 Let's talk about spring forces. We're all familiar with springs. They're these often coils of metal or maybe plastic. And some of them are set so that you can stretch them out. And some of them are set so that you can stretch or compress them. And there's other spring-like objects like rubber bands, which again are ones that stretch only. Well, the common thing about all these spring and spring objects is they have what we call a restoring force. What that means is that when I stretch the spring out, there's a force that pulls the spring back in. And if I compress the spring, there's a force which pushes the spring back out. So it's always trying to go back to its equilibrium position. Well, when we started trying to figure out an equation for it, there was a scientist named Hook who did a series of experiments where he stretched out springs. And as he stretched them, he carefully measured how much forces were involved, how much force it took to stretch the spring out, and how much force the spring pulled back with. And he found that almost all of these objects, as long as you didn't stretch them too far, followed a nice linear relationship here. And so Hook's law tells us that the force exerted by the spring is minus kx, where that k is the spring constant. And it's a measure of how stiff the spring is. And our x is the distance from equilibrium, or how far stretched or compressed that spring is. When it comes to those spring constant k, it depends on the spring itself. So a large value of k means that we have a very stiff spring, or it's very hard to pull that spring out. A small value of k is what we call a very soft spring. It's very easy to pull the spring out. If I take a look at the units, I start back with my equation that says force is minus kx. If I rearrange that to solve for k, I see that I've got minus f over x. So looking at the units, that means force would have units of newtons, and position would have a unit of meters. So our k value must have units of newtons per meter. Let's give an example. How much force does a 10 newton per meter spring exert if it's stretched to a distance of 1 meter? So again, this 10 newtons per meter, that's the spring constant. It's a description of the spring itself. Plugging that into our equation, we find that that's a force of minus 10 newtons. The minus 10 indicates that the spring is pulling back on whatever object is connected to the spring with a force of 10 newtons. If I were to move that out to 2.5 meters, it's now pulling back with 25 newtons. So the further I stretch it, the more force it's pulling back with. Likewise, if I compress it, I can plug that into my equations. In this case, I get a positive number because it's being compressed. It wants to push back outwards. Here's another example. What is the spring constant if it takes 30 newtons to stretch a spring 0.2 meters? This is actually how we go about measuring the spring constant experimentally for individual springs. We see how much force does it take to stretch at a certain distance. Again, starting with our basic equation and rearranging that for the spring constant. Now remember, this F was the force that the spring was pulling back. If I'm going to stretch that spring, I'm going to apply a force in the opposite direction. So I can also think about it as the k value is the applied force over the x. So in this case, I'm applying 30 newtons, and I'm stretching it 0.2 meters. So this spring has a spring constant of 150 newtons per meter. So there's the spring force. We're going to use it in a lot of interesting applications.