Mechanical Advantage (part 2) More on mechanical advantage, levers and moments.
Mechanical Advantage (part 2)
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- Welcome back.
- When I left off, I was hurrying a little bit.
- But we'd hopefully come to the conclusion that if I have a
- simple lever, like I have here, and I know the distances
- from where I'm applying the force, to the
- fulcrum, to the pivot.
- And I know the distance from the pivot to where the machine
- is essentially applying the force, the machine being the
- lever in this situation, I know the relationship between
- the two forces I'm applying.
- The input force-- so actually I shouldn't call this a force
- too, I should call this an input force-- anyway, the
- input force times the distance from the input force to the
- fulcrum is equal to the output force times the distance from
- the output force to the fulcrum.
- And that all fell out of what we did in the last video.
- The conservation of energy and that the work in has to equal
- the work out.
- And all work is, is a transfer of energy, so the transfer of
- energy in has to be the transfer of energy out,
- assuming we have no friction and none of the energy is
- And how is this useful?
- Well we could do a bunch of problems with this.
- Let's say that I have a 100 newton object
- right here, 100 newtons.
- And let's say that I know, no matter what I do, my maximum
- strength that I could push-- well let me draw this a little
- different-- let's say it's like this, cause of my goal is
- to lift the 100 newton object.
- So the 100 newton object is right here.
- That's a 100 newtons.
- And let's say I know that the maximum downward force that
- I'm capable of applying is only 10 newtons, right?
- So I want my force to be multiplied by 10
- to lift this force.
- So let's figure out what would happen.
- My input force is 10.
- And I want to figure out the distance.
- So let's say my input force is 10.
- And let's call this the input distance.
- And I want the output force to be 100, right?
- And let's call this the output distance.
- So if I have a fulcrum here, this is the input distance and
- this is the output distance.
- Let me switch colors.
- This is getting monotonous.
- This is the output distance, from here to here.
- And let's figure out what the ratio has to be, for the ratio
- of the input distance to the output distance.
- Well, if we just divide both sides by 10, we get the
- distance input.
- It has to be 10 times the distance output, right?
- 100 divided by 10.
- So if the distance from the fulcrum to the weight is, I
- don't know, 5 meters, then the distance from where I'm
- applying the force to the fulcrum has
- to be 10 times that.
- It has to be 50 meters.
- So no matter what, the ratio of this length to this length
- has to be 10.
- And now what would happen?
- If I design this machine this way, I will be able to apply
- 10 newtons here, which is my maximum strength, 10 newtons
- downwards, and I will lift a 100 newton object.
- And now what's the trade off though?
- Nothing just pops out of thin air.
- The trade off is, is that I am going to have to push down for
- a much longer distance, for actually 10 times the distance
- as this object is going to move up.
- And once again I know that because the work in has to
- equal the work out.
- I can't through some magical machine-- and if you were able
- to invent one, you shouldn't watch this video and you
- should go build it and become a trillionaire-- but a machine
- can never generate work out of thin air.
- Or it can never generate energy out of thin air.
- That energy has to come from some place.
- Most machines actually you lose energy to friction or
- whatever else.
- But in this situation, if I'm putting in 10 newtons of force
- times some distance, whatever that quantity is of work, the
- work cannot change.
- The total work.
- It can go down if there is some friction in the system.
- So let's do another problem.
- And really they're all kind of the same formula.
- And then I'll move into a few other types of simple systems.
- I should use the line tool.
- We'll make this up on the fly.
- And you could always create problems where you can
- compound it further and et cetera, et cetera, using some
- of the other concepts we've learned.
- But I won't worry about that right now.
- So let's say that I'm going to push up here.
- Well no let me see what I want to do.
- I want to push down here with a force of-- let's say that
- this distance right here is 35 meters, this distance is 5
- meters-- and let's say I'm going to push down with the
- force of 7 newtons, and what I want to figure out is how
- heavy of an object can I lift here.
- How heavy of an object.
- Well, all we have to do is use the same formula.
- But the moments-- and I know I used that word once before, so
- you might not know what it is-- but the moments on both
- sides of the fulcrum have to be the same.
- Or the input moment has to be the output moment.
- So what's the moment again?
- Well, the moment is just the force times the distance from
- the force to the fulcrum.
- So the input moment is 7 newtons times 35 meters.
- And realize that that does not work, because the distance
- this force is traveling is not 35 meters.
- The distance this force is traveling is
- something like, here.
- But this 35 meters is going to be proportional to the
- distance that this is traveling when you compare it
- to this other side.
- So this quantity, 7 newtons times 35
- meters, is the moment.
- And that is going to be equal to the moment on this side,
- the output moment.
- So that is equal to 5 meters times the force that I'm
- lifting, or the lifting force of the machine, times let's
- say the force out.
- So we can figure out the force out by just dividing both
- sides by 5.
- So let's see, 35 divided by 5 is 7, so you get 7 times 7
- equals the force out, or 49 newtons.
- And you can see that, because you can see that the length of
- this side of the lever is 7 times the length of this side
- of the lever.
- So when you input a force of 7, you output a force of 7
- times that.
- And of course, in order to move the block 1 meter up in
- this direction, you're going to have to
- push down for 7 meters.
- And that's where we know that the input work is equal to the
- output work.
- Well anyway hopefully I didn't confuse you and you have a
- reasonable sense of how levers work.
- In the next couple of videos, I'll introduce you to other
- machines, simple machines like a wedge-- I've always had
- trouble calling a wedge a machine, but it
- is one-- and pulleys.
- I'll see you in the next video.
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