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# Intro to Springs (Hooke's Law)

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Intro to Springs (Hooke's Law)

Concept #1: Intro to Springs

Transcript

Hey guys, so in this video I want to start talking about Springs and spring forces let's check out, so when you push or pull against the spring with a force let's call this force Fa an applied force the spring pushes back this is Newton's Third Law action reaction, you push against something it pushes back against you so the force of the spring will be the negative of the force that was applied on it and again Newton's action reaction that's why the same magnitude but opposite direction so this negative here means just opposite direction, so there's nothing new there what is new is that this also equals to -Kx and I'll talk about what kx is in just a second notice that there's another negative here and again that negative just means opposite direction that negative is you see this more later is almost sort of a conceptual negative to remind you that it's opposite direction but in a lot of calculations we just get rid of that negative to make things a little bit simpler, alright? So, what is K and X? I'm going to start with X, X is the deformation that the spring will experience so the idea is that if you push or pull against the spring the spring will either be compressed which means it's now shorter or it will be stretched which means obviously that it is now longer but X is the deformation It's not the actual length but it's the change in length so in springs what matters is not how long it is but how much longer or how much shorter it gets, OK? So X you can think of it as the absolute value of the final length-the initial length the reason why it's the absolute values because if you get a negative you just think of it as a positive because the direction doesn't matter, OK? So, for example here I have this first one here I was spring attached to a wall, this green thing is sort of like a base that you can sort of drag on the spring and if the spring is just sort of left hang in there it will have no deformation it's the original length of the spring X=zero we call this the relaxed position of the spring, right? Spring is chilling basically without having been compressed, in this situation over here this red dotted line here indicates the original length of the spring and now I'm to the right and that's because we're to the right of the spring here of the original length and that's because we pushed to the right with the force Fa, if I push to the right action reaction spring pushes back this way, force of spring is this way the gap between its original length and its new length we're going to call it's (deformation) we're going to called that X, OK? Now since I have two different situations I'm going to call this X1 we're going to use X2 for the bottom here, here the bottom I was originally the spring was originally here and then I pulled it this way so my applied force is Fa like that and the spring will push back with Fs this way and the gap between its original length and its new length is deformation X which I call X2, OK? So that's how F and X kind of work. K is the spring that's the second variable here K is the spring's force constants, OK? Now there's actually multiple names for this I've seen force constant I have seen spring coefficients I've seen stiffness constant or stiffness coefficient but basically this is the coefficient of how hard it is to compress a spring, K has to do with how stiff or how hard to compress or deform in general a spring is the higher the K the harder it is to the deform a spring so for example if you've ever played I'm sure you have with one of those pens that you push on it and the tip comes out you've seen inside of it there's a small spring the allows that to happens very simple and it's a thin spring and if you've ever played with it it's really easy to squeeze and sort of stretch it out and moves very easily so that spring has a very low K. Now if you had springs for example at the bottom of an elevator shaft that design for the safety if the elevator comes down following the spring maybe tries to hold the elevator in place those springs are going to be very stiff otherwise the elevator will crush them and they wouldn't do anything, right? So that K has to do with how hard it is to deform something, real quick the units for K are Newtons per meter and you can see this from the equation, force is Newton equals KX, X is meters so K has to be Newtons per meter so that this equation is dimensionally consistence, ok? So, if you ever forget the units you can just get it from the equation by isolating by leaving the X... solving the X or the K rather leaving it by itself and seeing that the units and you do unit analysis you get Newtons/meter or you can just remember that, OK? So Force, one more point to talk about the force the force of a spring is a restoring force and it's really important it's a restoring force what does that mean? It's always going to the spring is always trying to get back to its original length if you pull the spring the spring to the right the spring will pull back left and if you post a spring to the right I'm sorry to the left it pulls back to the right and if you pull to the right it pull back to the left, you can see here that we went to the right of equilibrium and the spring is trying to pull back to the left here we are to the left and the spring is pulling to the right, so if you're on the right you can be pulled to the left and vice versa so the spring is always pulling you back the spring force is always pulling the spring back to original length X=0, it starts relaxed it likes to being relaxed and it's going to try to get back to its original length, the force is always opposite to the deformation X, OK?