in this video we're going to talk about a certain type of simple machine known as the pulley now the pulley is a machine that can help us to multiply the force that we exert to lift up objects in this picture you can see this person trying to lift this 400 newton crate the question is how much force does he need to exert in order to lift up this crate let's ignore the effects of inertia and friction in this problem well we know that the weight force that gravity exerts on this object is 400 newtons and in order to lift it we need a force of at least 400 newtons in the upward direction now notice that we have two ropes in an ideal situation the forces acting on these two ropes also known as the tension force is going to be the same if they're the same and they have to add up to 400 that means that they both have to be half of 400 so the tension in a rope is always going to be the same so the tension throughout this rope is 200 newtons which means this person is pulling down with a force of 200 newtons now let's think about what this means he's applying an input force of 200 newtons but the pulley is lifting up a 400 newton object the pulley is applying an output force of 400 newtons so this machine magnified the man's force by a factor of two the ratio of the output force divided by the input force is two and that is the mechanical advantage of this particular pulley system it's equal to the output force divided by the input force and that's the purpose of this device it allows us to multiply the force that we input to this machine making the work a lot easier to do now there is a cost of pain this multiplication of force does not come free in order to lift up the crate by a distance of one meter the person has to pull down the rope by a longer distance of two meters why can we say that well as he pulls down this rope by a distance of two meters this rope is going to go up by one meter because this rope is going to go up by one meter so one meter plus one meter equal change of two meters on the other side so this goes up by one meter the distance here decreases by one meter and this part is going to decrease by one meter so this has to increase by two meters because the rope is not gonna gain or lose length by any chance if these two ropes go up by a total of two meters then this rope has to go down by a total of two meters they have to add up and be equal to each other now if these two ropes go up by one meter that means that the crate only moves up by one meter and in that sense there's a change in distance so when a person pulls down a rope two meters the crate goes up by one meter now let's calculate the work work is equal to the force times the displacement so we have a force of 400 newtons and the crate is being displaced one meter higher so 400 times one we're applying 400 joules of work on this crate now the person is applying a force of 200 newtons for a distance of 2 meters so 200 times 2 the work that he's applying is 400 joules so the pulley doesn't change the amount of work that needs to be done however it simply changes the force that you have to apply by changing the distance so because the person pulls the rope for a longer distance he can apply a much less a lower force in order to lift the crate over a short distance and so that's how these simple machines can multiply the force that we need to get the work done is by changing the distance over which that force is applied so if we want to create a large force acting over a shorter distance we need to apply a small force over a longer distance and that's the principle behind these machines how they work but the energy that's needed to get the job done is the same energy is neither created or lost in this process so the law of conservation of energy is consistent with this device energy is not created or destroyed here now there's something else that you want to take into consideration and that is that the mechanical advantage of the pulley is equal to the number of ropes that is being used to lift up the crate notice that we have two ropes being used to lift up the crate so the mechanical advantage is two now let's look at another example but one that contains more ropes being used to lift up the crate now looking at this pulley what would you say the mechanical advantage is notice the number of ropes that we're using to lift up the 800 newton crate we have a total of four ropes being used to lift it up therefore the mechanical advantage is simply going to equal 4. so just by knowing that we know that the person is going to apply an input force that is four times less than the force we see here so 800 divided by four gives us an input force of 200 newtons now let's think about why we need to lift up a weight or a crate that's 800 newtons and all of the forces here in this rope are going to be the same and they have to add up to 800 so it's 800 divided by 4 which is two hundred so this is going to be two hundred this is going to be two hundred and this is going to be two hundred and that's two hundred as well so if you add up 200 newtons four times you get a total force of 800 newtons so thus the mechanical advantage is equal to the number of ropes being used to lift up the crate and as we can see the tension in the rope is the same throughout the entire rope now let's talk about the distance here in order to lift up this crate a distance of one meter how far should the person pull down the rope well in order for the crate to go up a distance of one meter each rope has to go up by one meter in an ideal situation so we have four ropes going up by one meter that means that this rope has to go down by a total distance of four meters and thus the work that is applied is equal to lifting up an 800 newton crate by a distance of 1 meter so that's going to be 800 joules and on the input side we're applying a force of 200 newtons over a distance of 4 meters 200 times 4 is 8. so we can see that the the work that we apply at the input is equal to the work applied at the output given a situation of 100 efficiency if no energy is lost due to friction or dissipated in the form of heat now with this type of device you can have any number of ropes that you want if you were to use 10 ropes your mechanical advantage would be 10 which means your force will be multiplied by a factor of 10 however you will have to pull down the rope a distance that's 10 times as much so by pulling the rope 10 meters down the crate will only move up by one meter and that's the cost you pay for force multiplication now there's something else that we need to talk about when dealing with this type of pulley in an ideal situation each of these ropes will move up by the same distance but if you were to actually try this experiment you'll find that the ropes on the left will move more than the ropes on the right and this rope may not even move much at all and this particular pulley might be tilted towards the left but in an ideal situation we're assuming that all ropes move up at the same time but that's something you want to keep in mind if you were to actually try this experiment the ropes on the left will appear to move more in the upward direction than the ropes on the right for the simple fact that they're closer to this rope now let's take a minute just to review what we've learned regarding the pulley the mechanical advantage of the pulley is equal to the number of ropes it's also equal to the output force divided by the input force and in order to increase the force at the output you need to apply a smaller input force over a longer distance and you're going to get a larger output that's going to move over a shorter distance and second the input work is equal to the output work if you neglect things like friction and any any energy losses dissipate in the form of heat so those are some things you want to know when dealing with the pulley so that's it for this video thanks for watching and don't forget to 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