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# Introduction to work and energy

## Video transcript

welcome back I'm now going to introduce you to the concepts of work and energy and these are two words that are sure you use in your everyday life already and you have some notion of what they mean but maybe just not in the physics context although they're not completely unrelated so work and you know what work is work is when you do something you go to work you make a living in physics work is and I'm going to use a lot of words and and and they actually end up being kind of circular in their definitions but I think when we start doing the math you'll start to get at least a slightly more intuitive notion of what they all are so work is energy transferred by a force so I'll write that down energy transferred and I got this from Wikipedia cuz I wanted a good I guess relatively intuitive definition energy transferred by a force and that makes reasonable sense to me but then you're wondering well I know what a force is you know force is mass times acceleration but but what is energy and then I looked up energy on Wikipedia and I found this well entertaining but it also I think says tells you something that these are just concepts that we use to I guess work with what we perceive as motion and force and and work and all of these types of things but they really aren't independent notions they're they're related so wikipedia defines energy as the ability to do work so they kind of use each other to define each other ability to do to do work which is frankly as good of a definition as as I could find and so with just the words these kind of don't give you much information so what I'm going to do is move on to the equations and this will give you more quantitative feel of what these words mean so the definition of work in mechanics work is equal to Force Times distance so let's say that I have a block and let me do it in a different color just because this yellow might be getting tedious and I apply a force of let's say I apply force of 10 Newtons ten Newtons and I move that block by fourth by applying a force of ten yinz I I move that block let's say I move it I don't know seven meters seven meters so the work that I applied to that block or the energy that I transferred to that block the work is equal to the force which is ten Newton's ten Newton's times the distance times seven meters and that it would equal seventy ten times seven Newton meters so Newton meters is one-one I guess way of describing work and this is also defined as one Joule and I'll do another presentation on all of the things that a Joule did but Joule is the unit of work and it's also the unit of energy and they're kind of transferable because if we look at the definitions that wikipedia gave us work as energy transferred by a force and energy is the ability to do work so I'll leave these this relatively circular definition alone now but we'll use this definition which I think helps us a little bit more to understand the types of work we can do and then what kind of energy we are actually are transferring to an object when we do that type of work so let me do some examples let's say I have a block I have a block of mass M I have a block of mass M and it starts at rest and then I apply force let's say I apply a force F for a distance for a distance of I think you can guess what the distance I'm going to apply it is for a distance of D so I'm pushing on this block with a force of F for a distance of D and what I want to figure out is well we know what the work is the I mean by definition whoops work is equal to this force times this distance that I'm applying the block that I'm push that I'm pushing the block but what is the velocity going to be of this block over here right it's going to be something somewhat faster right because force isn't and I'm assuming that this is frictionless on on here so force isn't just moving the block with a constant velocity force is equal to mass times acceleration so I'm actually going to be accelerating in the block so even though it's stationary here by the time we get to this point over here that block is going to have some some some some velocity we don't know what it is because we're using with using all variables we're not using numbers but let's figure out what it is in terms of V so if you remember your Yorkie pneumatics equations and if you don't you might want to go back or if you've never seen the videos there's a whole set of videos on projectile motion and kinematics but we figured out that when we're accelerating an object over distance that the final velocity let me change colors just for variety the final velocity squared is equal to the initial velocity squared plus two times the acceleration times the distance and we proved this back then so I won't redo it now but in this situation what's the initial velocity well the initial velocity was zero right so the equation becomes VF squared is equal to two times the acceleration times the distance and then we could rewrite the acceleration in terms of what the force and the mass right so what is the acceleration well F equals MA or acceleration is equal to force divided by mass so we get VF squared is equal to two times the force divided by the mass times the distance and then we could take the square root of both sides if we want and we get the final velocity of this block at this point is going to be equal to the square root the square root of two times force times distance divided by mass and so that's how we could we could figure it out and and there's something interesting going on here there's something interesting and this what we did just now do you see something that looks a little bit like work well sure you have this Force Times distance expression right here force times distance right here so let's let's write another equation if we if we know the the given amount of velocity something has if we can figure out how much work needed to be put into the system to get to that velocity well we can just replace Force Times distance with work right because work is equal to Force Times distance so we could let's go straight from this equation because we don't have to Reese quare it so we get VF squared is equal to 2 times force times distance that's work took that definition right here 2 times work divided by the mass let's multiply both sides of this equation times the mass so you get mass times the velocity and we don't have to write I'm gonna get rid of this F because we know that we started at rest and that the velocity is going to be let's just call it V so M times V squared is equal to 2 times the work or let's divide both sides by 2 or that the work is equal to M V squared over 2 just divide both sides by 2 and of course the unit here is joules so this is interesting now if I know the velocity of an object if I know the velocity of an object I can figure out using this formula which hopefully wasn't too complicated to derive I can figure out how much work was imputed into that object to get it to that velocity and this by definition is called kinetic energy this is kinetic energy and once again the definition that that wikipedia gives us is the energy due to motion or the work needed to accelerate from from an object from being stationary to its current velocity and I'm actually almost out of time but what I will do is I will leave you with this formula that kinetic energy is mass times City Square divided by 2 or 1/2 MV squared it's a very common formula and I'll leave you that and and that is one form of energy and and I'll leave you with that idea and in the next video I will show you another form of energy and then I will introduce you to the law of conservation of energy and that's where things become useful because you can see how one form of energy can be converted to another to figure out what happens to an object I'll see you soon