Intro to springs and Hooke's Law Video

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Intro to springs and Hooke's Law

Let's learn a little bit about springs. So let say I have a spring—that’s the floor and I have a spring so along the floor. And so the spring looks something like this, this is my spring. And let say at this end it’s attach to a wall. And so this a spring when I don’t have any force acting one this is just natural state of the spring and we could call this or just naturally rest just to put the spring. And let say that when I was to apply a force of five Newton’s into the spring it looks something like this. So when I apply force of five Newton’s this spring looks like this. It compress it, right were often that we sit on the bed everyday or sofa. So let say compresses to here. So this was the normal resting, so this is where the spring was when I applied no force but when I apply five Newton’s so applied five Newton’s in that direction, let say that this distance right here is—let say that this was 10 meters. And so typical question that you'll see and then we’ll explain how to do it is you know a spring compresses or elongates when you apply a certain force by some distance how much will it compress when you apply different force? So my question is how much will it compress when I applied 10 Newton’s force. So your intuition that it will compress more is correct but is it, you know, is it linear to how much I compress it, is it a square of how much I compress it. Well how does it relate? I think you probably can guess it was actually work an experiment if or you can just keep watching the video. So let say I applied 10 Newton’s force, what would the spring look like? Well it will be more compress, right. 10 Newton’s and if this was the natural place for the spring would rest what is this distance? Well it turns out that it is linear, what do I mean by linear? Well it means that the more the force it’s equally proportional to how much the spring will compress and actually works the other way if you applied five Newton’s in this direction to the right you would gone 10 meters in this direction. So it goes whether you're elongating the spring or compressing the spring within some reasonable tolerance. We've all had this experience if you compress something too much or stretch it too much it doesn’t really go back to where it was before. But within some reasonable tolerance its proportional so what is that mean? That means that the restoring force of the spring is minus some number times the displacement of the spring. So what is this mean? So in this example right here what was the displacement of the spring? Well if we take +x to the right and –x to the left the displacement of the spring was what? The displacement in this example right here x is equal to -10 so one 10 to the left so it says that the restorative force is going to be equal to –k time—how much the distorted times -10 so the minus is cancel out so that equals 10k. What's the restorative force in this example? Well, you might say its five Newton’s because that’s the only force I've drawn here and you would be to some degree correct and actually since we’re doing positive and negative and this five Newton’s is to the left so into the negative and actually I call this –5 Newton’s. And I should call this -10 Newton’s because obviously these are vectors and we’re going to left and I'm pick the convention that to the left means negative. So what's the restorative force? Well in this example and we assume that k is a positive number for our purposes. In this example the restorative force is a positive number. So what is the restorative force? So that’s actually the force the counter acting force of the spring. That’s what this formula gives u. So if this spring is stationary when I apply this five Newton’s force that means that there must be another equal and opposite force that’s positive five Newton’s, right. If there weren’t so this spring would keep compressing. And if the force was more than five Newton’s the spring would go back this way. So the facts that I know that when apply five Newton’s force to the left or -5 Newton’s force the spring is no longer moving and means that there must be or no longer accelerating actually it means that there must be an equal and opposite force to the right and that’s the restorative force. Another way to think about it is if I were to let—so in this case the restorative force is five Newton’s so we can solve for k. We can say 5 is equal to 10k divide both sides by 10 you get k is equal to 1/2. So now we can use that information to figure out what is the displacement when I apply a -10 Newton’s force when I push the spring with 10 Newton’s in the leftward direction. So first of all what's the restorative force here? If the spring is no longer accelerating in either direction or the tip of the spring is no longer accelerating in either direction. We know that that the restorative force must be counter balancing this force that I'm compressing with, right. The force that the spring wants to expand back with is 10 Newton’s, positive 10 Newton’s, right. And we know the spring constant this k for this spring, for this material whatever it might be is ½ so we know the restorative force is equal to ½ times the distance, right. Oh no, formula is –k, all right. And then what is the restorative force in this example? Well I say 10 Newton’s so we know that 10 Newton’s is equal to -1/2x and so what is x or multiply both sides by -2 and you get -20 is equal to x. So 2 – 20 so x goes to the left to 20 units. So that’s all that it’s telling us and this law is called Hook’s Law and its named after a physicist in the 17th century, burns physicist and he figure it out that the amount of force necessary to keep a spring compress is proportional to how much you’ve compress it. And that’s all that this formula says and that negative number, remember this formula gives us the restorative force so it says that the force is always in the opposite direction of how much you just place it. So for example, if you were to displace the spring in this direction, if you were to apply a force and x were a positive and you were to go in that direction the force—this is where the spring rest. If you were to apply some force and take the spring out to here this negative number tells us that the spring will essentially try to pull back with the restorative force in the other direction. So let's do one more problem and I think this will be clear to you. So let say I have a spring and all of these problems kind of go along—so let say when I apply a force of two Newton’s so this is what I apply. When I apply a force of two Newton’s—well let say at this way, let say when I stretch the spring. Let say this is the spring and when I apply a force of two Newton’s to the right the spring gets stretch—oh, I don’t know. Let say the spring gets stretch one meter. So first of all let's figure out what k is. So if the spring is stretch to it by one meter out here its restorative force will be two Newton’s back this way, right. So its restorative force is two Newton’s will equal minus k times how much I just place it. Oh, I just place it by one meter so then we get multiply both sides by negative one and we get k is equal to minus two. So then we can use Hook’s Law to know the equation to figure out the restorative force for this particular spring and it would be -2x. And then I said well how much force what I have to apply to distort the spring by two meters while it’s 2 × 2 would be 4, 4 Newton’s to just place it by two meters and of course the restorative force will then be in the opposite direction and that’s where we get the negative number. Anyway, I've run out of time and I'll see you in the next video.

