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# Intro to springs and Hooke's law

## Video transcript

let's learn a little bit about Springs so let's say I have a spring let me let me draw the ground so we know what's going on with the spring so let me say this is the floor that's the floor and I have a spring it's along the floor I'll use a thicker one just to show the spring let's say the spring looks something like this whoops I'm still using the line tool this spring looks like this this is my spring my amazingly drawn spring let's say that this end it's attached to a wall that's a wall and I know that and so this is the spring when I don't have any force acting on it this is just a natural state of the spring and we could call this we could call this you know where it just naturally rests this tip of the spring and let's say that when I were to apply a force of I don't know 5 Newtons into the spring it looks something like this let me draw a redraw everything so when I apply a force of 5 Newtons let me draw under the wall in magenta now when I apply a force of 5 Newtons the spring looks like this I'm still using the wrong tool it compresses right we're all familiar this we sit on a bed every day or a sofa so let's say it compresses to here let me whoops ok so if this was the normal resting so this is where the spring was when I applied no force but when I apply 5 Newtons so I applied 5 Newtons in that direction 5 Newtons let's say that this distance right here is I don't know let's say that this was 10 meters 10 meters and so a typical question that you'll see and then we'll explain how to do it is you know spring compresses or you know elongates when you apply a certain force by some distance how much will it compress when you applied different for so my question is how much will it compress when I applied 10 Newton force so your intuition that it'll compress more is correct but is it you know is it a linear to 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 could guess it's actually worth an experiment if or you could just keep watching the video so let's say I apply a 10 Newton force what will the spring look like well it'll it'll be more compressed right draw my force 10 Newton's 10 Newtons and if this was the natural place where 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 Newtons this direction to the right you would have gone 10 Newton 10 meters in this direction so it goes whether you're along getting the spring or compressing the spring within some reasonable tolerance if you we've all had this experiment experience if you compress something too much and you stretch it too much it doesn't really go back to where it was before but within some reasonable tolerance it's proportional so what does that mean that means that the restoring force of the spring the restoring force of the spring is minus some number times the displacement of the of the spring so what does this mean so in this example right here what was the displacement of the spring well if we take positive x to the right and negative x to the left the displacement of the spring was what the displacement in this example right here X is equal to minus 10 right because I want 10 to the left and so and so it says that the restorative force is going to be equal to the rest rate of force is equal going to be equal to minus K times how much it's distorted times minus 10 so the minuses cancel out so it equals 10 what's the restaurant of force in this example well you might say it's five newtons just because that's the only force I've drawn here and and and you you would be the to some degree correct and actually since we're doing positive and negative and this five Newton is to the net to the left so into the negative x-direction i should actually call this minus five Newtons and i should call this minus ten Newtons because obviously these are vectors and we're going to the left and i'm pick the convention that the left means negative so what's the rest root of force well in this example and we assume that K is a positive number for our purposes in this example the rest root of force is a positive number so what is the rest your force so that's actually the force the counteracting force of the spring that's what this formula gives us so if this bring is stationary when I apply this five Newton force that means that there must be another equal and opposite force that's positive five Newton's right if there weren't the spring would keep compressing and if the force was more than five Newton's the spring would go back this way so the fact that I know that when I applied five Newton force to the left or negative five Newton force the spring is no longer moving it 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 restaurant of force another way to think about it is if I were to let well I won't go in there now so in this case the restive force is five Newton's so we can solve for K we could say 5 is equal to 10 K 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 the displacement when I apply 10 a negative 10 Newton force when I push the spring intend with 10 Newtons in the leftward direction so first of all what's the rest root of force here well if the spring is is is no longer accelerating in either direction or this tip of the spring is no longer accelerating in either direction we know that the rest root of force must be counterbalancing this force that I'm compressing with right the force that the the spring wants to expand back with is 10 Newtons positive 10 Newtons right and we know this bring constant this K for this spring for this material whatever it might be is 1/2 so we know the rest rate of force is equal to 1/2 x times the distance right and when the formulas - ok all right and then what is the rest root of force in this example wise it's 10 Newton's so we know that 10 Newton's is equal to minus 1/2 X and so what is X we'll multiply both sides by minus 1/2 and you get minus 20 I'm sorry multiply both sides by minus 2 you get minus 20 is equal to X so it's minus 20 whoops minus 20 so X goes to the left - 20 units so that's all that it's it's telling us and this law is called Hookes law and it's named after I'll read a physicist in the 17th century British physicist and he figured out that the amount of force necessary to keep a spring compressed is proportional to how much you've compressed it and that's all that this this formula says and that negative number remember this formula gives us the rest rooted force so it says that the force is always in the opposite direction of how much you displace it so for example if you were to displace this bring in this direction if you were to apply a force and X were positive and you were to go in that direction the force oh sorry this was where the right 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 rest root of force in the other direction so let's do one more problem and I think this will be clear to you so let's say I have a spring and and all of these problems kind of go along so let's say when I apply a force of 2 Newtons so this is what I apply when I apply a force of 2 Newtons well so let's say let's say it this way let's say when I stretch the spring what am i doing let's say this is the spring and when I apply a force of two Newtons to the right the spring gets stretched oh I don't know let's say the spring gets stretched one meter so first of all let's figure out what K is so if the spring is stretched to it by one meter out here it's rest root of force will be two Newtons back this way right so it's rester to force this to Newtons will equal minus K times how much I displaced it so I displaced it by one meter so then we get multiplied both sides by negative one and we get K is equal to minus two so then we could use hooks clot to note the the equation for this to figure out the restroom force for this particular spring and be minus 2x and then I said well how much force would I have to apply to distort this spring by two meters well it's two times two would be four for Newton's two to displace it by two meters and of course the rest root of force will then be in the opposite direction and that's where we get the negative number anyway I've run out of time I'll see you in the next video