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# Work and energy (part 2)

## Video transcript

welcome back in the last video I showed you or hopefully I did show you that if I apply a force of F to a stationary an initially stationary object with mass m and I apply that force for a distance D that that force times distance the force times the distance that I'm pushing the object is equal to one-half MV squared where m is the mass of the object and V is the velocity object after pushing it for a distance of D and we defined in that last video we just said that this is work force times distance by definition is work and one-half MV squared I said this is called kinetic energy kinetic energy and so by definition kinetic energy is the amount of work and I mean this is the definition right here it's the amount of work you need to put into an object or apply to an object to get it from rest to its current velocity so it's velocity over here so let's just say I looked at an object here with mass m and it was moving with the velocity V I would say well this has this has a kinetic energy of one-half MV squared and if the numbers are confusing you let's say the mass was I don't know let's say this was a five kilogram object and it's moving at seven meters per second so I would say the kinetic energy of this object is going to be five one-half times the mass times 5 times 7 squared times velocity squared times 49 so let's see one-half times 49 that's a little under 25 so it'll be approximately 125 Newton meters which is approximately a Newton meter is just a Joule 125 joules so this is f we actually put numbers in and so when we immediately know this even if we didn't know what happened how did this object get to this B let's say we didn't know that you know someone else had applied a force of M for a a distance of D to this object just by calculating its kinetic energy as 125 joules we immediately know that that's the amount of work that was necessary and we don't know if this is exactly how this object got to this velocity but we know that that is the amount of work that was necessary to accelerate the object to this velocity of seven meters per second so let's give another example and in this instead of this time just pushing something in a horizontal direction and accelerating it I'm just an example we're gonna push something up but it's it's velocity really isn't gonna change invert let's say I have a different situation and we're on this planet we're not in deep space and I have a mass of M and I were to apply a force so let's say the force that I apply is equal to mass times the acceleration of gravity mass times let's just call that gravity right 9.8 meters per second squared and I would apply this force for a distance of D upwards right or the stead of D let's say H H for height right so in this case the force times the distance is equal to well the force is mass times the acceleration of gravity right and remember I'm pushing with the acceleration of gravity upwards while the exact acceleration of gravity is pulling downwards so let's say so the force is mass times gravity and I'm applying that for a distance of H right D is H so the force is this this is the force and then the distance I'm applying is going to be H and what's interesting is and this is a bit of less I mean if you want to think of an exact situation imagine an an elevator that is already moving because you would actually have to apply a force slightly larger than the acceleration of gravity just to get the object moving but let's say that the object is already a constant velocity let's say it's an elevator and it is just going up with a constant velocity and let's say the mass of the elevator is that 10 kilograms 10 kilograms and it moves up with a constant velocity it moves up I don't know it moves up 100 meters so we know that the work done by whatever was pulling on this elevator probably was the tension in this wire that was pulling up on the elevator but we know that the work done is the force necessary to pull up on it well that's just going to be the force of gravity so we're assuming that the elevator is not accelerating right because if the accelerator was accelerating upwards than the force applied to it would be more than the force of gravity and if the Excel if the elevator was accelerating downwards or if it was slowing down upwards then the force being applied would be less than the acceleration of gravity but since the elevator is at a constant velocity moving up we know that the force pulling upwards is completely equal to the force pulling downwards right no net force because gravity and this force are at the same level so there's no change in velocity I think I said that two times so we know that this upward force is equal to the force of gravity so this is at least in magnitude in the opposite direction so this is this is mg so what's M M is 10 kilograms times the acceleration of gravity let's say that's 9.8 meters per second squared I'm not writing the unit's here but we're all assuming you know kilograms and meters per second squared and we're moving that for a distance of 100 meters 100 meters so how much work was put into this elevator I get or into this object it doesn't have to be an elevator by whatever force that was essentially pushing up on it or pulling up on it and so let's see this would be 98 times 100 so it's 9800 Newton meters or 9800 joules and when we're at the top of when we after we've moved up 100 meters notice there's no change in velocity so so the question is where did all that that work get put into the object and and the answer here is is that the work got transferred to something called potential energy so and potential energy is defined as well gravitational potential energy will work with other types of potential energy later with and things potential energy is defined as mass times the force of gravity times the height that the object is at and why is this called potential energy because at this point the energy work had to be put into the object to get it to this in the case of gravitational potential energy work had to be put into the object to get it to this height but the object now it's not moving or anything so it doesn't have any kinetic energy but it now has a lot of potential to do work and what do I mean that what do I mean by potential to do work well after I move an object up 100 meters into the air what's its potential to do work well I could just let go of it and and and have no no outside force other than gravity the gravity will still be there and because of gravity the object will come down and be in a very very fast velocity when it lands and you know maybe I could apply this to some machine or something and this thing could do work and and if that's a little confusing let me give you an example it all works together with our so let's say I have an object that is oh I don't know a 1 kilogram object and we're on earth and let's say that it is 10 meters above the ground 10 meters above the ground so we know that it's potential energy potential energy is equal to mass times gravitational acceleration times height so mass is 1 gravitational acceleration let's just say gravitational acceleration is 10 meters per second squared times 10 meters per second squared times 10 meters which is the height so it's approximately equal to 100 Newton meters which is the same thing as 100 joules fair enough and what did we know about this we know that it would take about a hundred ignore exactly 100 joules of work to get this object from the ground to this point up here now what we can do now is use our traditional kinematics formulas to figure out well if I just let this object go how fast will it be when it hits the ground and we could do that but what I'll show you is even a faster way and this is where all of the work and energy really becomes useful we have something called the law of conservation of energy is that energy cannot be created or destroyed it just gets transferred from one form to another and there is some minor caveats to that for but for our purposes we'll just stick with that so in this situation where I just take the object and I let go up here up here it has a ton of potential energy right and what by the time it's down here it has no potential energy because the height becomes zero right what's its potential inner so here potential energy is equal to 100 and here potential energy is equal to zero and so the natural question is I just told you the law of conservation of energy but if you look at this example all the potential energy just disappeared and it looks like I'm running out of time but what I'll show you in the next video is that that potential energy gets converted into another type of energy and I think you might be able to guess what type that is because this object is going to be moving really fast right before it hits the ground I'll see in the next video