in this video we're going to talk about kinetic energy and potential energy but let's begin our discussion with kinetic energy what is kinetic energy well think about the word kinetic what is what does that tell us kinetic kinetics has to do with motion so kinetic energy really represents energy in motion anything that moves has kinetic energy so if you have a ball moving at 5 m/s it has kinetic energy if you have a block that's at rest it's just sitting on the ground doing nothing it has no kinetic energy so anything with mass and speed has kinetic energy the formula for it is K is equal to 12 mv^ 2 so kinetic energy depends on the mass and the speed of the object the units for m is the kilogram the units for Speed typically is in me/ second and if you use those units the kinetic energy will be in Jewels now a typical question that you might see on a physics exam would be something like this if you double the mass of an object that's moving what happens to the kinetic energy and what what about if you double the speed how do you answer those types of questions so let's talk about it first let's rewrite the Formula K is equal to 12 M v^2 and notice that m is raised to the first Power if you don't see a number there it's a one now if we double the mass the kinetic energy will double what you can do for a question like this is replace everything with a one except the stuff that's changing so we're only changing the mass so we're going to ignore the 1/2 we're going to replace M with two we're not changing the speed so we're going to put a one this will give us two this tells us that the kinetic energy doubles now what if we double the speed we're not changing the mass we're going to ignore the constant but we are doubling the speed if you replace V with a two 2^2 is 4 so this tells us that the kinetic energy quadruples if you double the speed now based on that here's another question let's say if you increase the mass by a factor of three and if you quadruple the speed if you increase it by a factor of four how much will the kinetic energy change from its original value so in this case once again we're going to ignore the 1 half we're going to Triple the mass quadruple the speed 4^2 is 16 3 * 16 is 48 so the kinetic energy will increase by a factor of 48 and that's a typical question that you might see on a physics exam but that's how you can answer it at least that's a shortcut method of answering those types of problems now what about potential energy what is potential energy you could think of this as a form of stor energy it's basically the energy due to position so let's say this is the ground and we have object a and object B which one has more gravitational potential energy now object B is at a higher position relative to the ground so object B has more potential energy than object a assuming of course that they have the same mass so poten poal energy is really energy due to position object B can fall a greater distance than object a and so it has more potential energy the formula for gravitational potential energy is M GH where m is the mass in kilog G is the gravitational acceleration which is in m/s squared and H is the height above ground level which is typically meters the gravitational acceleration is 9.8 m/s squared so these are the two formulas you need to know this one for gravitational potential energy and this one for kinetic energy and that is a two it's a terrible looking two but it's a two now let's say this is the ground and we have a ball let's say it's a a 10 kg ball and it's currently 50 m above the ground so at this position let's call it position a how much potential energy does the ball have at this position so to calculate it we could use this formula MGH so we have a mass of 10 kg the gravitational acceler is 9.8 and the height is 50 so let me pull out a calculator and so this is going to be 10 * 9.8 * 50 so the gravitational potential energy is 4,900 jewles now let's say if we release the ball from rest so it begins to fall just before it hits the ground call that position B what is the kinetic energy at position B what would you say it's important to understand that as the ball Falls from position a to position B its potential energy is being converted to kinetic energy why do we say that well as it goes from A to B its position or rather its height relative to the ground is decreasing and as the height decreases its potential energy is decreasing however as it falls it's accelerating towards the ground and so it's speeding up it's moving faster and faster so as the speed increases the kinetic energy is increasing so the net result is that as the ball Falls from position A to B the gravit excuse me the gravitational potential energy is decreasing but the kinetic energy is increasing so one form of energy is being converted to another at position B just above the ground level basically the potential energy is zero so at that point all of the potential energy has been converted to kinetic energy so at position B let me just get rid of this the kinetic energy is going to be equal to 4900 Jew this number so the potential energy at Point a is equal to the itic energy at point B when it can fall no more so B is the lowest position that the ball can reach at that point all of the potential energy has been converted to kinetic now here's another question for you at position B just before the ball touches the ground how fast is it moving how can we find an answer to that question well we could use this formula kinetic energy is equal to 12 * the mass times the square of the speed and so we could replace K with 4900 Jew and we have the mass it's 10 kg and so we could solve for V half of 10 is 5 so we have 4900 is equal to 5 v^2 and so I this point it's all math our next step is to divide both sides by five 4900 ID 5 is 980 and so that's equal to V ^2 next we're going to take the square root of both sides and the square root of 980 is approximately 31.3 so the object is going to be moving at a speed of 31.3 m/s just before it hits the ground and so using the principle of conservation of energy you could answer questions like these now for those of you who want more difficult problems in in terms of uh kinetic energy potential energy work power and stuff like that check out the links in the description section Below in this video and I'm going to post some other videos that can help you with harder problems if you need help in that area so feel free to take a look at that when you get a chance now there are some other forms of potential energy another one that you might see in the first semester physics is something known as elastic potential energy now some Physics textbooks instead of using PE for potential energy you might see a capital u symbol and the formula for elastic potential energy is 12 kx2 so here's an example of when you would have a situation that has elastic potential energy let's say if you have a spring now if you apply a force you can compress the spring and once you release that force that energy that you use to compress the spring has been stored and once you release a spring that spring will have the tendency to go back to its original length so this is fa the the force that you apply and F FR is the restoring Force it's the force that wants to bring the spring back to its position of equilibrium now let's talk about this equation 12 kx^ 2 K represents the spring constant which is measured in Newtons per meter and X represents how far the spring has been compressed or stretched from its equilibrium position so the sign of X really doesn't matter because once you square it it's going to be positive but it's how far it is from its natural length and it's typically in meters now to understand the spring constant the spring constant tells you how stiff or how loose the spring is so for example let's say if we have spring one with a spring constant of 100 Newtons per meter versus spring 2 which has a spring constant of 500 Newtons per meter which one is loose and which one is more stiff this spring is going to be more loose because it's very easy to stretch or compress it this one is going to be more stiff because it's harder to stretch or compress it but let's think about what this number actually means 100 Newtons per meter what does that mean it means that for this particular spring a force of 100 Newtons is required to stretch or compress the spring by a distance of 1 meter now the second spring requires five times the amount of force so you need 500 Newtons of force to stretch or compress the spring by 1 meter and that's why we could say that this spring is more stiff because it's much harder to stretch or compress the spring by the same amount of distance so this is another form of energy that you may or may not have to know depending on what class you're taking so elastic potential energy it's another form of stored energy and there's other forms of potential energy like chemical energy the energy stored in chemical bonds you also have the electric potential energy the energy stored between a charge based on its position in an electric field and I'm not going to go into those topics but just understand that there's many different forms of potential energy so that's basically it for this video if you like it feel free to subscribe and don't forget to check out the links in the description section below if you want access to harder problems related to this topic thanks again for watching