Lever Problems Made Simple

hello I'm your teacher Mr Davenport and this lesson is a short lesson that deals with lever problems I entitled it lever problems made simple because my purpose in this lesson is to make this as simple as possible I'm going to introduce you to some concepts that really apply not just the levers but to all simple machines and that's my purpose in this lesson in this lesson we're only going to talk about one kind of lever we're going to talk about a first class lever and in doing so you're going to understand and learn about some concepts that apply to all types of simple machines levers first-class second-class and third-class concepts also apply to pulleys and block and tackles it also applies to things like inclined planes or gears for that matter so all of the concepts that you learn here are going to carry through to future lessons so pay real close attention I'm going to make this as simple as I possibly can I think you'll understand it by the time I'm done well a lever is a simple machine it's a simple machine like this first class lever in this first class lever is so simple it only is made of basically two parts the triangle that you see here is what's called a fulcrum the top of that triangle is a pivot point and sitting on that pivot point is this beam simple machines do work in one motion you notice I didn't qualify that that by saying that levers do work in one motion all simple machines no matter what they are do work in one motion that's what identifies a machine as a simple machine it can do work in one motion sure you push down on one side of this beam with a force and you can lift a weight on the other side so if you put a mass on one side you can lift it upwards by pushing down with a force on the other side this is a first class lever why is it a first class lever well I'll talk more about this in a later video but this is a first class lever because the fulcrum is in between the force you apply to it over here and the force that you're lifting over here the mass that you're lifting so that's what makes it a first class lever as opposed to a second class or a third class lever but like I said we'll spend some time talking about three kinds of levers in a future video simple machines do work in one motion all simple machines have two sides here's our first class lever look at this we have an input side that's aside where I'm going to put a force into this machine it also has an output side a side where the force comes out of the machine on the input side you put work in a force in on the output side you get work out a force out so those are the two sides of any simple machine and again any simple machine not just a lever not just a first class lever could be an inclined plane a block and tackle a pulley any type of simple machine that you can think of they all have two sides that's it an input side and an output side a side where you put it forward sin aside where you get a force out aside where you put work in the input side and aside where you get work out the output side all simple machines produce what's referred to as a mechanical advantage of course they do you want to use a machine to make work easier to do mechanical advantage tells you literally how much a machine is going to help you the mechanical advantage tells you how much the machine will multiply any force that you put into it here is our first class lever again I know by looking at this lever that this lever will multiply any force that I put into it by a factor of one and only one what does that mean that means that whatever force I put in on one side that's the only force I can lift on the other side how do I know that the mechanical advantage here is one well the input side is two meters long guess what the output side is also two meters long and it's because the two sides the input side and the output side are the same length the same distance from the fulcrum that's what tells me that the mechanical advantage of this machine is one and that it will multiply any force I put into it by a factor of just one so does this mean that the machine doesn't make work easier to do of course not whether or not a machine makes work easier to do or not depends on what you want the machine to do in this case this machine as is designed enables you to change the direction of the force that you put into it rather than increase the force it allows you to change the direction of the force so if you want to design a machine to make work easier by allowing you to change the direction of a force this is the machine a good example would be the pulley at the top of a flagpole if you put 10 Newtons into pulling the Rope down you can lift the same force as a flag on the other side but the flag goes up the pole while the force that you're pulling on the rope with goes down the pulley at the top simply changes the direction of that force so it does just exactly what it's designed to do well let's take this to the next step what happens if we change the length of the input side with respect to the output side well here's what happens here's our first class lever again the input side here is 2 meters long the output side measured from the fulcrum to where the weight is that you're going to be lifting is 1 meter the two sides are different lengths input side here 2 meters output side 1 meter if I apply a force of 100 Newton's to the input side of this lever then I might ask how much force can I get out on the output side and I can figure that out by figuring out the mechanical advantage and specifically what I'm going to do here is I'm going to figure out something called the ideal mechanical advantage why is it ideal mechanical advantage and not just mechanical advantage well the ideal mechanical advantage or ima ideal mechanical advantage means that we're not taking into account the friction involved in this machine it is a perfect machine which really doesn't exist it's an ideal machine with no friction so I can calculate the mechanical advantage the ideal mechanical advantage for this machine I do it like this