Mechanical Engineering: Particle Equilibrium (11 of 19) Why are Pulleys a Mechanical Advantage?

welcome to a lecture online now we're going to talk about pulleys and there's so many different combinations of pulleys that we can encounter we're going to do several videos on that but let's start with this basic principle of of pulleys first of all pulleys are used to gain mechanical advantage in two ways one of them is that you can redirect a force required to lift an object so instead of lifting an object like this you can lift it by pulling on something and secondly you can arrange pulleys in such a way that the amount of force required to pull an object up it's less than the weight of the object itself and it depends how the pulleys are arranged so here we have four different arrangements here's the most simple arrangement that we can have which is called the Atwood machine notice the object hanging from the pulley here has a weight of 100 Newtons and the question is how much force is required to pull this weight up well it turns out one of the things that you can do is you can draw a Freebody diagram around the object that you're pulling up and if you do that you can see that there's only one one rope or one cable that's holding the weight up of the object and so there's only one place where this objects being upheld and therefore the amount of force required to hold this up against gravity has to be equal to the weight because there's only one and so therefore you know that this requires a hundred Newton's of force now another principle of pulleys is that if there is a cable or a rope going around the pulley that the force or the tension on one side of the pulley must equal the force of the tension on the other side of the pulley now that's of course only true if the pulley does not have any mass so to speak with other words we can ignore the moment of inertia and secondly the pulley doesn't have any friction now that's of course never the case pulley always has friction there's always some moment of inertia but if it can consider that them to be so small that we can ignore them then we don't have to worry about it and so in that case if the tension here must be equal to the tension there then the force here must be a hundred Newtons and they have to be equal so therefore one hundred Newtons so there's no advantage as far as the amount of force required you simply can redirect the force and it's easier because you can pull down on it to pull the checked up ran have to lift it up on the second combination here we have a second pulley again if we draw a Freebody diagram around the pulley that holds the weight like this you can now see that there's two cables or two ropes that are holding up the weight of that and if we assume that the force or the tension is the same on both sides and again the reason why we can assume that is because that's one of the rules of pulleys that if the pulley has no mass or no friction not the tension on one side of the pulley has to be the same as the tension on the other side of pulley so since the tension has to be the same and they have to add up to 100 Newtons you know that this has to be 50 Newtons and therefore this has to be 50 Newtons then you come up here in your real lives that this rope right here is the same as the rope on the other side and therefore the tension here must be the same as the tension there therefore you know that this must be a 50 Newton force required to lift it up which means that you only have to pull up with a force of 50 Newtons to lift an object of 100 Newtons one of the things that happens though is that you'll have to move this twice as far to move this up a certain distance for example if you want to lift it up one meter you'll have to pull down on the Rope by two meters to make it lift one meter going on to the third pulley system right here now we have three pulleys and if you draw a Freebody diagram around this portion of the pulley you can see that these three ropes are holding up the weight of 100 Newtons and then if you use the principle let me go ahead and Mark that here so we have this one this one in this one and notice that the tension here must equal to the tension there so those must be equal to one another and you know that the tension here must be equal to the tension there because that rope goes around the pulley which means that all three must be equal therefore they each carry a force of 33 Newtons so 33 Newtons there 33 Newtons there 33 Newtons there which means that since this has to be equal to the tension over here the force here is also 33 Newtons which means you only need 1/3 the force equivalent of the weight of this object to pull the object up which also means that if you want to lift us up one meter you'll have to pull down in the world by 3 meters the last combination here there's four police again what we can do here is draw a Freebody diagram around this portion let's do that right here let me use the black pen so I'm going to drive Freebody diagram like this and again we have to assume that the pull is half no mass so they do not play a role in the weight being held up by the police and you can see here that there's four places in which the weight is being upheld you're holding a weight of 100 Newtons notice that this tension must be equal to this tension and this tension must be equal to this engine and this tension must be equal to that tension so they all must have the same force the same tangent 25 Newtons 4 times 25 is 100 so this one here is 25 Newtons 25 Newtons 25 Newtons 25 Newtons of course the tension here must be the same as the tension over there so the force here must also be 25 Newtons which means that if you want to lift up this way by one meter you have to pull down here a distance of 4 meters to lift the buoyed up 1 meter into the air so that's how we can take a look at these types of pulley systems you can see the mechanical advantage comes in that if you have more pulleys connected like that you have to have less force to lift up an object that's why we use pulleys

Channel: Michel van Biezen

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Keywords: ilectureonline, ilectureonline.com, Mike, Mike van Biezen, van Biezen, ilecture, ilecture online, Mechanical Engineering, Particle Equilibrium, Mechanics (Field Of Study), Force (Dimension), Component, Static, Sum of the Forces = 0, Resultant Force, Why are Pulleys a Mechanical Advantage?, Pulley (Product Category), Atwood Machine, Tension, Engineering (Industry)

Id: 6GuldysCVjI

Length: 5min 51sec (351 seconds)

Published: Tue Jun 23 2015