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# Introduction to mechanical advantage

## Video transcript

welcome back will now use a little bit of what we've learned about work and energy and the conservation of energy and apply it in two simple machines and we'll learn a little bit about mechanical advantage so I've drawn a simple lever here and then you've probably been exposed to simple Leivers before they're really just kind of like a seesaw this place where the lever pivots this is called the fulcrum just really the pivot point and you can kind of view this as either a seesaw a big plank of wood on top of a triangle which essentially is what I've drawn so in this example I have the big blank of wood at one end I have this 10 Newton weight and I've written 10 in there and what we're going to figure out is 1 how much force well we could figure out a couple of things how much force do I have to apply here to just keep this to keep this level right because this weights going to be pushing on that one in downward so it would naturally want this whole lever to rotate clockwise so what I want to figure out is how much force do I have to apply to either keep the lever level or to actually rotate the sleeve or counter clockwise and when I when I rotate the lever counterclockwise what's happening I'm pushing down on this left hand side and I'm lifting this 10 Newton block so let's do a little thought experiment and see what happens after I rotate this lever a little bit so let's say this what I've drawn here and move that's our starting position and then yellow I'm going to draw the finishing position so the finishing position is going to look something like this try my best to draw it the finishing position is something like this oh and also I want one thing I want to figure out I wanted to write is let's say that the distance that this distance right here from where I'm applying to the for whenever where I'm applying the force to the fulcrum let's say the bed distance is whoops I'm using the wrong tool that distance is 2 and from the fulcrum to the weight that I'm lifting that distance is 1 let's just say that just for the sake of argument let's say it's 2 meters and 1 meter go there could be 2 kilometers and 1 kilometers we'll soon see and what I did is I press down with some force and I rotated it through an angle theta right so if that's theta then this is also theta right so my question to you and we'll have to take out a little bit of our trigonometry skills is how much did this object move up so essentially what was this distance what's its distance in the vertical direction how much did it go up and also for what distance did I have to apply the force downwards here so that's this distance in order for this weight to move up this distance over here so let's figure out either one so this distance is what well we have theta this is the opposite this is a 90-degree angle right because we started off at level so this is opposite and this is what this is the adjacent angle right so what do we have there opposite over adjacent so toe opposite over adjacent opposite over adjacent that's Toa or tangent so in this situation we know that the tangent of theta is equal to let's call this the distance the object the distance that we move the weight right so that equals opposite over adjacent the distance that we move the weight over one right and then if we go on to this side we can do the same thing tangent is opposite over adjacent so this is let's call this the distance of the force so here the opposite is a distance of the force and the adjacent is this two meters right because this is the hypotenuse right here so we also have that tangent of theta now using this triangle is equal to the opposite side the distance of the force over two meters so this is interesting they're both equal to tangent of theta so they must we don't even have to figure out what the tangent of theta is we know that this quantity is equal to this quantity right and we can write it here we could write the distance of the force that's the distance that we have to push down on the side of the lever downwards over two is equal to the distance of the weight the distance the weight traveled upwards is equal to the distance the weight divided by one or we could say this this one we could ignore write something divided by 1 is just 1 or we could say that the distance of the force is equal to 2 times the distance of the weight and this is interesting because now we can apply what we just learned here to figure out what the force was and how do I do that well when I'm applying a force here over some distance I'm putting energy into the system I'm doing work work is just the transfer of energy into this machine and when I do that that machine is actually transferring that energy to this block it's actually doing work on the block by lifting it up so we know the law of conservation of energy and resuming that this is a frictionless system and that nothing is being lost to heat or whatever else so the work in has to be equal to the work out and so what's the work in well it's the force that I'm applying downward times the distance of the force so this is the work in force times the distance of the force I'm going to switch colors just to keep things interesting and that has to be the same thing as the work out right well what's the work out well it's the it's the force of the weight pulling downwards right so we have to it's essentially the lifting force of the lever right it had to counteract the force of the weight pulling downwards actually sorry I miss set it a little bit but so this lever is essentially going to be pushing up on this weight right the way it ends up here so it pushes up with a force equal to the weight of the object so that's the weight of the object which is I said it was a 10 Newton object right so it's equal to 10 Newtons that's the force the upward force here and it does that for a distance of 1 well we figure it out this object this weight moves up with the distance D sub W times D sub W all right and we know what the distance of the force is in terms of the distance of W so we can rewrite this as force times substitute here to DW is equal to 10 DW divide both sides by 2 and you have or actually divide both sides by two DW and you get force is equal to ten DW over two DW which is equal to DW z-- cancel out and you're just left with five so this is interesting and I think you'll see where this is going and we did a little complicated this time but hopefully you'll realize a general theme this was a 10 Newton weight and I only had to press down with 5 Newtons in order to lift it up but at the same time I pressed down with five Newtons but I had to push down for twice as long so my force was half as much but my distance that I had to push was twice as much and here it's the opposite the distance is twice as much I mean sorry the force is twice as much but the distance that traveled is half as much and what essentially just happened here is I multiplied my force and because I multiplied my force I essentially lost lost some distance but when I multiplied my force because I inputted a five Newton force and I got a 10 Newton force out although the 10 Newton force traveled for Less distance because the work was constant and this is called mechanical advantage if I have an input force of five and I get an output force of 10 the mechanical advantage is 2 so mechanical advantage is equal to output force over input force and that should hopefully make a little intuitive sense to you and another thing that maybe you're starting to realize now is that proportion the proportion of the mechanical advantage was actually the ratio of this length to this length and we figured that out by taking the tangent and doing these ratios but in general it makes sense because for this force times this distance has to be equal to this force times this distance and we know that the distance this goes up is proportional to the length of this from the fulcrum to the weight and we know on this side the distance that you're pushing down is proportional to the length from where you're applying the weight to the fulcrum and now I'll introduce you to a concept of moments in just a moment so in general if I have and this is really all you have to learn that last thought exercise was just to kind of show it to you if I have a fulcrum here and if we call this distance d1 and we call this distance d2 and if I if I have a force if I want to apply an upward force here let's call this f1 and I have a downward force f2 in this machine f2 times d2 is equal to d1 times f1 and this is really all you need to know and this just all falls out of the work in is equal to the work out now this quantity isn't exactly the work in the work in whiz this force so our f2 is this force times this distance but this distance is proportional is going to be proportional to this distance and that's what you need to realize and this quantity right here is actually called the moment in the next video which I'll start because very soon because this video is about to end I'm laying out of time I will use these quantities to solve a bunch of mechanical advantage problems see you soon