I compare the two sides of the machine we have an input side here and we have an output side the ideal mechanical advantage is simply the ratio between the input side and the output side the idea mechanical advantage then is the input side two meters divided by the output side one meter and what this means is then when I find the answer the answer is ideal mechanical advantage is equal to two this lever will multiply any force that I put into it on the input side by a factor of two because it's ideal mechanical advantage is to the ratio between the input side and the output side is two by the way the input side is also referred to as the effort side and the output side is referred to as the resistance side so I'm moving a resistance force with an effort force I put an effort force in I can move a resistance force and in this case you can see here that the resistance force I can move is 200 Newtons the input force the effort force is multiplied by this machine by a factor of two which allows me in this case to lift two times as much as I put into it that's a good introduction to how this works so let's go ahead now and work on a few very simple lever problems to get used to using this idea of ideal mechanical advantage all right let's go ahead and solve a problem and problem one here is obviously a first class lever just like we've been looking at and the first thing to do here when you look at a lever is to identify the input side the output side well the input side is where you put a force or work into the machine so over here where we have a force of effort of 200 Newtons that's going to be the input side and I'll label that with an eye and over here where we have an object that's being lifted then I'm going to label that oh for output so we have an input side and output side the first step here is to go ahead and figure out what the ideal mechanical advantage of this machine is ideal mechanical advantage if you recall is equal to the input side divided by the output side and when we plug some numbers in here here's what we get the input side is 4 meters long the output side is 1.5 meters long so when we solve this problem we get my little calculator I get an ideal mechanical advantage of 2.7 meter of course cancels out this is a ratio between the input and output sides and so what we're saying here is that whatever force we put into this machine is going to be multiplied by a factor of 2.7 and that would give us the weight that we can lift on the other side the question here is what is the resistance force that we can lift with a 200 Newton input force if we put a force of effort of 200 Newtons in how much resistance can we move on the other side of this lever well we can figure that out like this we can say that the force of resistance is equal to the ideal mechanical advantage multiplied times the force of effort in other words the resistance that we can lift is the ideal mechanical advantage times the effort remember what ideal mechanical advantage is it tells us how much our force of effort is multiplied to give you a particular force of resistance it allows you to predict what you can lift with this simple machine so we solve this the ideal mechanical advantage remember was two point seven and we're going to multiply that by the force of effort the force for putting into the machine on the input side and that forces 200 Newtons so our force of resistance that we can lift is 2.7 times 200 and that gives me 540 Newtons so there's our answer the answer here is 540 Newtons right there problem solved well let's go ahead and work on another problem and problem two is a little bit different in problem 2 we're going to be finding the effort force rather than the resistance force so in problem 2 we're going to start with the ideal mechanical advantage that's going to be our starting point so let's go ahead and do that ideal mechanical advantage is equal to the input side divided by the output side and we can plug some numbers in here ideal mechanical advantage is equal to the input side which is 4.6 meters divided by the output side and that's 2.2 meters and if I solve this for the ideal mechanical advantage I wind up with it looks like two point one I'm going to round it to two point one and again meters factor out so it's just a ratio there's no unit of measurement here now what can we do with this ideal mechanical advantage remember that the ideal mechanical advantage multiplies your effort force to allow you to predict what resistance force you can lift like this ideal mechanical advantage is used to find the resistance force force of resistance is equal to the I MA times the force of effort but in this case we're trying to find the force of effort so we're going to have to rearrange this to solve for force of effort in order to do that I'm going to divide the IMA out of each side just like that so the new relationship here is force of effort is equal to the force of resistance divided by the I M a and you know that just stands to reason that's just logical think about it the ideal mechanical advantage for any machine will multiply your effort force to tell you what resistance force you can lift and so therefore it must divide the resistance force so we can plug some numbers in here the force of effort is equal to our resistance force 150 Newton's divided by the ideal mechanical advantage which is 2.1 and when I solve this our force of effort works out to seventy one point four rounds two seventy one point four and that's going to be Newtons and there's our answer seventy one point four Newtons all right problem three well problem three is very similar to problem two in this case we're going to be figuring out what the effort force is not the resistance force but we're going to have the same starting point we're going to find the ideal mechanical advantage and of course the ideal mechanical advantage is the input divided by the output sides and if we plug some numbers in here the input side is six meters long the output side is only one meter long and when we solve this we wind up with an ideal