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Let's learn a little bit about springs. So let say I have a spring—that’s the floor and I have a spring so along the floor. And so the spring looks something like this, this is my spring. And let say at this end it’s attach to a wall.

And so this a spring when I don’t have any force acting one this is just natural state of the spring and we could call this or just naturally rest just to put the spring. And let say that when I was to apply a force of five Newton’s into the spring it looks something like this. So when I apply force of five Newton’s this spring looks like this. It compress it, right were often that we sit on the bed everyday or sofa. So let say compresses to here.

So this was the normal resting, so this is where the spring was when I applied no force but when I apply five Newton’s so applied five Newton’s in that direction, let say that this distance right here is—let say that this was 10 meters. And so typical question that you'll see and then we’ll explain how to do it is you know a spring compresses or elongates when you apply a certain force by some distance how much will it compress when you apply different force? So my question is how much will it compress when I applied 10 Newton’s force. So your intuition that it will compress more is correct but is it, you know, is it linear to how much I compress it, is it a square of how much I compress it. Well how does it relate? I think you probably can guess it was actually work an experiment if or you can just keep watching the video.

So let say I applied 10 Newton’s force, what would the spring look like? Well it will be more compress, right. 10 Newton’s and if this was the natural place for the spring would rest what is this distance? Well it turns out that it is linear, what do I mean by linear? Well it means that the more the force it’s equally proportional to how much the spring will compress and actually works the other way if you applied five Newton’s in this direction to the right you would gone 10 meters in this direction. So it goes whether you're elongating the spring or compressing the spring within some reasonable tolerance.

We've all had this experience if you compress something too much or stretch it too much it doesn’t really go back to where it was before. But within some reasonable tolerance its proportional so what is that mean? That means that the restoring force of the spring is minus some number times the displacement of the spring. So what is this mean? So in this example right here what was the displacement of the spring? Well if we take +x to the right and –x to the left the displacement of the spring was what? The displacement in this example right here x is equal to -10 so one 10 to the left so it says that the restorative force is going to be equal to –k time—how much the distorted times -10 so the minus is cancel out so that equals 10k.

