this using energy, OK? So, let's talk a little bit more about the types of energies that we care about the most which are these over here and kinetic energy it's represented by KE kinetic energy or simply K, it's an uppercase K, OK? Has to do with an object's velocity or more specifically actually speed, OK? Has to do with an object's speed, look at the equation here for kinetic energy 1/2MV squared an object that is moving has obviously of a velocity and if you have a velocity you have a kinetic energy that's it, if you have a velocity you have a kinetic energy and you should be able to tell which types of energy an object has, potential energy is represented by PE but the most usual one is actually U, OK? So, potential energy is U and it has to do with an object's position. Now there's two types of potential energy gravitational and elastic an object that is above the ground has gravitational potential energy since there are two types of potential energy we use a subscript to differentiate between them so potential energy is U but if it's of the type gravitational it's Ug and you can see this here if you're above the ground you have a height and if you have a height your potential energy is 0....I'm sorry not 0 but if you don't have a height if you're on the floor then H would be 0 and the potential should be 0, OK? A spring that is compressed or stretched both of these terms could be referred to as deformed, right? A deformation is either stretching or compressing a spring so an object a spring that is deformed has an elastic potential energy and that's going to be Uel right here, OK? X is deformation if you have an X you have a Uel OK? So, kinetic energy requires a V, elastic potential energy requires an X and gravitational potential energy requires an H, OK? Over here if you ever see the letter U by itself without a G or without a EL U by itself just means you either Uel or it means Ug + Uel so if you see U by itself it means both Us it's just a shortcut simpler version or compressed version of writing it, right? Mechanical energy over here, right? Mechanical energy encompasses all these three and to calculate the mechanical energy of an object you're simply going to sum it's going to be the sum of kinetic and potential energy so you would compute MGH, 1/KX squared, 1/2MV squared add up all three of them, OK? And lastly the unit that we're going to use for energy the official SI unit for energy is Joules and its abbreviated J, right? Let's do a very quick example here.

I have example one a 3 kilogram bird flies horizontally at 20 meters above the ground with 10 meters per second, 3 kilogram bird flying at a heights of 20 meters and it's flying horizontally so it looks like this with 10 meters per second, I want to calculate its total mechanical energy well how do I find mechanical energy? mechanical energy is K+U, let me write this up here I don't think I wrote that there, kinetic energy right here is the total K which is this guy plus U and U is both of these together so if you want you can expand this it's K + Ug + Uel, how do you know which types of energies you have? Well this one depends on a V, this one depends on an H and this one depends on a spring compression X, there are no springs around so I don't have this I have a velocity so I have a kinetic energy, I have a height so I have a potential energy and now itÕs just plug and chug right so 1/2MV squared + MGH, 1/2 the mass is 3 the velocity is 10 squared + M (3) for gravity I'm going to use 10 just to make it faster, OK? But it's 9.8 and then H is 20 and if you add up all of this you get 750 Joules and that's itÕs just plug and you're done, OK? LetÕs do this next one here.

Example #1: Intro to Energy


Alright so here you are dropping a 1 kilogram object from the top of a 100-meter building so let me draw that real quick so 1 kilogram object.100 meters building so it falls from here to here and you're dropping so the initial velocity is 0 and the mass is 1 kilogram and I want to know A What is the mechanical energy at the top? In other words, what is the mechanical energy initial? mechanical energy is kinetic plus potential so it's kinetic initial + potential and there are two types of potential energy; elastic and gravitational there are no springs here so we're dealing only with gravitational potential energy. What about kinetic energy? There is no kinetic energy, kinetic energy is 0 because my velocity is 0 and for potential energy the only type you have is gravitational potential energy which is the equation is MGH so this is in the beginning so it's my initial height because my height will be changing but the one that matters is the initial, the mass is 1 for gravity I'm going to use 10 just make this faster and the heights is 100 meters so this is 1000 Joules of energy.

Part B I want to know what is the mechanical energy at the bottom? So, what is mechanical energy final? Well it's the same set up its kinetic final + potential final, is the kinetic energy at the bottom? And remember the bottom is right before it hits the ground, right before hitting the ground you have a velocity so you will have this, but right before you hit the ground you were really close to the ground 0.0001 away so we're going to say that your height is 0 therefore you have no potential energy, so mechanical energy is simply 1/2MV squared, I know the mass is 1 but I don't have the final velocity so what I'm going to do is I'm going to use a motion equation one of these guys were here from back in the day to find the final velocity, OK? So, if you look at the information you have I know my initial velocity I know my Delta Y, let me list my variables here V initial = 0 Delta Y I'm falling I'm going to say the going up is positive so my delta Y is -100 because I'm going down and I also going to know the acceleration is -10 meters per second squared gravity, right? What am I looking for? I'm looking for V final and the ignored variable here is my delta T so that means that I should be using the only equation that doesn't have delta T in it is the second equation so I'm going to use V final squared = V initial + 2AX or in this case Delta Y, OK? This is 0 and then I have that the final velocity is the square root of 2, acceleration is -10, Delta Y is -100 this is a square root of 2000 which is notice how the negatives cancel so this is 44.7 meters per second and this final is exactly what I want to go here 44.7 and when you do this you should get exactly 1000 joules, OK? notice that this is the same as this the mechanical at the top and mechanical energy at the bottom is conserved even though I changed types of energies, here I had only potential and here I have only kinetic so I can see here that mechanical energy is conserved now in some cases mechanical energy is not conserved but we're going to talk about this more later, OK? Here in fact what happened is that all my potential energy became kinetic final, there's a full conversion of energy in fact if you were to graph this and again we're going to talk about this more later your potential energy would look like this U gravitational and your kinetic energy would look like this kinetic energy so you're losing potential while gaining kinetic, another way of thinking about this is that you're losing height as you're gaining speed, OK? In such a way that the sum of these two is always the same, the sum of them would be somewhere over here, OK? That's it for this one let's keep going.