mechanical advantage of six now we're finding the effort force recall what we said in problem two we said that the ideal mechanical advantage multiplies the effort to tell you what the resistance is or it divides the resistance to what the effort is so we're going to divide the resistance force by the ideal mechanical advantage so it's going to be force of resistance divided by the ideal mechanical advantage and that's going to tell us what our force of effort is how much input force do we have to put into this to actually be able to lift this 840 Newtons so we can solve that it's easy all we have to do is divide 840 Newtons by the ideal mechanical advantage which is 6 and that looks like it gives us a hundred and forty Newtons that's pretty good we can lift 840 Newtons with a forty a one hundred and forty Newton input or effort force problem solved ok let's go ahead and give this one more try with one more simple problem and then we'll review a little bit problem 4 says we have a force of effort of 100 Newtons and we're going to figure out how much resistance we can move with that effort that input force of 100 Newtons and again the beginning point is to calculate the ideal mechanical advantage and the ideal mechanical advantage is equal to remember the input side that's the length of the input side over the length of the output side well when we figure that out we have the input side is 2 meters and the output side is going to be one meter and so our ideal mechanical advantage for this particular first class lever is simply going to be two in other words whatever force we put into it the machine is going to multiply that by two so we can figure out what the resistance force is remember that the ideal mechanical advantage multiplies the effort force to help you predict what the resistance force is going to be so the resistance force is simply the ideal mechanical advantage times the effort force and if we plug some numbers in here the ideal mechanical advantage is two and the effort force remember was 100 Newtons and so the force of resistance that we can lift with this particular first class lever is going to be 200 Newtons now we stop and think about this we're talking about forces here we're not talking about work remember that work is a force times a distance and one very important concept that we learned in the past is that work and energy are equivalent and if you look at the law of conservation of energy you can't get any more energy or work out of a machine than you put into it so even though we can move a resistance force of 200 Newtons it moves up only half as far as we push this side down and that keeps the work the same on both sides so we can just throw this out if we push down on this effort side and we push this side down a distance of I'll just say 5 centimeters then this side is only going to move up half of that or 2.5 centimeters why because remember work is Force Times distance and we can't get out of the machine any more work than we put in it has to be the same it's the conservation of energy well let's go ahead and end this lesson with a little bit of review remember a lever is a simple machine and simple machines do work in just one motion good example of a simple machine here was our first class lever it's simple in construction it only has two parts the fulcrum and the beam and it does work in one motion remember also all simple machines have only two sides an input side and an output side and remember I said all simple machines wouldn't have to be a lever it could be any simple machine they all have only two sides an input side and an output side aside where you put work or force into the machine and aside where you get work and force out of the machine remember all simple machines have a mechanical advantage they produce a mechanical advantage that tells you how much the machine will help you how much it will multiply any force that you put into it also keep in mind that the work that you put into a machine and the work that come out have to always be the same ok also remember that the lever we looked at here had both arms the same length and that gave it an ideal mechanical advantage of one so this one didn't increase any force you put into it this one simply changed the direction of the force which is one of the things that any Massell any simple machine can do a machine can be designed to do nothing more than change the direction of a force I do mechanical advantage doesn't take into account the friction that machines produce it's for an ideal machine a machine that doesn't have any friction but it's useful in being able to predict the effort force or resistance force the force that you have to put in to move an object or how much force you can lift by putting a certain amount of force in in this case if you looked at this problem we had a machine a first class lever that had an ideal mechanical advantage of two it multiplied the effort force 100 Newtons by two and told us that we could expect to be able to lift about 200 Newtons with this particular lever remember also that ideal mechanical advantage or ima is the ratio between the input and the output sides of any simple machine it multiplies the input or effort force to allow you to predict the output or resistance force or it does just the opposite it divides the output or resistance force to tell you what the effort force is and that's what you should have learned in this lesson

Channel: davenport1947

Views: 116,050

Rating: 4.8229165 out of 5

Keywords: Lever, calculations, mechanical, advantage, simple, machine, machines, lever problems, lesson, force, work, energy, simple machines, simple machine calculations, effort, output, input, levers, IMA, AMA, efficiency, calculate IMA, output force, input force, distance, lifted, classes of levers, how to, how can i, how is, how is IMA, how is AMA, simple machine, calculating simple machine, calculating work done, first class lever, second class lever, third class lever, block and tackle

Id: kBCsyGSS9DE

Length: 24min 19sec (1459 seconds)

Published: Thu Jul 24 2014