What's the restorative force in this example? Well, you might say its five Newton’s because that’s the only force I've drawn here and you would be to some degree correct and actually since we’re doing positive and negative and this five Newton’s is to the left so into the negative and actually I call this –5 Newton’s. And I should call this -10 Newton’s because obviously these are vectors and we’re going to left and I'm pick the convention that to the left means negative. So what's the restorative force? Well in this example and we assume that k is a positive number for our purposes. In this example the restorative force is a positive number. So what is the restorative force? So that’s actually the force the counter acting force of the spring. That’s what this formula gives u.

So if this spring is stationary when I apply this five Newton’s force that means that there must be another equal and opposite force that’s positive five Newton’s, right. If there weren’t so this spring would keep compressing. And if the force was more than five Newton’s the spring would go back this way. So the facts that I know that when apply five Newton’s force to the left or -5 Newton’s force the spring is no longer moving and means that there must be or no longer accelerating actually it means that there must be an equal and opposite force to the right and that’s the restorative force.

Another way to think about it is if I were to let—so in this case the restorative force is five Newton’s so we can solve for k. We can say 5 is equal to 10k divide both sides by 10 you get k is equal to 1/2. So now we can use that information to figure out what is the displacement when I apply a -10 Newton’s force when I push the spring with 10 Newton’s in the leftward direction.

So first of all what's the restorative force here? If the spring is no longer accelerating in either direction or the tip of the spring is no longer accelerating in either direction. We know that that the restorative force must be counter balancing this force that I'm compressing with, right. The force that the spring wants to expand back with is 10 Newton’s, positive 10 Newton’s, right.

And we know the spring constant this k for this spring, for this material whatever it might be is ½ so we know the restorative force is equal to ½ times the distance, right. Oh no, formula is –k, all right. And then what is the restorative force in this example? Well I say 10 Newton’s so we know that 10 Newton’s is equal to -1/2x and so what is x or multiply both sides by -2 and you get -20 is equal to x.

So 2 – 20 so x goes to the left to 20 units. So that’s all that it’s telling us and this law is called Hook’s Law and its named after a physicist in the 17th century, burns physicist and he figure it out that the amount of force necessary to keep a spring compress is proportional to how much you’ve compress it. And that’s all that this formula says and that negative number, remember this formula gives us the restorative force so it says that the force is always in the opposite direction of how much you just place it.

So for example, if you were to displace the spring in this direction, if you were to apply a force and x were a positive and you were to go in that direction the force—this is where the spring rest. If you were to apply some force and take the spring out to here this negative number tells us that the spring will essentially try to pull back with the restorative force in the other direction.

So let's do one more problem and I think this will be clear to you. So let say I have a spring and all of these problems kind of go along—so let say when I apply a force of two Newton’s so this is what I apply. When I apply a force of two Newton’s—well let say at this way, let say when I stretch the spring. Let say this is the spring and when I apply a force of two Newton’s to the right the spring gets stretch—oh, I don’t know. Let say the spring gets stretch one meter. So first of all let's figure out what k is.

So if the spring is stretch to it by one meter out here its restorative force will be two Newton’s back this way, right. So its restorative force is two Newton’s will equal minus k times how much I just place it. Oh, I just place it by one meter so then we get multiply both sides by negative one and we get k is equal to minus two. So then we can use Hook’s Law to know the equation to figure out the restorative force for this particular spring and it would be -2x. And then I said well how much force what I have to apply to distort the spring by two meters while it’s 2 × 2 would be 4, 4 Newton’s to just place it by two meters and of course the restorative force will then be in the opposite direction and that’s where we get the negative number.

Anyway, I've run out of time and I'll see you in the next video.

Transcription by: Scribe4you Transcription Services