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# Conservation of energy

## Video transcript

welcome back at the end of the last video I left you with a bit of a question we had a situation where we had a 1 kilogram object see this is the 1 kilogram object which I have drawn neater in this video is 1 kilogram and where on earth and it is and I need to mention that because gravity is different from planet to planet but as I mentioned it's I'm holding it let's say I'm holding it 10 meters above the ground so this distance or this height is 10 meters 10 meters and we're assuming the acceleration of gravity you know acceleration of gravity which we also write is just G is let's assume it's just 10 meters per second squared just for the simplicity of the mass of the 9.8 so we learned in the last video is that the potential energy in this situation the potential energy which equals M times G times H is equal to the mass is one kilogram times the acceleration of gravity just 10 meters per second squared I'm not going to write the unit's now to just to save space all your you should do this when you do it on your test and then the height is 10 meters and the unit's if you work them all out it's Newton meters or joules and this equals so it's equal to 100 joules that's the potential energy when I'm holding it up there and I asked you well when I let go what happens well the block obviously will start falling and not only falling it will start accelerating to the ground at 10 meters per second squared roughly and right before it hits the ground let me draw that in brown for ground right before the object hits the ground or actually right when it hits the ground what will be the potential energy of the object well it has no height right potential energy is mg H the mass and the acceleration of gravity stay the same but the height is zero so this they're all multiplied by each other so down here the potential energy is going to be equal to zero and I told you in the last video that we have the law of conservation of energy that energy is conserved it cannot be created or destroyed it can just be converted from one form to another but I'm just showing you I had this object had a hundred joules of energy in this case gravitational potential energy and down here it has no energy or at least it has no gravitational potential energy and that's the key that gravitational potential energy was converted into something else and that something else that was converted into is kinetic energy and in this case since it has no potential energy all of that previous potential energy all of this hundred joules that it has up here all of this hundred joules is now going to be converted into kinetic energy and we can use that information to figure out its velocity right before it hits the ground so how do we do that well what's the formula for kinetic energy and we we solved it two videos ago and hopefully it shouldn't be too much of a mystery to you it's something good to memorize but it's also good to know how we got it and go back to videos if if you forgot so kinetic energy so first we know that all the potential energy was converted into kinetic energy we had 100 joules of potential energy so we're still going to have 100 joules but now all of its going to be kinetic energy and kinetic energy is one-half MV squared so we know that one-half MV squared or the kinetic energy is now going to equal 100 joules but what's the mass the mass is 1 and we can solve for V now one-half V squared is equal hundred joules V squared is equal to 200 and then we get V is equal to square root of 200 which is something over 14 we can get the exact number C 200 square root fourteen point one roughly velocity is going to be fourteen point one meters per second squared down roots right before the object touches the ground right before it touches the ground and you might say well Sal that's nice and everything that's you know we learn a little bit about energy but what you know I could have solved that or hopefully you could have solved that problem just using your Kino Mattox formula so what's the whole point of introducing these concepts of energy and I will now show you so let's say they have the same 1 kilogram object up here and it's 10 meters in the air but I'm going to change things a little bit I'm going to change things a little bit so let me let me see if I can competently erase all of this nope that's not what I wanted to do okay there you go trying my best to erase this all of this stuff okay so I have the same object it's still 10 meters in the air and I'll write that in a second but it and I'm still going to and I'm just holding there I'm still going to drop it but something interesting is going to happen instead of it going straight down it's actually going to drop on this ramp of ice so it's good it's good that ice has lumps on it it's kind of and then this is the bottom this is the ground down here this is the ground so what's going to happen this time I'm still 10 meters in the air so let me draw that that's still 10 meters and I should switch colors just so not everything is ice so that's still 10 meters but instead of the object going straight down now it's going to go down here then start sliding right it's going to go sliding along this hill and then at this point it's going to be going really fast in the horizontal direction right now we don't know how fast and just using our Kino Mattox formula this would have been a really tough formula this would have been difficult I mean you would have had to I mean you could have attempted it actually you've taken calculus because the angle of the slope changes continuously we don't even know the formula for the angle of the slope you would have had to break it out into vectors you would have to do all sorts of complicated things this would have been a nearly impossible problem but using energy we can actually figure out what the velocity of this object is at this point and we use the same idea here we have a hundred joules of potential energy we just figure that out down here what's the height above the ground well the height is zero so all the potential Energy's disappeared and just like in the previous situation all of the potential energy is now converted into kinetic energy and so what is that kinetic energy going to equal it's going to be equal to the initial potential energy so here the kinetic energy is equal to Kut joules hundred joules and that equals one-half MV squared just like we just solved and if you solve for V use you know the mass is one kilogram so the velocity in the horizontal direction will be if you saw four it 14.1 meters per second instead of going straight down now it's going to be going in Indy in the horizontal to the right and the reason why I said it was Isis because I wanted us to be frictionless and I didn't want any lot energy loss to heat or anything like that anyway I'd say okay so that's kind of interesting and you kind of got the same number then when for the velocity than if I just dropped the object straight down and that's interesting but you know what that's what what else can this do for me and this is where it's really cool not only can I figure out the the velocity right when all of the potential energies disappeared but I can figure out the velocity at any point and this is fascinating along this slide so let's say when the box is sliding down here so let's say the box is at this point so slightly it changes colors to as it falls so this is the one kilogram box right Falls and it slides down here and let's say at this point at this point it's height above the ground is five meters so what's its what's its potential energy here so let's just write something all the energy is conserved right so the initial potential energy plus the initial kinetic energy is equal to the final potential energy plus the final kinetic energy right I'm just saying energy is conserved here up here we what was the initial total energy in the system well the potential energy is 100 and the kinetic energy is zero because it's it's stationary I haven't dropped it yeah I haven't I'm not even I haven't let go of it yet so it's just stationary so the initial energy is going to be equal to 100 joules that's because this is zero and this is 100 so the initial energy is 100 joules at this point at this point what right here what's the potential energy well we're five meters up so mass times gravity times height mass is 1 times gravity 10 meters per second squared times height times 5 so it's 50 joules that's our potential energy at this point and then we must have some kinetic energy going roughly with the velocity going roughly in that direction plus our kinetic energy at this point and we know that no energy was destroyed it's just converted so we know the total energy still has to be 100 joules so essentially what happened if we solve for this is very easy subtract 50 from both sides we know that the kinetic energy is now also going to be equal to 50 joules so what happened halfway down essentially half of the potential energy got converted to kinetic energy and we can use this information that the kinetic energy is 50 joules to figure out the velocity at this point one-half MV squared is equal to 50 the mass is 1 multiply both sides by 2 you get V squared is equal to 100 the velocity is 10 meters per second along this crazy icy slide and that is something that I would have challenged you to solve using traditional kinematics formulas especially considering that we don't know really much about the surface of this of this of this slide and even if we did that would have been a million times harder than just using it just using the law of conservation of energy and realizing that at this point half the potential energy is now kinetic energy and it's going along the direction of slide I will see you in the next video